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A Theoretical Perspective on Molecular Polaritonics
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  • Mónica Sánchez-Barquilla
    Mónica Sánchez-Barquilla
    Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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  • Antonio I. Fernández-Domínguez
    Antonio I. Fernández-Domínguez
    Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
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    Orcidhttps://orcid.org/0000-0002-8082-395X
  • Johannes Feist*
    Johannes Feist
    Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
    *E-mail: [email protected]
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    Orcidhttps://orcid.org/0000-0002-7972-0646
  • Francisco J. García-Vidal*
    Francisco J. García-Vidal
    Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
    Institute of High Performance Computing, Agency for Science, Technology, and Research (A*STAR), Connexis, Singapore, 138632 Singapore
    *E-mail: [email protected]
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    Orcidhttps://orcid.org/0000-0003-4354-0982
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ACS Photonics

Cite this: ACS Photonics 2022, 9, 6, 1830–1841
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https://doi.org/10.1021/acsphotonics.2c00048
Published June 2, 2022

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Abstract

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In the past decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light–matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light–matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modeling of interacting molecular and optical states with increasing complexity.

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1. Introduction

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Polariton is a general term used to describe a hybrid light–matter excitation and has been employed in many different situations in the history of physics. (1) In this Perspective, we focus on a small subset of these situations, namely, those in which electronic transitions in molecules (often organic dyes) are used to provide the material component. Even within this small subset, a wide range of new phenomena are enabled by polariton formation, among them Bose–Einstein condensation and polariton lasing, (2,3) quantum information processing, (4) long-range excitation transport, (5,6) and control of chemical reaction rates. (7) After a short overview of basic physical concepts, we discuss our view on the current state of the field and the challenges it faces, interesting recent developments, and promising future directions. Despite the focus on molecules, we here restrict the discussion mostly to “physical” properties and ignore “chemical” properties such as (photo)reactivity that have been the focus of a recent related perspective on polaritonic chemistry. (8)
Polaritons arise when the interaction strength between light modes and material excitations in a system becomes large enough that the system enters the strong coupling (SC) regime. (9,10) In this regime, the eigenstates of the system are not even approximately represented by pure material or pure electromagnetic excitations (photons). The resultant hybrid light–matter excitations are then called polaritons. They were first observed in 1965 (11) in a crystal, while surface exciton–polaritons where observed approximately a decade later. (12) Before introducing strong coupling in more detail, we note that the apparently simple question of what should be called a “light mode” is actually somewhat subtle, and, as for any question of semantics, its answer is to some degree arbitrary. The only “pure” light modes are free-space modes in vacuum. When using any material structure that confines the EM field (often called “cavity” in general in this context), the resulting “cavity photon modes” are always partially material excitations. (8,13) As an operational definition, the cavity modes are usually understood as the modes supported by those parts of the full system for which the relevant dynamics can be well-approximated through macroscopic electromagnetism under linear response. This distinction leads naturally to the framework of macroscopic QED, (13−21) discussed in more detail below. The resulting electromagnetism (EM) modes then include those of optical (Fabry–Pérot) cavities (22,23) (as depicted in Figure 1a), photonic crystals, (24,25) and often also plasmonic nanostructures (as illustrated in Figure 1b), whose resonances are formed due to geometrical restriction of the free electron motion in metals and allow strongly subwavelength field confinement to be achieved. (26−28) However, plasmon modes are physically quite distinct from “optical” modes. In Fabry–Pérot or photonic crystal cavities, the energy is mostly stored in the electric and magnetic fields, and the dielectric functions of the materials can often be treated as approximately constant within the relevant range of frequencies. In contrast, the energy in plasmonic resonances is stored in the electric field and the kinetic energy of the electrons, (29) such that the resulting modes are more correctly referred to as surface plasmon polaritons themselves. We note that such structures should more correctly be called plasmonic “resonators” or “antennas” rather than “cavities”, although the latter use has become common in the field.

Figure 1

Figure 1. Schematic representations of typical situations in molecular polaritonics. (a) Molecular ensemble inside a photonic microcavity and (b) single emitter coupled to a plasmonic nanoantenna.

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Plasmonic and other deep-subwavelength cavities are also somewhat special in another regard. The EM fields at close distance to such structures, where emitters are typically placed, are dominantly electrostatic (or more precisely, quasistatic), as they are due to the Coulomb fields of the displaced charges (e.g., electrons oscillating collectively). This has fundamental consequences on the light–matter interaction, as the local electric fields are then to a good approximation purely longitudinal (corresponding to Coulomb interactions). In the standard Coulomb gauge, they arise from the scalar potential and not the vector potential that describes propagating radiation modes (i.e., transverse EM fields). (8,13,30) As an additional complication, plasmonic systems can have complex internal dynamics after excitation, e.g., leading to hot-electron generation, which in turn can have significant effects on chemistry. (31,32) In this Perspective, we do not discuss such hot-electron effects.
Once a suitable definition of what constitutes the light modes in the system has been chosen, it becomes possible to distinguish between the weak and strong-coupling regimes within that model. We note that strong coupling itself is not necessarily a quantum effect and can often be modeled through classical electromagnetism. (10,33) In that case, the material excitations are represented through the dielectric function of the medium (e.g., through a resonance of Drude–Lorentz form) or through a polarizable dipole for single emitters. (34,35)
For a single quantum emitter approximated as a two-level system coupled to a single photon mode within the rotating wave approximation, the dynamics is described by the Jaynes–Cummings model. (36)
(1)
where â and ↠are the annihilation and creation operators of the photonic mode inside the cavity, σ̂± are the quantum emitter excitation and de-excitation operators given by the corresponding Pauli matrices, g is the coupling strength between both constituents, and ωc and ωe are the cavity mode and emitter frequencies, respectively. When the emitter and photon mode are on resonance, the strong-coupling regime is entered when their mutual interaction overcomes decoherence in the system, i.e., g ≳ γ, where γ is a typical decoherence rate (the exact criterion that should be used is somewhat arbitrary with several valid choices; see ref (10) for a discussion). In this regime, energy exchange between light and matter becomes a coherent process: if only one of the components is initially excited, this energy exchange is seen as an oscillatory behavior of the population between both subsystems, the so-called vacuum Rabi oscillations occurring at the vacuum Rabi frequency (or Rabi splitting), which in general is given by
(2)
where μ⃗ is the transition dipole moment of the emitter and is the quantized electric field strength of the mode, associated with one photon, at the emitter position. Here, V is the effective volume of the cavity mode, which gives an estimate of the volume within which a photon is confined in such a structure, the correct definition of which in nanophotonic devices has been the subject of intense theoretical activity over the past decade. (37−39) Furthermore, we note that its definition in systems with translation symmetry (e.g., a 2D Fabry–Pérot cavity consisting of formally infinitely extended parallel mirrors) is somewhat arbitrary, as it depends on the chosen quantization volume and carries no physical information in that case.
Physically, vacuum Rabi oscillations correspond to the situation where a photon can be emitted and reabsorbed several times before it disappears from the system. In these conditions, the eigenstates of the coupled system are hybrid light–matter states, and a thorough understanding of the system can only be reached by considering the coupled system as a whole. The two original excited states (emitter and photon) transform into polaritonic states that are shifted up and down in frequency by the coupling strength, with their difference in energy given by the Rabi splitting. These two states are conventionally called the lower polariton (LP) and upper polariton (UP). Figure 2a schematically shows the formation of the upper and lower polaritons when the cavity mode and the emitter frequency are on resonance, while Figure 2b shows the evolution of the polariton frequencies when ωc and ωe are detuned from each other.

Figure 2

Figure 2. (a) Scheme of the hybridization of one EM mode (purple) and one quantum emitter (yellow). In the strong-coupling regime, an upper (UP) and lower (LP) polariton are formed and are separated by the Rabi splitting ΩR. (b) Energies of the polaritons under nonzero detuning. The dashed lines show the uncoupled frequencies.

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We mention here that some care should be taken to distinguish between the concepts of polaritonic states and polaritons. The former are the hybrid eigenstates of the coupled system, which do not depend on the state of the system at any point in time and in that sense always exist. The latter are the excitations of the system in a quasi-particle picture, and thus only exist when the system is in one of the polaritonic states. For one or a few emitters, each polaritonic state is unique. However, for macroscopic systems containing many emitters, excitons behave (approximately) as bosons, (40) a feature that is inherited by the polaritons. The excitons and photonic modes are then approximately harmonic oscillators, and their coupling produces new (polaritonic) normal modes. Each of these modes contains a (formally) infinite number of polaritonic Fock states |0⟩P, |1⟩P, |2⟩P, .... In this picture, having n polaritons in mode P means that the system is in state |n⟩P. In the literature, the distinction between polaritons, polaritonic states, and polaritonic modes is not always made explicit, which can cause some confusion. Which of the three is meant is usually clear from the context.
For single emitters, reaching the SC regime is extremely challenging, as the single-emitter coupling strength g has to become comparable to the emitter and cavity decoherence rates. This can be achieved by either increasing the coupling strength or decreasing the decoherence rates sufficiently. This was first achieved in 1985 by working with long-lived emitters and cavities at cryogenic temperatures, in a microwave cavity with superconducting mirrors. (41) Rabi oscillations in the system were explicitly measured two years later. (42) In 2004, the SC regime for a single quantum dot in a semiconductor micropillar cavity was achieved, with a Rabi splitting of ∼100 μeV. (43) These approaches, where the absolute coupling strength is a small fraction of the excitation energy, necessarily require very long-lived emitters and cavity modes, which in turn implies cryogenic temperatures. More recently, the strong-coupling regime has been approached at room temperature for single quantum emitters by using extremely localized surface plasmons in narrow gaps, (44,45) which support light confinement in deeply subwavelength volumes. (46−48) The estimated single-emitter Rabi splitting achieved in refs (44) and (45) was 120 and 90 meV, respectively, both at the limit of the strong-coupling regime. Very recently, strong coupling and quantum nonlinearity have been observed for a single molecule at cryogenic temperature, (49) where the molecule behaves as an effective two-level system.
Strong light–matter coupling is much easier to achieve in the collective case where an ensemble of N close to identical quantum emitters interacts with a photonic mode (as described by the Tavis–Cummings model (50)). In that case, the effective coupling strength increases with the number of emitters as gN = g√N. (40) This enhancement significantly simplifies entering the strong-coupling regime and is the basis for most experiments in the field of molecular polaritonics. It occurs because an excitation in this case can be coherently distributed over the N emitters, forming a so-called bright state with increased light–matter coupling. At the same time, all N – 1 orthogonal ways of distributing an excitation over the emitters show negligible coupling to the cavity mode due to destructive interference between the dipole transitions in the different emitters. These superpositions are the so-called dark states, which play a major role in molecular polariton dynamics. (51,52)
Collective strong coupling was first realized in 1975 using molecular vibrations coupled to surface phonon polariton modes (53) and soon after for molecular excitons coupled to surface plasmon polaritons (54) and atoms coupled to high-Q cavities, first in the microwave (55) and then in the optical (56) regime. Strong coupling to semiconductor (Wannier) excitons was first realized in 1992. (57) Such systems reach Rabi splittings in the range of 1–20 meV. (57−59) Organic semiconductors support much larger Rabi splittings, ΩR ≳ 100 meV, due to their high density and large dipole moments, so that strong coupling can be observed at room temperature. (60) We note that the maximally reachable Rabi splitting for a given material is determined by the density of dipoles, but largely independent of the specifics of the photon mode. (61−63) This can be understood by noticing that
(3)
where ρ is the molecular number density, and we have used the fact that the effective mode volume is related to the physical volume occupied by the mode. The number of molecules interacting with the mode is thus proportional to the molecular density times the volume. A more careful calculation shows that the Rabi splitting depends on the dipole density multiplied by a “filling factor” between 0 and 1 that determines what fraction of the mode volume is filled with the molecular material (weighted with the position-dependent quantized field strength). (39,61) When a cavity is completely filled with the material in question, the Rabi splitting is equal to the bulk polariton splitting obtained by Hopfield in 1958. (64) These facts explain why similar Rabi splittings have been observed in the literature for very different photonic systems, such as Fabry–Pérot cavities, (60) plasmonic surfaces, (65) plasmonic hole arrays, (66) isolated particles and arrays of them, (67,68) and nanoparticle-on-mirror setups. (45) Several kinds of organic materials can reach the so-called ultrastrong-coupling regime, (69) in which the Rabi splitting is a significant fraction of the bare excitation energy, with record values close to and above ΩR = 1 eV. (70−72) Apart from the molecular density, the alignment of the dipole moments of the molecules relative to the electric field inside the cavity also modifies the Rabi splitting. While most experiments use disordered materials with randomly oriented molecules, a factor of up to √3 can be gained in the Rabi splitting when the molecules are perfectly aligned with the electric field. Exploiting this has allowed large Rabi splittings up to ΩR = 1.8 eV to be achieved. (73) The large reachable coupling strengths in organic materials also mean that cavity modes with very large decay rates κ (or equivalently, short lifetimes τ = 1/κ or low quality factors ωc/κ) can be used while still reaching the strong-coupling regime.
As noted before, organic molecules are very well-suited for reaching large Rabi splittings due to the large transition dipole moments and high densities. However, they have complex internal structure due to their rovibrational degrees of freedom and often cannot be approximated as two-level systems. On one hand, this complicates their use and study as idealized (two-level) quantum emitters. On the positive side, this opens up the opportunity to modify their internal structure and dynamics through strong light–matter coupling or conversely to exploit the internal dynamics to achieve new photonic functionalities. The former type of applications are exemplified by the field of polaritonic chemistry, which aims at modifying chemical processes such as photochemical reactions through strong light–matter coupling. (8) The latter type of applications typically rely on the fact that molecules show strong exciton–vibration interactions, such that molecular vibrations can drive polariton relaxation or transfer between different polaritonic states. (74,75) This can enable processes such as organic exciton–polariton lasing and condensation (3,76,77) or energy transfer between different molecular species even over long spatial distances. (5,6,78−82) Note that it has been also shown that, even under the two-level system approximation, SC phenomena involving organic molecules offer possibilities for nonclassical light generation not attainable by means of other types of quantum emitters. (83,84)
When describing light–matter interactions in molecular systems, in particular in the strong-coupling regime, including all the degrees of freedom in both constituents is an arduous task. Then, many models are focused on taking into account the complexity of one of them; that is, the theoretical effort is focused either on the description of the complexity of the photonic structures or to include to some extent the vibrational structure of the molecules. In what follows, we summarize some of the theoretical challenges that remain in both paths.

2. EM Field Quantization in Complex Geometries

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Many different kinds of “cavities” can be used to achieve strong coupling in the collective regime, while few- or single-molecule strong coupling necessarily requires deep-subwavelength confinement of light. In general, any cavity setup is determined by “macroscopic” structures consisting of large numbers of atoms, such as Fabry–Pérot cavities, photonic crystals, and metallic nanoparticles or surfaces. Within these setups, one or several microscopic quantum emitters such as atoms, molecules, or point defects are placed. As discussed above, it is then customary to treat the macroscopic structure through Maxwell’s equations and formally treat the modes arising from these equations as the EM modes of the system.
In order to describe light–matter interactions at a quantum level, these EM modes have to be quantized, which is significantly more challenging than the quantization of free EM modes in conventional quantum electrodynamics. For one, the presence of material structures complicates the solution of eigenmodes, which often is only possible numerically. Nowadays, many commercial and open source packages are available to solve Maxwell’s equations in these situations. Furthermore, these light modes will be lossy, often highly so, due to both material losses and leakage to the far field. Only in some approximations do lossless states exist, e.g., when assuming the existence of perfectly conducting mirrors or infinitely long lossless and defect-free waveguides, etc. None of these are typically good approximations for the kinds of structures used in molecular polaritonics. Still, when losses are small enough, it can be a reasonable strategy to quantize fully bound modes in a fictitious lossless system and then treat the losses as small perturbations on top of that.
Alternatively, when dealing with small enough nanoparticles with localized resonances (such as plasmonic nanoparticles) for which radiative losses are small due to inefficient emission, the so-called quasistatic approximation is often applicable. In this approximation, retardation effects, and therefore EM propagation into free space (or bulk dielectric media), is neglected, resulting in purely longitudinal fields. In this limit, semianalytical solutions are often again possible, e.g., using transformation optics, (85−87) with the resulting modes being fully bound while still describing the material losses. Since subwavelength confinement is a prerequisite for the quasistatic approximation, these material losses will always be significant. (29) One advantage of the quasistatic approximation is that the EM modes can be described by a scalar potential, which simplifies the treatment of beyond-dipole interactions. (88−90) Another advantage of the quasistatic approximation is that for metals described by a dielectric function of Drude form the resulting eigenmodes will always correspond to uncoupled Lorentzians in the spectral density (discussed in more detail below), which allows for a straightforward quantization procedure of the resulting modes. (88,90,91) Radiative losses can also be included a posteriori, e.g., by calculating the effective dipole moment of the localized resonances. (88,92,93) These quasistatic treatments of plasmonic modes have led to analytical insights into different aspects of strong light–matter coupling in metal nanostructures. On one hand, they have shown that molecular degrees of freedom such as the presence of light-forbidden transitions can be harnessed to tailor polaritonic properties. (88,92) On the other hand, they have also revealed different strategies to exploit the polaritonic (originally excitonic) quantum nonlinearities for nonclassical light generation in these deeply subwavelength systems. (93)
When the quasistatic approximation is not appropriate and retardation effects have to be taken into account, the most general and powerful approach to nonetheless obtain a quantized description of the EM field is macroscopic QED. This is a formalism that quantizes the EM field in arbitrary structures, including dispersive and absorbing materials. A particularly appealing feature of this approach is that the quantized EM modes are fully described by the dyadic Green’s function G(r, s, ω) of the classical Maxwell equations, which can be obtained from numerical solvers. This can be conceptually understood from the fact that Maxwell’s equations are the wave equations describing the dynamics of EM fields, which remains true after quantization. A recent review about macroscopic QED in the context of nanophotonics can be found in ref (13). We note here that, although the classical description of the EM environment is valid for a wide variety of physical situations, it breaks down when the material and the emitters are physically close enough that electronic wave functions overlap, (94,95) which happens at subnanometer separations.
Within macroscopic QED, (19,20) the Hamiltonian for multiple emitters in the multipolar coupling scheme (Power–Zienau–Woolley picture) and within the dipole approximation can be written as
(4)
where f̂λ(r, ω) and f̂λ†(r, ω) are bosonic annihilation and creation operators of the medium-assisted EM field, with λ = {e, m} labeling electric and magnetic contributions. Hk and μk are the bare Hamiltonian and dipole operator of emitter k. The electric field operator Ê(r) = Ê+(r) + Ê–(r), where Ê+(r) = (Ê–(r))† is defined by
(5)
where Gλ(r, s, ω) is closely related to the standard dyadic Green’s function G(r, s, ω). (19,20)
It can be shown that the action of the EM environment on the emitters is fully characterized by the generalized spectral density
(6)
which is determined by the classical dyadic Green’s function and which we give here directly in the form generalized to several emitters and several possible dipole orientations per emitter. (96) Here, n and m are combined labels for the emitter and the transition directions that are taken into account (up to three per emitter), with un the unit vector describing the orientation and rn the position of the corresponding emitter. The diagonal elements n = m define the coupling between the EM field and each dipole transition, while the off-diagonal elements n ≠ m define the photon-mediated interaction between emitters. Notice that in the weak-coupling limit, the Markov approximation can be used to obtain decay rates and environment-induced dipole–dipole interactions, which are determined by the imaginary and real parts of the Green’s function, respectively. (97)
For a single emitter with only a single relevant dipole transition (i.e., a two-level system), the matrix-valued generalized spectral density reduces to a scalar function. It is then customary to include the (single) dipole transition matrix element into the definition, giving the conventional scalar spectral density
(7)
where μ is the transition dipole moment and r is the position of the single emitter. A schematic picture of this physical magnitude is rendered in the top panel of Figure 3b. For the many situations where the classical EM spectral density can be used, i.e., in systems where the electronic wave function overlap between material elements and emitters is negligible, the EM environment is a continuum that can be treated as a bath. This makes all the theoretical tools of the field of open quantum systems available. As noted above, in the weak-coupling regime, the bath can be treated perturbatively through the Markov approximation, which just induces level shifts (often assumed to be included in the emitter frequency ωe and thus neglected) and radiative decay with rate γr = 2πJ(ωe).

Figure 3

Figure 3. (a) Sketch of the chain mapping model: (i) quantum system coupled to a discrete set of environment modes; (ii) quantum system coupled to the (collective) reaction mode, with this mode coupled to a residual bath of modes; (iii) chain mapping for the environment modes after n steps, with a residual bath of N – n modes at the end of the chain. (b) Sketch of the few-mode quantization model for one quantum emitter. The spectral density of the model can be fitted to the one obtained classically from the Green’s function. Therefore, the couplings to the interacting modes gi, their frequencies and coupling ωij, and the dissipative terms κi can be known. Panel (a) is reprinted from ref (98) under the terms of the Creative Commons Attribution 4.0 International license. Copyright 2021 MDPI. Panel (b) is reprinted from ref (99) under the terms of the Creative Commons Attribution 4.0 International license. Copyright 2021 American Physical Society.

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In the more interesting situation where the Markovian approximation is not applicable, there are several available methods to treat a bath of harmonic oscillators (the photon modes) exactly using advanced computational tools. One possibility is to solve the Heisenberg equations of motion while adding stochastic quantum noise. (100) Another alternative is the cumulant expansion, (101−103) which is based on solving the Heisenberg equations of motion for the correlations between operators and truncating the resulting expansion at a given order. It is in this sense an extension of mean-field approaches to arbitrary order. For small numbers of molecules (or a single one), relatively high orders of the correlations are needed to accurately describe the dynamics even in the presence of photonic continua, (104) while for large numbers of molecules, the expansion converges much earlier. (105) For cases where it works, this expansion provides a relatively low-cost approach that can handle situations that are difficult to treat using other approaches. For example, it can predict the effects of fluctuations on the lasing behavior of an organic-molecule polaritonic system taking into account the multimode character of the cavity, which leads to a switching of lasing behavior between different polaritonic modes, either those resonant with maximal gain or those at the bottom of the polariton dispersion. (105)
Several other commonly used approaches rely on the so-called chain mapping, an orthogonal transformation that maps the Hamiltonian of one emitter coupled to a continuum of modes to a chain-like Hamiltonian where the emitter is only coupled to the first site, which corresponds to a reaction mode, i.e., a collective environment mode, in an infinite string of modes coupled through nearest-neighbor interactions. (106−108)Figure 3a shows a sketch of this transformation. In this form, tensor network approaches that represent a high-dimensional wave function as a product of many lower-dimensional matrices (a so-called matrix product state) become highly efficient as the entanglement in an effective 1D system such as a chain is limited. Tensor network approaches depend exactly on a truncation of the possible entanglement between different parts of the system. In the context of molecular polaritonics, they have been shown to allow the description of several molecules coupled to complex environments. (109−111) A fully converged tensor network calculation gives exact results, but becomes computationally challenging when long propagation times are desired as the entanglement grows over time. Furthermore, the formally infinite chain has to be truncated at finite length in any realistic calculation, with the required length increasing with propagation time (to prevent unphysical reflections from the end of the chain). In order to decrease the length of the chain and access long times with low computational effort, it is possible to introduce fictitious losses along it that lead to damping of the propagating excitations (similar to the absorbing potentials used in many areas of physics). (98) Another approach is to employ transfer tensors, which can be used to propagate to arbitrary times with linear computational cost, (112) or the construction of process tensors and their recompression through tensor network techniques. (113)
While the description of the EM modes as a structured continuum described by the spectral density is formally exact, it is often advantageous and desired to obtain a description of the environment in terms of a few discrete modes, corresponding to the physical image of isolated cavity modes. When losses are included, these are not true eigenmodes of the system, but resonances with a given line width embedded in the continuum. Several methods to achieve such a few-mode quantized description have been developed in the past few years. One is based on quasinormal modes, which are eigenmodes of the Maxwell equations including losses with complex frequencies. (114,115) They can be used to expand the electric field solutions based on a master equation approach (116) or explicitly quantized such that the EM field is represented in terms of discrete bosonic modes. (117,118) In this approach, the discrete modes are defined as superpositions of the bosonic field operators f̂λ(r, ω) of macroscopic QED with coefficients determined by the quasinormal modes obtained from classical EM calculations, and the resulting modes are orthonormalized to obtain approximate discrete lossy modes.
An alternative approach that does not require calculation and explicit quantization of quasinormal modes is based on the fact that two systems with the same spectral density are indistinguishable for an emitter. This allows the construction of a model system consisting of a few coupled discrete modes that are themselves coupled to a background bath and reproduce the full spectral density. (99)Figure 3b shows a sketch of that model. The parameters of the model, which are obtained through fitting of the spectral density, are the coupling between the emitter and the discrete modes gi, the frequencies of these modes and their couplings ωij, and their dissipation κi. The coupling to the background modes is spectrally flat (by construction) and thus leads to Markovian dynamics that can be represented in a Lindblad master equation, such that the full EM continuum is represented by a collection of lossy and coupled discrete modes in the master equation. This approach is not only computationally efficient but also allows describing the EM environment in the language of cavity QED and quantum optics. The fact that the discrete modes are mutually coupled makes it able to reproduce even complex interference phenomena between the EM modes in the spectral density. This is especially relevant for hybrid cavities where different types of EM modes (such as localized plasmonic resonances and standing-wave modes) interfere. The coexistence of several interacting and decaying modes in such subwavelength cavity QED systems can lead to complex emitter and field dynamics that are not captured by standard models of quantum optics and cavity QED and are only starting to be explored. While originally developed for a single emitter, (99) we have recently extended the approach to the case of several emitters (96) or one emitter with several contributing transitions (such as different orientations of the dipole moments). A similar model as in the single-emitter case can then be used to fit the generalized spectral density, eq 6. This approach is then able to capture the effect of a complex mode structure on emitter dynamics and, for example, population transfer between emitters. As an example, it can describe how the dynamics of population transfer between two emitters coupled through a multimode cavity can be modified by the presence and excitation state of a third emitter. (96)

3. Introducing Molecular Complexity

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For the description of the molecules, we focus on approaches that are well-adapted for describing “good” molecular emitters, meaning ones where the first electronically excited state is relatively stable against nonradiative decay and photochemical reactions do not take place. For such emitters, it is often a good approximation to represent the nuclear potential energy surfaces as harmonic oscillators, which significantly simplifies the treatment. When more chemical detail is needed, a wide variety of methods are nowadays available, but doing so typically limits the level of description of nuclear motion. A discussion of such methods focusing on chemically accurate descriptions can be found in a related recent perspective on polaritonic chemistry. (8)
As detailed in the Introduction, the simplest approach is to treat molecules as two-level systems. This can be well-justified for studies at cryogenic temperatures where vibrational sublevels are individually resolved and addressable. (49,119) At room temperature, the influence of the vibrational motion of the molecule can be approximately included by adding a pure dephasing term in a Lindblad master equation description. This can be understood as arising from an exciton–vibration coupling term treated through the Markov approximation. Such a treatment allows modeling the influence of molecular vibrations on processes where vibration-induced transitions between the polaritons and dark states do not dominate the dynamics. One such example is coherent polariton-mediated long-range exciton conductance (i.e., energy transport). (120,121) In such systems, it was found that the coherent nature of the polaritons only becomes realized and significantly enhances transport when the Rabi splitting significantly surpasses the dephasing rate.
While modeling pure dephasing through a Lindblad term can give some insight into the vibration-induced decoherence of the molecules, this treatment is not fully correct. Since under strong coupling the molecular exciton state gets distributed over the polaritonic modes, the Markov approximation that was originally performed for the emitter by itself to obtain a pure dephasing term is not valid anymore. (122) Including it without further modification in the strongly coupled system leads to artificial population transfer between the polaritons and dark states, with equal rates for pumping of energy from the reservoir of vibrations to the system as for loss of energy from the system to the reservoir. This is unphysical when the Rabi splitting is comparable to or larger than the thermal energy, a condition that is essentially always fulfilled in molecular exciton–polariton strong coupling. This problem can be resolved by applying the Markov approximation after taking into account the strong coupling, e.g., by using a Bloch–Redfield approach. (79,80,123,124) This approach captures the fact that vibration-induced transitions between states preferably lead to relaxation, i.e., loss of energy to the bath of molecular vibrations. This one-way transfer to the lowest state in the excitation manifold can be exploited to selectively excite states with a desired characteristic in polaritonic systems and in particular can be exploited to induce long-range energy transfer between different molecular species driven by their local vibrations and enabled by the nonlocal character of the polaritons. (5,6,78−82)
When the exciton–phonon coupling is sufficiently strong that the above approach breaks down, it becomes necessary to explicitly include the vibrational modes of the molecules. The simplest approach is the so-called Holstein model, which treats only a single vibrational mode and describes each molecule as two displaced harmonic oscillators. For multiple emitters, this leads to the so-called Holstein–Tavis–Cummings model, (125,126) within which each electronic level is represented by several vibrational sublevels. Within this model, the effect of the vibronic coupling can be studied, so an analysis of nuclear dynamics in molecules under strong coupling is feasible. Along this line, it has been predicted that electron transfer between different excited states can be enhanced or suppressed. (126) The physical effect behind these changes is a decoupling of vibrational modes from the polaritons due to the collective nature of the excitation. Similar effects also occur in molecular J- and H-aggregates outside of cavities, where the collective nature arises due to dipole–dipole interactions between the monomers and leads to significantly reduced line widths. (127) Within the Holstein–Tavis–Cummings model, the inclusion of vibronic sublevels and the concomitant emergence of dark vibronic polaritons (collective light–matter states that weakly absorb but strongly emit radiation) allows for a better description of the spectroscopy and dynamics of organic microcavities in the strong-coupling regime. (128−130) The inclusion of vibrational levels is also highly relevant for the description of phenomena such as organic polariton lasing and polariton condensation. (125,131,132)
An extension of the Holstein–Tavis–Cummings model that allows for more realistic molecular structure is to consider more complex potential energy curves instead of harmonic oscillators, permitting the treatment of vibrational nonlinearities and (photo)chemical reactions within a relatively simple model (especially if only a single vibrational degree of freedom is treated). The hybridization of the potential energy surfaces in the strong coupling regime then leads to hybridized polaritonic potential energy surfaces (PoPES), which have mixed photon–matter properties. (51,133,134) A schematic representation of these PoPES can be found in Figure 4. Within this approach, the polariton decoupling of the vibrational modes can be easily understood from the fact that a single excitation is distributed over many molecules in a polaritonic state; that is, each molecule is only excited with a small probability amplitude and spends most of the time in its electronic ground state. The polaritonic potential energy surface then follows the ground-state one. This fact allows designing new potential energy landscapes in the coupled system by “copying and pasting” together excited-state and ground-state-like potentials from different nuclear configurations depending on whether the system is on resonance with the cavity or not at the specific configuration. (134)

Figure 4

Figure 4. Conceptual potential energy surfaces for one cavity mode and one molecule at different coupling strengths: (a) weak coupling; (b, c) strong coupling. The color represents the fraction of each constituent. Reprinted with permission from ref (51). Copyright 2017 American Chemical Society.

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Assuming that vibrational modes are harmonic oscillators but taking into account all degrees of freedom for the molecules (typically hundreds), and potentially of the surrounding solvent or polymer host material, one can again rely on tensor network techniques as discussed above for the photonic modes. The molecular vibrations are then represented by an independent chain of harmonic oscillators. (109−111,135) This approach describes the initial coherent oscillation of the nuclear wavepacket and its influence on the polariton dynamics, as well as its gradual suppression due to the presence of a multitude of modes. When the exact dynamics of the vibrational modes are not desired, the bath of harmonic vibrational modes can be represented through its correlation function and simulated using the time-evolving matrix product operator (TEMPO) method. (136,137) This uses a tensor network to describe the system’s history over a finite memory time and can thus represent non-Markovian dynamics. Combining this technique with a mean-field approximation further reduces the problem size. (138) This method can thus describe the vibration-induced dynamics and dephasing of the molecular wavepackets over long times within a fully quantized approach.
We note at this point that although many effects can be understood by the use of the previous models, all of them constitute strong approximations for the molecular structure. In particular, the use of harmonic oscillators to describe the vibrational modes precludes the description of any nonlinear vibrational effects or of chemical transition states, conical intersections, etc. However, a full quantum description of the molecules is an extremely challenging task and only possible for small molecules. To give a more complete picture by including all degrees of freedom inside the molecules requires utilizing quantum chemistry and ab initio approaches. (8)

4. Summary and Outlook

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In this article we have provided a perspective on the current status of the theoretical investigation devoted to analyzing the exciting physics in the emergent field of molecular polaritonics. This area of research deals with the strong light–matter coupling regime that appears between electronic/vibrational excitations within (organic) molecules and confined light fields. As for the light field component, a photonic structure that acts as a cavity is needed. Depending on the cavity used, strong coupling can be reached by utilizing a large ensemble of molecules or just one or a few of them, depending on whether or not subwavelength confinement is achieved.
The theoretical description of the EM modes that arise in these photonic structures, which in general are lossy, is then a challenging task. When the cavities present small losses, they can be treated perturbatively, while for small enough subwavelength cavities, the quasistatic approximation can be used, which allows for semianalytical solutions. However, in many physical situations, a fully quantized description of the EM field in photonic structures is required. Here we have shown how the macroscopic QED formalism provides the necessary theoretical and numerical tools to accurately describe light–matter strong coupling in arbitrary structures. Within this framework, the spectral densities that characterize the coupling between one or several quantum emitters and confined EM modes are fully determined by the classical Green’s functions, which are calculated using standard numerical solvers of Maxwell’s equations in complex EM media. Based on macroscopic QED, it is then feasible to develop approaches that allow for a tractable treatment of complex photonic environments. Among these simplified treatments, the most promising approaches are those based on the concept of quasinormal EM modes and a very recent one that relies on the construction of a model system involving a small number of lossy and interacting EM modes whose parameters are fitted to exactly reproduce the spectral densities associated with the photonic structure under study.
Regarding the matter component, organic molecules also have a complex internal structure, which prevents them from being theoretically modeled as just two-level systems in many situations. To include molecular complexity in the theoretical description, it is then mandatory to add some ingredients to the standard two-level model to describe the vibrational modes of the molecules. Depending on the strength of the vibronic coupling, a pure dephasing term, the Bloch–Redfield approximation, or the explicit inclusion of the vibrational modes needs to be utilized. Within this last approach, the most used framework is the so-called Holstein–Tavis–Cummings model, which only takes into account one vibrational mode, modeled as a harmonic oscillator, which has proven to be very successful in providing physical insight. Going beyond this model can be achieved either by including more of the (typically hundreds of) vibrational modes of a molecule or by substituting the harmonic oscillators by more realistic potential energy surfaces. The first approach captures vibration-induced dephasing and decoherence, while the second naturally accounts for the vibrational nonlinearities and has also allowed for a fundamental description of (photo)chemical reactions induced by strong light–matter coupling. Nevertheless, in order to have a more accurate description of the internal structure of organic molecules, numerical formalisms that rely on quantum chemistry codes or ab initio approaches need to be utilized.
At this stage, for the case of collective strong coupling in which a large (macroscopic) number of molecules is involved, the current status of the theoretical research on molecular polaritonics does not allow for both a realistic treatment of the internal structure of the organic molecules and a detailed account of the complex EM media. This is indeed very frustrating, as the majority of the experiments carried out in this field belong to the category of collective strong coupling. Therefore, a quantitative agreement between ab initio theory and experiment is not within reach nowadays. As a concrete example, current ab initio theoretical models do not correctly predict the experimentally observed decay rates from the exciton reservoir to the lower polariton. This is why during the past decade most theoretical research has focused either on giving fundamental support to some of the experimental findings or to propose new effects that result from theoretical approaches based on simplified models. On a more positive note, for the case in which only a single or few molecules participate in the strong-coupling phenomenon, after 10 years of intense research, we now have the adequate theoretical and numerical tools to accurately describe both the internal vibrational modes of the organic molecules and the complexity of the subwavelength EM fields associated with nanophotonic (mainly plasmonic) structures. We expect that these theoretical developments will help to open new and exciting avenues for research in molecular polaritonics.

Author Information

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  • Corresponding Authors
    • Johannes Feist - Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain;  Orcidhttps://orcid.org/0000-0002-7972-0646;  Email: [email protected]
    • Francisco J. García-Vidal - Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain;  Institute of High Performance Computing, Agency for Science, Technology, and Research (A*STAR), Connexis, Singapore, 138632 Singapore;  Orcidhttps://orcid.org/0000-0003-4354-0982;  Email: [email protected]
  • Authors
    • Mónica Sánchez-Barquilla - Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
    • Antonio I. Fernández-Domínguez - Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain;  Orcidhttps://orcid.org/0000-0002-8082-395X
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work has been funded by the European Research Council through Grant ERC-2016-StG-714870 and by the Spanish Ministry for Science, Innovation, and Universities–Agencia Estatal de Investigación through grants RTI2018-099737-B-I00, PCI2018-093145 (through the QuantERA program of the European Commission), and CEX2018-000805-M (through the María de Maeztu program for Units of Excellence in R&D). We also acknowledge financial support from the Proyecto Sinérgico CAM 2020 Y2020/TCS-6545 (NanoQuCo-CM) of the Community of Madrid.

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    cf. ibid. 102, 385(1956). A quantum analog of the classical electron oscillator model is developed. The Hamiltonian of long-wave excitations of matter is equiv. to that of an assembly of oscillators under very general assumptions. These oscillators are coupled with the electromagnetic field oscillators and the normal modes of the coupled system are analyzed. The normal modes of longitudinal and transverse excitation have different spectra; the transverse frequencies depend strongly on the wave length but the longitudinal ones do not. If the "longitudinal photons" are eliminated after the transformation to normal modes, the resulting Coulomb law has the dielec. const. in the denominator. The dielec. response law is expressed as a series of oscillations and also in terms of Van Hove's correlation function (C.A. 48, 9803a). Born approximation theory of the collisions of fast charged particles with the assembly of normal mode (longitudinal and transverse) oscillators yields the same total cross section as does Fermi's macroscopic theory (C.A. 34, 3977.8). The transverse excitations include the Cherenkov radiation.
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    Quantization of the electromagnetic field in dielectrics
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    Recently a quantization scheme for the phenomenol. Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielec. medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface. Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commutation relations of QED are preserved for an arbitrarily space-dependent, Kramers-Kronig consistent permittivity. Further, an extension of the quantization scheme to linear media with bounded regions of amplification is given, and the problem of anisotropic media is briefly addressed.
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    Macroscopic field quantization is presented for a nondispersive photonic dielec. environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivs. shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are detd. and in particular, the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielec. a dipole couples to a field that is neither the (transverse) elec. nor the macroscopic displacement field. The dielec. function is different from the bulk dielec. function at the position of the dipole, so that local-field effects must be taken into account.
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    In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the std. mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated at. systems and magnetoelec. bodies, and serves as an important tool for the understanding of surface-assisted at. relaxation effects and the intimately connected position-dependent energy shifts which give rise to Casimir-Polder and van der Waals forces.
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    Applied Physics Letters (1996), 69 (4), 449-451CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    A Ga/As/AlAs planar cavity contg. a collection in InAs quantum boxes in its core region was grown in a single step by mol. beam epitaxy, and processed by electron-beam lithog. and reactive ion etching into pillar microresonators. The optical study by photoluminescence of these localized light emitters allows a systematic and precise detn. of the energies of the 1st confined photon modes of such microstructures, in a good agreement with theor. ests. More generally, such probes facilitate the exptl. study of the modes of complex photonic microstructures and of the spontaneous emission alteration they entail on a quasimonochromatic light emitter.
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    Science (Washington, D. C.) (2000), 287 (5457), 1447-1453CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    The motion of individual Cs atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM). A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. An inversion algorithm then allows individual atom trajectories to be reconstructed from the record of cavity transmission and reveals single atoms bound in orbit by the mech. forces assocd. with single photons. In these initial expts., the ACM yields 2-μm spatial resoln. in a 10-μs time interval. Over the duration of the observation, the sensitivity is near the std. quantum limit for sensing the motion of a Cs atom.
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    Science (Washington, D. C.) (1999), 284 (5421), 1819-1821CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    A laser cavity formed from a single defect in a two-dimensional photonic crystal is demonstrated. The optical microcavity consists of a half wavelength-thick waveguide for vertical confinement and a two-dimensional photonic crystal mirror for lateral localization. A defect in the photonic crystal is introduced to trap photons inside a vol. of 2.5 cubic half-wavelengths, approx. 0.03 cubic micrometers. The laser is fabricated in the indium gallium arsenic phosphide material system, and optical gain is provided by strained quantum wells designed for a peak emission wavelength of 1.55 μm at room temp. Pulsed lasing action has been obsd. at a wavelength of 1.5 μm from optically pumped devices with a substrate temp. of 143 K.
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    Lodahl, P.; Mahmoodian, S.; Stobbe, S. Interfacing Single Photons and Single Quantum Dots with Photonic Nanostructures. Rev. Mod. Phys. 2015, 87, 347,  DOI: 10.1103/RevModPhys.87.347
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    Interfacing single photons and single quantum dots with photonic nanostructures
    Lodahl, Peter; Mahmoodian, Sahand; Stobbe, Soren
    Reviews of Modern Physics (2015), 87 (2), 347-400CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
    Photonic nanostructures provide a means of tailoring the interaction between light and matter and the past decade has witnessed tremendous exptl. and theor. progress on this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics expts. on, e.g.. spontaneous- emission control, modified Lamb shifts, and enhanced dipole-dipole interaction. Furthermore, highly efficient single-photon sources and giant photon nonlinearities may be implemented with immediate applications for photonic quantum-information processing. This review summarizes the general theor. framework of photon emission including the role of dephasing processes and applies it to photonic nanostructures of current interest, such as photonic-crystal cavities and waveguides, dielec. nanowires, and plasmonic waveguides. The introduced concepts are generally applicable in quantum nanophotonics and apply to a large extent also to other quantum emitters, such as mols., nitrogen vacancy centers, or atoms. Finally, the progress and future prospects of applications in quantum-information processing are considered.
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    Fernández-Domínguez, A. I.; García-Vidal, F. J.; Martín-Moreno, L. Unrelenting Plasmons. Nat. Photonics 2017, 11, 8,  DOI: 10.1038/nphoton.2016.258
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    Unrelenting plasmons
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    Nature Photonics (2017), 11 (1), 8-10CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
    Worldwide research efforts on plasmonics and metamaterials have been growing exponentially for the past ten years. Will this course hold true over the next decade.
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    Fernández-Domínguez, A. I.; Bozhevolnyi, S. I.; Mortensen, N. A. Plasmon-Enhanced Generation of Nonclassical Light. ACS Photonics 2018, 5, 3447,  DOI: 10.1021/acsphotonics.8b00852
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    Plasmon-Enhanced Generation of Nonclassical Light
    Fernandez-Dominguez, Antonio I.; Bozhevolnyi, Sergey I.; Mortensen, N. Asger
    ACS Photonics (2018), 5 (9), 3447-3451CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    A review. Strong light-matter interactions enabled by surface plasmons have given rise to a wide range of photonic, optoelectronic, and chem. functionalities. In recent years, the interest in this research area has focused on the quantum regime, aiming to developing ultracompact nanoscale instruments operating at the single (few) photon(s) level. In this perspective, we provide a general overview of recent exptl. and theor. advances as well as near-future challenges toward the design and implementation of plasmon-empowered quantum optical and photoemitting devices based on the building blocks of nanophotonics technol.: metallo-dielec. nanostructures and microscopic light sources.
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    Baumberg, J. J.; Aizpurua, J.; Mikkelsen, M. H.; Smith, D. R. Extreme Nanophotonics from Ultrathin Metallic Gaps. Nat. Mater. 2019, 18, 668,  DOI: 10.1038/s41563-019-0290-y
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    Extreme nanophotonics from ultrathin metallic gaps
    Baumberg, Jeremy J.; Aizpurua, Javier; Mikkelsen, Maiken H.; Smith, David R.
    Nature Materials (2019), 18 (7), 668-678CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
    A review. Ultrathin dielec. gaps between metals can trap plasmonic optical modes with surprisingly low loss and with vols. below 1 nm3. We review the origin and subtle properties of these modes, and show how they can be well accounted for by simple models. Particularly important is the mixing between radiating antennas and confined nanogap modes, which is extremely sensitive to precise nanogeometry, right down to the single-atom level. Coupling nanogap plasmons to electronic and vibronic transitions yields a host of phenomena including single-mol. strong coupling and mol. optomechanics, opening access to at.-scale chem. and materials science, as well as quantum metamaterials. Ultimate low-energy devices such as robust bottom-up assembled single-atom switches are thus in prospect.
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    Khurgin, J. B. How to Deal with the Loss in Plasmonics and Metamaterials. Nat. Nanotechnol. 2015, 10, 2,  DOI: 10.1038/nnano.2014.310
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    How to deal with the loss in plasmonics and metamaterials
    Khurgin, Jacob B.
    Nature Nanotechnology (2015), 10 (1), 2-6CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
    A review with commentary. Metal losses affect the performance of every plasmonic or metamaterial structure; dealing with them will det. the degree to which these structures will find practical applications.
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    Galego, J.; Climent, C.; Garcia-Vidal, F. J.; Feist, J. Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity. Phys. Rev. X 2019, 9, 021057
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    Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity
    Galego, Javier; Climent, Claudia; Garcia-Vidal, Francisco J.; Feist, Johannes
    Physical Review X (2019), 9 (2), 021057CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    A review. Here, we present a fundamental study on how the ground-state chem. reactivity of a single mol. can be modified in a QED scenario, i.e., when it is placed inside a nanoscale cavity and there is strong coupling between the cavity field and vibrational modes within the mol. We work with a model system for the mol. (Shin-Metiu model) in which nuclear, electronic, and photonic degrees of freedom are treated on the same footing. This simplified model allows the comparison of exact quantum reaction rate calcns. with predictions emerging from transition state theory based on the cavity Born-Oppenheimer approach. We demonstrate that QED effects are indeed able to significantly modify activation barriers in chem. reactions and, as a consequence, reaction rates. The crit. phys. parameter controlling this effect is the permanent dipole of the mol. and how this magnitude changes along the reaction coordinate. We show that the effective coupling can lead to significant single-mol. energy shifts in an exptl. available nanoparticle-on-mirror cavity. We then apply the validated theory to a realistic case (internal rotation in the 1,2-dichloroethane mol.), showing how reactions can be inhibited or catalyzed depending on the profile of the mol. dipole. Furthermore, we discuss the absence of resonance effects in the present scenario, which can be understood through its connection to Casimir-Polder forces. Finally, we treat the case of many-mol. strong coupling and find collective modifications of reaction rates if the mol. permanent dipole moments are oriented with respect to the cavity field.
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    Zhang, Y.; He, S.; Guo, W.; Hu, Y.; Huang, J.; Mulcahy, J. R.; Wei, W. D. Surface-Plasmon-Driven Hot Electron Photochemistry. Chem. Rev. 2018, 118, 2927,  DOI: 10.1021/acs.chemrev.7b00430
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    Surface-plasmon-driven hot electron photochemistry
    Zhang, Yuchao; He, Shuai; Guo, Wenxiao; Hu, Yue; Huang, Jiawei; Mulcahy, Justin R.; Wei, Wei David
    Chemical Reviews (Washington, DC, United States) (2018), 118 (6), 2927-2954CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
    A review. Visible-light-driven photochem. has continued to attract heightened interest due to its capacity to efficiently harvest solar energy and its potential to solve the global energy crisis. Plasmonic nanostructures boast broadly tunable optical properties coupled with catalytically active surfaces that offer a unique opportunity for solar photochem. Resonant optical excitation of surface plasmons produces energetic hot electrons that can be collected to facilitate chem. reactions. This review sums up recent theor. and exptl. approaches for understanding the underlying photophys. processes in hot electron generation and discusses various electron-transfer models on both plasmonic metal nanostructures and plasmonic metal/semiconductor heterostructures. Following that are highlights of recent examples of plasmon-driven hot electron photochem. reactions within the context of both cases. The review concludes with a discussion about the remaining challenges in the field and future opportunities for addressing the low reaction efficiencies in hot-electron-induced photochem.
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    Zhou, L.; Swearer, D. F.; Zhang, C.; Robatjazi, H.; Zhao, H.; Henderson, L.; Dong, L.; Christopher, P.; Carter, E. A.; Nordlander, P.; Halas, N. J. Quantifying Hot Carrier and Thermal Contributions in Plasmonic Photocatalysis. Science 2018, 362, 69,  DOI: 10.1126/science.aat6967
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    Quantifying hot carrier and thermal contributions in plasmonic photocatalysis
    Zhou, Linan; Swearer, Dayne F.; Zhang, Chao; Robatjazi, Hossein; Zhao, Hangqi; Henderson, Luke; Dong, Liangliang; Christopher, Phillip; Carter, Emily A.; Nordlander, Peter; Halas, Naomi J.
    Science (Washington, DC, United States) (2018), 362 (6410), 69-72CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Photocatalysis based on optically active, "plasmonic" metal nanoparticles has emerged as a promising approach to facilitate light-driven chem. conversions under far milder conditions than thermal catalysis. However, an understanding of the relation between thermal and electronic excitations has been lacking. We report the substantial light-induced redn. of the thermal activation barrier for ammonia decompn. on a plasmonic photocatalyst. We introduce the concept of a light-dependent activation barrier to account for the effect of light illumination on electronic and thermal excitations in a single unified picture. This framework provides insight into the specific role of hot carriers in plasmon-mediated photochem., which is critically important for designing energy-efficient plasmonic photocatalysts.
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    Tanji-Suzuki, H.; Leroux, I. D.; Schleier-Smith, M. H.; Cetina, M.; Grier, A.; Simon, J.; Vuletić, V. Interaction between Atomic Ensembles and Optical Resonators: Classical Description. Adv. At. Mol. Opt. Phys. 2011, 60, 201,  DOI: 10.1016/B978-0-12-385508-4.00004-8
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    Interaction between atomic ensembles and optical resonators: classical description
    Tanji-Suzuki, Haruka; Leroux, Ian D.; Schleier-Smith, Monika H.; Cetina, Marko; Grier, Andrew T.; Simon, Jonathan; Vuletic, Vladan
    Advances in Atomic, Molecular, and Optical Physics (2011), 60 (), 201-237CODEN: AAMPE9; ISSN:1049-250X. (Elsevier Inc.)
    Many effects in the interaction between atoms and a cavity that are usually described in quantum mech. terms (cavity quantum electrodynamics, cavity QED) can be understood and quant. analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit expressions for the coupling of single atoms and at. ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role and is given a geometrical interpretation. The classical anal. yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions assocd. with the self-organization of the ensemble-light system.
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    Kewes, G.; Binkowski, F.; Burger, S.; Zschiedrich, L.; Benson, O. Heuristic Modeling of Strong Coupling in Plasmonic Resonators. ACS Photonics 2018, 5, 4089,  DOI: 10.1021/acsphotonics.8b00766
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    Heuristic Modeling of Strong Coupling in Plasmonic Resonators
    Kewes, Guenter; Binkowski, Felix; Burger, Sven; Zschiedrich, Lin; Benson, Oliver
    ACS Photonics (2018), 5 (10), 4089-4097CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    A heuristic modeling approach is presented for strongly coupled systems based on plasmonic nanoparticles and dipolar emitters that accounts for such broadening and elucidates on recent expts. with single emitters. The focus is explicitly on a clear and intuitive classical description that uses established methods, easy to use within typical Maxwell solvers. The heuristic model (i) provides exptl. relevant nos. such as emitter densities, and spectra, (ii) allows discrimination of systems which can reach the strong coupling regime from those which cannot, (iii) allows identification of optimization routes and (iv) nicely matches with exptl. findings. An approach related to quasi normal modes and extinction simulations where the excitonic system is represented by a frequency dependent permittivity is used. Two configurations with many but also single emitters which were studied in recent expts. are examples.
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    Sáez-Blázquez, R.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Theory of Energy Transfer in Organic Nanocrystals. Adv. Opt. Mater. 2020, 8, 2001447,  DOI: 10.1002/adom.202001447
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    Theory of Energy Transfer in Organic Nanocrystals
    Saez-Blazquez, Rocio; Feist, Johannes; Garcia-Vidal, Francisco J.; Fernandez-Dominguez, Antonio I.
    Advanced Optical Materials (2020), 8 (23), 2001447CODEN: AOMDAX; ISSN:2195-1071. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Recent expts. have shown that highly efficient energy transfer can take place in org. nanocrystals at extremely low acceptor densities. This striking phenomenon has been ascribed to the formation of exciton polaritons thanks to the photon confinement provided by the crystal itself. An alternative theor. model that accurately reproduces fluorescence lifetime and spectrum measurements in these systems without such an assumption is proposed. The approach treats mol.-photon interactions in the weak-coupling regime, and describes the donor and acceptor population dynamics by means of rate equations with parameters extd. from electromagnetic simulations. The phys. insight and predictive value of this model also enables the authors to propose nanocrystal configurations in which acceptor emission dominates the fluorescence spectrum at densities orders of magnitude lower than the exptl. ones.
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    Jaynes, E. T.; Cummings, F. W. Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser. Proc. IEEE 1963, 51, 89,  DOI: 10.1109/PROC.1963.1664
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    Kristensen, P. T.; Van Vlack, C.; Hughes, S. Generalized Effective Mode Volume for Leaky Optical Cavities. Opt. Lett. 2012, 37, 1649,  DOI: 10.1364/OL.37.001649
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    Generalized effective mode volume for leaky optical cavities
    Kristensen P T; Van Vlack C; Hughes S
    Optics letters (2012), 37 (10), 1649-51 ISSN:.
    We show explicitly how the commonly adopted prescription for calculating effective mode volumes is wrong and leads to uncontrolled errors. Instead, we introduce a generalized mode volume that can be easily evaluated based on the mode calculation methods typically applied in the literature, and which allows one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.
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    Cognée, K. G.; Yan, W.; China, F. L.; Balestri, D.; Intonti, F.; Gurioli, M.; Koenderink, A. F.; Lalanne, P. Mapping Complex Mode Volumes with Cavity Perturbation Theory. Optica, OPTICA 2019, 6, 269,  DOI: 10.1364/OPTICA.6.000269
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    Tserkezis, C.; Fernández-Domínguez, A. I.; Gonçalves, P. A. D.; Todisco, F.; Cox, J. D.; Busch, K.; Stenger, N.; Bozhevolnyi, S. I.; Mortensen, N. A.; Wolff, C. On the Applicability of Quantum-Optical Concepts in Strong-Coupling Nanophotonics. Rep. Prog. Phys. 2020, 83, 082401,  DOI: 10.1088/1361-6633/aba348
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    On the applicability of quantum-optical concepts in strong-coupling nanophotonics
    Tserkezis, Christos; Fernandez-Dominguez, Antonio I.; Goncalves, P. A. D.; Todisco, Francesco; Cox, Joel D.; Busch, Kurt; Stenger, Nicolas; Bozhevolnyi, Sergey I.; Mortensen, N. Asger; Wolff, Christian
    Reports on Progress in Physics (2020), 83 (8), 082401CODEN: RPPHAG; ISSN:1361-6633. (IOP Publishing Ltd.)
    Rooted in quantum optics and benefiting from its well-established foundations, strong coupling in nanophotonics has experienced increasing popularity in recent years. With nanophotonics being an expt.-driven field, the absence of appropriate theor. methods to describe ground-breaking advances has often emerged as an important issue. To address this problem, the temptation to directly transfer and extend concepts already available from quantum optics is strong, even if a rigorous justification is not always available. In this review we discuss situations where, in our view, this strategy has indeed overstepped its bounds. We focus on exciton-plasmon interactions, and particularly on the idea of calcg. the no. of excitons involved in the coupling. We analyze how, starting from an unfounded interpretation of the term N/V that appears in theor. descriptions at different levels of complexity, one might be tempted to make independent assumptions for what the no. N and the vol. V are, and attempt to calc. them sep. Such an approach can lead to different, often contradictory results, depending on the initial assumptions (e.g. through different treatments of V as the-ambiguous in plasmonics-mode vol.). We argue that the source of such contradictions is the question itself-How many excitons are coupled, which disregards the true nature of the coupled components of the system, has no meaning and often not even any practical importance. If one is interested in validating the quantum nature of the system-which appears to be the motivation driving the pursuit of strong coupling with small N-one could instead focus on quantities such as the photon emission rate or the second-order correlation function. While many of the issues discussed here may appear straightforward to specialists, our target audience is predominantly newcomers to the field, either students or scientists specialised in different disciplines. We have thus tried to minimise the occurrence of proofs and overly-tech. details, and instead provide a qual. discussion of analyses that should be avoided, hoping to facilitate further growth of this promising area.
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    Garraway, B. M. The Dicke Model in Quantum Optics: Dicke Model Revisited. Philos. Trans. R. Soc. A 2011, 369, 1137,  DOI: 10.1098/rsta.2010.0333
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    One-atom maser
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    Physical Review Letters (1985), 54 (6), 551-4CODEN: PRLTAO; ISSN:0031-9007.
    The exchange of photons between single Rydberg atoms and a single mode of a superconducting cavity with a quality factor Q = 8 × 108 at 2 K was obsd. Signals could still be detected with an av. no. of only 0.06 atom simultaneously in the cavity. With 1 Rydberg atom, the linewidth of the maser transition at ∼21 GHz was power broadened and at higher densities asymmetry of the transition was obsd., which is ascribed to an a.c. Stark effect.
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    Rempe, G.; Walther, H.; Klein, N. Observation of Quantum Collapse and Revival in a One-Atom Maser. Phys. Rev. Lett. 1987, 58, 353,  DOI: 10.1103/PhysRevLett.58.353
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    Observation of quantum collapse and revival in a one-atom maser
    Rempe, Gerhard; Walther, Herbert; Klein, Norbert
    Physical Review Letters (1987), 58 (4), 353-6CODEN: PRLTAO; ISSN:0031-9007.
    The dynamics of the interaction of a single Rydberg atom with a single mode of an electromagnetic field in a superconducting cavity was investigated. Velocity-selected atoms were used, and the evolution of the at. inversion as atom and field exchange energy was obsd. The quantum collapse and revival predicted by the E.T. Jaynes-F.W. Cummings (1963) model were demonstrated exptl. The evaluation of the dynamic behavior of the atoms allows detg. the statistics of the few photons in the cavity.
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    Reithmaier, J. P.; Sȩk, G.; Löffler, A.; Hofmann, C.; Kuhn, S.; Reitzenstein, S.; Keldysh, L. V.; Kulakovskii, V. D.; Reinecke, T. L.; Forchel, A. Strong Coupling in a Single Quantum Dot–Semiconductor Microcavity System. Nature 2004, 432, 197,  DOI: 10.1038/nature02969
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    Strong coupling in a single quantum dot-semiconductor microcavity system
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    Nature (London, United Kingdom) (2004), 432 (7014), 197-200CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    The authors report the observation of strong coupling of a single 2-level solid-state system with a photon, as realized by a single quantum dot in a semiconductor microcavity. The strong coupling is manifest in photoluminescence data that display anti-crossings between the quantum dot exciton and cavity-mode dispersion relations, characterized by a vacuum Rabi splitting of ∼140 μeV.
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    Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Vacuum Rabi Splitting in a Plasmonic Cavity at the Single Quantum Emitter Limit. Nat. Commun. 2016, 7, 11823,  DOI: 10.1038/ncomms11823
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    Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit
    Santhosh, Kotni; Bitton, Ora; Chuntonov, Lev; Haran, Gilad
    Nature Communications (2016), 7 (), ncomms11823CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    The strong interaction of individual quantum emitters with resonant cavities is of fundamental interest for understanding light-matter interactions. Plasmonic cavities hold the promise of attaining the strong coupling regime even under ambient conditions and within subdiffraction vols. Recent expts. revealed strong coupling between individual plasmonic structures and multiple org. mols.; however, strong coupling at the limit of a single quantum emitter has not been reported so far. Here we demonstrate vacuum Rabi splitting, a manifestation of strong coupling, using silver bowtie plasmonic cavities loaded with semiconductor quantum dots (QDs). A transparency dip is obsd. in the scattering spectra of individual bowties with one to a few QDs, which are directly counted in their gaps. A coupling rate as high as 120 meV is registered even with a single QD, placing the bowtie-QD constructs close to the strong coupling regime. These observations are verified by polarization-dependent expts. and validated by electromagnetic calcns.
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    Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Single-Molecule Strong Coupling at Room Temperature in Plasmonic Nanocavities. Nature 2016, 535, 127,  DOI: 10.1038/nature17974
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    Single-molecule strong coupling at room temperature in plasmonic nanocavities
    Chikkaraddy, Rohit; de Nijs, Bart; Benz, Felix; Barrow, Steven J.; Scherman, Oren A.; Rosta, Edina; Demetriadou, Angela; Fox, Peter; Hess, Ortwin; Baumberg, Jeremy J.
    Nature (London, United Kingdom) (2016), 535 (7610), 127-130CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Photon emitters placed in an optical cavity experience an environment that changes how they are coupled to the surrounding light field. In the weak-coupling regime, the extn. of light from the emitter is enhanced. But more profound effects emerge when single-emitter strong coupling occurs: mixed states are produced that are part light, part matter, forming building blocks for quantum information systems and for ultralow-power switches and lasers. Such cavity quantum electrodynamics has until now been the preserve of low temps. and complicated fabrication methods, compromising its use. Here, by scaling the cavity vol. to less than 40 cubic nanometers and using host-guest chem. to align one to ten protectively isolated methylene-blue mols., we reach the strong-coupling regime at room temp. and in ambient conditions. Dispersion curves from more than 50 such plasmonic nanocavities display characteristic light-matter mixing, with Rabi frequencies of 300 millielectronvolts for ten methylene-blue mols., decreasing to 90 millielectronvolts for single mols.-matching quant. models. Statistical anal. of vibrational spectroscopy time series and dark-field scattering spectra provides evidence of single-mol. strong coupling. This dressing of mols. with light can modify photochem., opening up the exploration of complex natural processes such as photosynthesis and the possibility of manipulating chem. bonds.
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    Liu, R.; Zhou, Z.-K.; Yu, Y.-C.; Zhang, T.; Wang, H.; Liu, G.; Wei, Y.; Chen, H.; Wang, X.-H. Strong Light-Matter Interactions in Single Open Plasmonic Nanocavities at the Quantum Optics Limit. Phys. Rev. Lett. 2017, 118, 237401,  DOI: 10.1103/PhysRevLett.118.237401
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    Strong light-matter interactions in single open plasmonic nanocavities at the quantum optics limit
    Liu, Renming; Zhou, Zhang-Kai; Yu, Yi-Cong; Zhang, Tengwei; Wang, Hao; Liu, Guanghui; Wei, Yuming; Chen, Huanjun; Wang, Xue-Hua
    Physical Review Letters (2017), 118 (23), 237401/1-237401/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Reaching the quantum optics limit of strong light-matter interactions between a single exciton and a plasmon mode is highly desirable, because it opens up possibilities to explore room-temp. quantum devices operating at the single-photon level. However, two challenges severely hinder the realization of this limit: the integration of single-exciton emitters with plasmonic nanostructures and making the coupling strength at the single-exciton level overcome the large damping of the plasmon mode. Here, we demonstrate that these two hindrances can be overcome by attaching individual J aggregates to single cuboid Au@Ag nanorods. In such hybrid nanosystems, both the ultrasmall mode vol. of ∼71 nm3 and the ultrashort interaction distance of less than 0.9 nm make the coupling coeff. between a single J-aggregate exciton and the cuboid nanorod as high as ∼41.6 meV, enabling strong light-matter interactions to be achieved at the quantum optics limit in single open plasmonic nanocavities.
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    Li, W.; Zhou, Q.; Zhang, P.; Chen, X.-W. Bright Optical Eigenmode of 1 nm3 Mode Volume. Phys. Rev. Lett. 2021, 126, 257401,  DOI: 10.1103/PhysRevLett.126.257401
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    Bright Optical Eigenmode of 1 nm3 Mode Volume
    Li, Wancong; Zhou, Qiang; Zhang, Pu; Chen, Xue-Wen
    Physical Review Letters (2021), 126 (25), 257401CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode vols. of about 1 nm3. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4x107 times intensity enhancement.
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    Wu, T.; Yan, W.; Lalanne, P. Bright Plasmons with Cubic Nanometer Mode Volumes through Mode Hybridization. ACS Photonics 2021, 8, 307,  DOI: 10.1021/acsphotonics.0c01569
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    Bright Plasmons with Cubic Nanometer Mode Volumes through Mode Hybridization
    Wu, Tong; Yan, Wei; Lalanne, Philippe
    ACS Photonics (2021), 8 (1), 307-314CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    We propose a new interpretation for light confinement in picocavities formed by ultrasmall metallic protuberances inside the gap of metal-insulator-metal nanoresonators. We demonstrate that the protuberances support dark resonances with mode vols. comparable to their geometric vols. and that their brightness can be enhanced by several orders of magnitude when they are strongly coupled with the modes of nanoresonators with nanometric dielec. spacers. With a simple and accurate closed-form expression, we clarify the role of gap plasmons in this coupling. Based on this understanding, we propose a general strategy, exploiting strong coupling to design extremely localized modes with cubic nanometer vols. and so-far unreached brightness.
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    Pscherer, A.; Meierhofer, M.; Wang, D.; Kelkar, H.; Martín-Cano, D.; Utikal, T.; Götzinger, S.; Sandoghdar, V. Single-Molecule Vacuum Rabi Splitting: Four-Wave Mixing and Optical Switching at the Single-Photon Level. Phys. Rev. Lett. 2021, 127, 133603,  DOI: 10.1103/PhysRevLett.127.133603
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    Single-Molecule Vacuum Rabi Splitting: Four-Wave Mixing and Optical Switching at the Single-Photon Level
    Pscherer, Andre; Meierhofer, Manuel; Wang, Daqing; Kelkar, Hrishikesh; Martin-Cano, Diego; Utikal, Tobias; Goetzinger, Stephan; Sandoghdar, Vahid
    Physical Review Letters (2021), 127 (13), 133603CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    A single quantum emitter can possess a very strong intrinsic nonlinearity, but its overall promise for nonlinear effects is hampered by the challenge of efficient coupling to incident photons. Common nonlinear optical materials, on the other hand, are easy to couple to but are bulky, imposing a severe limitation on the miniaturization of photonic systems. In this Letter, we show that a single org. mol. acts as an extremely efficient nonlinear optical element in the strong coupling regime of cavity quantum electrodynamics. We report on single-photon sensitivity in nonlinear signal generation and all-optical switching. Our work promotes the use of mols. for applications such as integrated photonic circuits operating at very low powers.
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    Feist, Johannes; Galego, Javier; Garcia-Vidal, Francisco J.
    ACS Photonics (2018), 5 (1), 205-216CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    A review. The authors present an overview of the general concepts of polaritonic chem. with org. mols., i.e., the manipulation of chem. structure that can be achieved through strong coupling between confined light modes and org. mols. Strong coupling and the assocd. formation of polaritons, hybrid light-matter excitations, lead to energy shifts in such systems that can amt. to a large fraction of the uncoupled transition energy. This has recently been shown to significantly alter the chem. structure of the coupled mols., which opens the possibility to manipulate and control reactions. The authors discuss the current state of theory for describing these changes and present several applications, with a particular focus on the collective effects obsd. when many mols. are involved in strong coupling.
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    Mol. polaritons are the optical excitations which emerge when mol. transitions interact strongly with confined electromagnetic fields. Increasing interest in the hybrid mol.-photonic materials that host these excitations stems from recent observations of their novel and tunable chem. Some of the remarkable functionalities exhibited by polaritons include the ability to induce long-range excitation energy transfer, enhance charge cond., and inhibit or accelerate chem. reactions. In this review, we explain the effective theories of mol. polaritons which form a basis for the interpretation and guidance of expts. at the strong coupling limit. The theor. discussion is illustrated with the anal. of innovative applications of strongly coupled mol.-photonic systems to chem. phenomena of fundamental importance to future technologies.
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    A study of the influence of thin dielec. (LiF) films on the sapphire and rutile surface polaritons was carried out by the attenuated total reflection (ATR) technique and the results indicated that the LO oscillation of the 100-Å LiF film causes a splitting in the min. of the surface polariton ATR reflectivity. The splitting increases with increasing film thickness. In all cases the splitting was obsd. around a frequency lower than the LO frequency of bulk LiF indicating that the LO film frequency may be lower than the LO bulk frequency due to a film structure different from the structure of bulk LiF.
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    Pockrand, I.; Brillante, A.; Moebius, D.
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    Langmuir-Blodgett monolayer assemblies, which contained dye mols., were deposited on Ag films. Exciton-surface plasmon interactions were studied by attenuated total reflection (ATR) spectroscopy. Reflectivity and dispersion curves for plasmon surface polaritons (PSP's) at the metal interface are reported for both angular and wavelength scans. In agreement with theory, dispersion curves from angle scans exhibit a double back bending at the transverse exciton frequency ωT (due to PSP interaction with the in plane component of the dye transition dipole moment) and at the longitudinal frequency ωL (due to PSP interaction with a perpendicular component). Correspondingly, dispersion curves from wavelength scans break into sep. branches at these frequencies.
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    Physical Review Letters (1983), 51 (13), 1175-8CODEN: PRLTAO; ISSN:0031-9007.
    A collection of N Rydberg atoms and a resonant millimeter-wave cavity exchange energy back and forth at a rate 2(d/ℏ)E0√N, where d is the elec. dipole matrix element of the at. transition and E0 the field photon in the cavity. This expt. is a demonstration of self-induced Rabi oscillations in a 2-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of ringings in superradiant emission.
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    Physical Review Letters (1992), 68 (8), 1132-5CODEN: PRLTAO; ISSN:0031-9007.
    An investigation of the spectral response of a small collection of two-state atoms strongly coupled to the field of a high-finesse optical resonator is described for mean no. ‾N ≤ 10 atoms. For weak excitation, a coupling-induced normal-mode splitting is obsd. even for one intracavity atom, representing a direct spectroscopic measurement of the so-called vacuum Rabi splitting for the atom-cavity system.
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    Weisbuch, C.; Nishioka, M.; Ishikawa, A.; Arakawa, Y. Observation of the Coupled Exciton-Photon Mode Splitting in a Semiconductor Quantum Microcavity. Phys. Rev. Lett. 1992, 69, 3314,  DOI: 10.1103/PhysRevLett.69.3314
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    Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity
    Weisbuch, C.; Nishioka, M.; Ishikawa, A.; Arakawa, Y.
    Physical Review Letters (1992), 69 (23), 3314-17CODEN: PRLTAO; ISSN:0031-9007.
    The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splittings when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons and the electromagnetic field of the microcavity. An exciton oscillator strength of 4 × 1012 cm-2 is deduced for 76-Å quantum wells.
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    Houdré, R.; Weisbuch, C.; Stanley, R. P.; Oesterle, U.; Pellandini, P.; Ilegems, M. Measurement of Cavity-Polariton Dispersion Curve from Angle-Resolved Photoluminescence Experiments. Phys. Rev. Lett. 1994, 73, 2043,  DOI: 10.1103/PhysRevLett.73.2043
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    Measurement of cavity-polariton dispersion curve from angle-resolved photoluminescence experiments
    Houdre, R.; Weisbuch, C.; Stanley, R. P.; Eesterle, U.; Pellandini, P.; Ilegems, M.
    Physical Review Letters (1994), 73 (15), 2043-6CODEN: PRLTAO; ISSN:0031-9007.
    We study the photoluminescence of quantum well excitons imbedded in monolithic microcavities. In the strong coupling regime, a coupled-mode situation develops, the cavity polariton. We describe a model of the photoluminescence phenomenon in this regime, which by comparison with expts. enables us to det. the cavity-polariton dispersion curve. An excellent agreement with a theor. model is found.
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    Kelkar, P.; Kozlov, V.; Jeon, H.; Nurmikko, A. V.; Chu, C.-C.; Grillo, D. C.; Han, J.; Hua, C. G.; Gunshor, R. L. Excitons in a II-VI Semiconductor Microcavity in the Strong-Coupling Regime. Phys. Rev. B 1995, 52, R5491,  DOI: 10.1103/PhysRevB.52.R5491
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    Excitons in a II-VI semiconductor microcavity in the strong-coupling regime
    Kelkar, P.; Kozlov, V.; Jeon, H.; Nurmikko, A. V.; Chu, C. C.; Grillo, D. C.; Han, J.; Hua, C. G.; Gunshor, R. L.
    Physical Review B: Condensed Matter (1995), 52 (8), R5491-R5494CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    Microcavities which contained Zn-Cd-Se quantum wells as the resonant medium were fabricated and tested at blue-green wavelengths. The authors saw clear evidence of coupled-mode behavior at the n=1 heavy-hole exciton in both angle and temp. tuning expts., with anticrossing (vacuum-Rabi) splittings approaching 20 meV. The exciton-cavity interaction was consistent with predictions by theory in the strong-coupling regime, and illustrated the impact of the large oscillator strength available in II-VI compds.
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    Lidzey, D. G.; Bradley, D. D. C.; Skolnick, M. S.; Virgili, T.; Walker, S.; Whittaker, D. M. Strong Exciton-Photon Coupling in an Organic Semiconductor Microcavity. Nature 1998, 395, 53,  DOI: 10.1038/25692
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    Strong exciton-photon coupling in an organic semiconductor microcavity
    Lidzey, D. G.; Gradley, D. D. C.; Skolnick, M. S.; Virgili, T.; Walker, S.; Whittaker, D. M.
    Nature (London) (1998), 395 (6697), 53-55CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)
    The modification and control of exciton-photon interactions in semiconductors is of both fundamental and practical interest, being of direct relevance to the design of improved light-emitting diodes, photodetectors and lasers. In a semiconductor microcavity, the confined electromagnetic field modifies the optical transitions of the material. Two distinct types of interaction are possible: weak and strong coupling. In the former perturbative regime, the spectral and spatial distribution of the emission is modified but exciton dynamics are little altered. In the latter case, however, mixing of exciton and photon states occurs leading to strongly modified dynamics. Both types of effect were obsd. in planar microcavity structures in inorg. semiconductor quantum wells and bulk layers. But org. semiconductor microcavities were studied only in the weak-coupling regime. An org. semiconductor microcavity that operates in the strong-coupling regime is reported. Characteristic mixing is seen of the exciton and photon modes (anti-crossing), and a room-temp. vacuum Rabi splitting (an indicator of interaction strength) that is an order of magnitude larger than the previously reported highest values for inorg. semiconductors. The results may lead to new structures and device concepts incorporating hybrid states of org. and inorg. excitons, and suggest that polariton lasing may be possible.
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    (a) Abujetas, D. R.; Feist, J.; García-Vidal, F. J.; Gómez Rivas, J.; Sánchez-Gil, J. A. Strong Coupling between Weakly Guided Semiconductor Nanowire Modes and an Organic Dye. Phys. Rev. B 2019, 99, 205409,  DOI: 10.1103/PhysRevB.99.205409
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    Strong coupling between weakly guided semiconductor nanowire modes and an organic dye
    Abujetas, Diego R.; Feist, Johannes; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez; Sanchez-Gil, Jose A.
    Physical Review B (2019), 99 (20), 205409CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    The light-matter coupling between electromagnetic modes guided by a semiconductor nanowire and excitonic states of mols. localized in its surrounding media is studied from both classical and quantum perspectives, with the aim of describing the strong-coupling regime. Weakly guided modes (bare photonic modes) are found through a classical anal., identifying those lowest-order modes presenting large electromagnetic fields spreading outside the nanowire while preserving their robust guided behavior. Exptl. fits of the dielec. permittivity of an org. dye that exhibits excitonic states are used for realistic scenarios. A quantum model properly confirms through an avoided mode crossing that the strong-coupling regime can be achieved for this configuration, leading to Rabi splitting values above 100 meV. In addn., it is shown that the coupling strength depends on the fraction of energy spread outside the nanowire, rather than on the mode field localization. These results open up a new avenue towards strong-coupling phenomenol. involving propagating modes in nonabsorbing media.
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    (b) Abujetas, D. R.; Feist, J.; García-Vidal, F. J.; Rivas, J. G.; Sánchez-Gil, J. A. Erratum: Strong Coupling between Weakly Guided Semiconductor Nanowire Modes and an Organic Dye. Phys. Rev. B 2020, 102, 239901,  DOI: 10.1103/PhysRevB.102.239901
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    61b
    Erratum: Strong coupling between weakly guided semiconductor nanowire modesand an organic dye [Phys. Rev. B 99, 205409 (2019)]
    Abujetas, Diego R.; Feist, Johannes; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez; Sanchez-Gil, Jose A.
    Physical Review B (2020), 102 (23), 239901/1CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    There is no expanded citation for this reference.
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    Canales, A.; Baranov, D. G.; Antosiewicz, T. J.; Shegai, T. Abundance of Cavity-Free Polaritonic States in Resonant Materials and Nanostructures. J. Chem. Phys. 2021, 154, 024701,  DOI: 10.1063/5.0033352
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    Abundance of cavity-free polaritonic states in resonant materials and nanostructures
    Canales, Adriana; Baranov, Denis G.; Antosiewicz, Tomasz J.; Shegai, Timur
    Journal of Chemical Physics (2021), 154 (2), 024701CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Strong coupling between various kinds of material excitations and optical modes has recently shown potential to modify chem. reaction rates in both excited and ground states. The ground-state modification in chem. reaction rates has usually been reported by coupling a vibrational mode of an org. mol. to the vacuum field of an external optical cavity, such as a planar Fabry-Perot microcavity made of two metallic mirrors. However, using an external cavity to form polaritonic states might (i) limit the scope of possible applications of such systems and (ii) might be unnecessary. Here, we highlight the possibility of using optical modes sustained by materials themselves to self-couple to their own electronic or vibrational resonances. By tracing the roots of the corresponding dispersion relations in the complex frequency plane, we show that electronic and vibrational polaritons are natural eigenstates of bulk and nanostructured resonant materials that require no external cavity. Several concrete examples such as a slab of the excitonic material and a spherical water droplet in vacuum are shown to reach the regime of such cavity-free self-strong coupling. The abundance of cavity-free polaritons in simple and natural structures points at their relevance and potential practical importance for the emerging field of polaritonic chem., exciton transport, and modified material properties. (c) 2021 American Institute of Physics.
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    Barra-Burillo, M.; Muniain, U.; Catalano, S.; Autore, M.; Casanova, F.; Hueso, L. E.; Aizpurua, J.; Esteban, R.; Hillenbrand, R. Microcavity Phonon Polaritons from the Weak to the Ultrastrong Phonon–Photon Coupling Regime. Nat. Commun. 2021, 12, 6206,  DOI: 10.1038/s41467-021-26060-x
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    Microcavity phonon polaritons from the weak to the ultrastrong phonon-photon coupling regime
    Barra-Burillo Maria; Catalano Sara; Autore Marta; Casanova Felix; Hueso Luis E; Muniain Unai; Aizpurua Javier; Esteban Ruben; Casanova Felix; Hueso Luis E; Hillenbrand Rainer; Aizpurua Javier; Esteban Ruben; Hillenbrand Rainer
    Nature communications (2021), 12 (1), 6206 ISSN:.
    Strong coupling between molecular vibrations and microcavity modes has been demonstrated to modify physical and chemical properties of the molecular material. Here, we study the less explored coupling between lattice vibrations (phonons) and microcavity modes. Embedding thin layers of hexagonal boron nitride (hBN) into classical microcavities, we demonstrate the evolution from weak to ultrastrong phonon-photon coupling when the hBN thickness is increased from a few nanometers to a fully filled cavity. Remarkably, strong coupling is achieved for hBN layers as thin as 10 nm. Further, the ultrastrong coupling in fully filled cavities yields a polariton dispersion matching that of phonon polaritons in bulk hBN, highlighting that the maximum light-matter coupling in microcavities is limited to the coupling strength between photons and the bulk material. Tunable cavity phonon polaritons could become a versatile platform for studying how the coupling strength between photons and phonons may modify the properties of polar crystals.
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    Hopfield, J. Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals. Phys. Rev. 1958, 112, 1555,  DOI: 10.1103/PhysRev.112.1555
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    Theory of the contribution of excitons to the complex dielectric constant of crystals
    Hopfield, J. J.
    Physical Review (1958), 112 (), 1555-67CODEN: PHRVAO; ISSN:0031-899X.
    A more complete theory is developed which is better than the semi-classical theory which, while satisfactory for interband transition absorption, is inadequate for exciton state light absorption. Excitons are approx. bosons, and, in interaction with the electromagnetic field, their field assumes the role of the classical polarization field. The eigenstates of the crystal-field system are photon-exciton mixtures. The ordinary one-quantum optical lifetime of an excitation is infinite; absorption occurs only on introduction of 3-body processes. The theory includes local field effects, leading to Lorentz local field correction when it is applicable. A Smakula equation is derived for the oscillator strength in terms of the integrated absorption const.
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    Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J. Strong Coupling between Surface Plasmons and Excitons in an Organic Semiconductor. Phys. Rev. Lett. 2004, 93, 036404,  DOI: 10.1103/PhysRevLett.93.036404
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    Strong Coupling between Surface Plasmons and Excitons in an Organic Semiconductor
    Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J.
    Physical Review Letters (2004), 93 (3), 036404/1-036404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The authors report on the observation of a strong coupling between a surface plasmon and an exciton. Reflectometry expts. were performed on an org. semiconductor, namely, cyanide dye J aggregates, deposited on a Ag film. The dispersion lines present an anticrossing that is the signature of a strong plasmon-exciton coupling. Mixed states are formed in a similar way as microcavities polaritons. The Rabi splitting characteristic of this coupling reaches 180 meV at room temp. The emission of the low energy plasmon-exciton mixed state was obsd. and is largely shifted from the uncoupled emission.
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    Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W. Strong Coupling between Surface Plasmon-Polaritons and Organic Molecules in Subwavelength Hole Arrays. Phys. Rev. B 2005, 71, 035424,  DOI: 10.1103/PhysRevB.71.035424
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    Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays
    Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W.
    Physical Review B: Condensed Matter and Materials Physics (2005), 71 (3), 035424/1-035424/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    The interaction of a J-aggregate and surface plasmon polariton modes of a subwavelength hole array were studied. By measuring the effects of hole array period, angular dispersion and concn. of the J-aggregate on the transmission of the array, the existence of a strong coupling regime is demonstrated with a Rabi splitting of 250 meV. This large splitting is explained by the high oscillator strength of the dye and by the high local field amplitudes generated by surface plasmons of the metallic structure.
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    Zengin, G.; Wersäll, M.; Nilsson, S.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Realizing Strong Light-Matter Interactions between Single-Nanoparticle Plasmons and Molecular Excitons at Ambient Conditions. Phys. Rev. Lett. 2015, 114, 157401,  DOI: 10.1103/PhysRevLett.114.157401
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    Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions
    Zengin, Gulis; Wersaell, Martin; Nilsson, Sara; Antosiewicz, Tomasz J.; Kaell, Mikael; Shegai, Timur
    Physical Review Letters (2015), 114 (15), 157401/1-157401/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Realizing strong light-matter interactions between individual two-level systems and resonating cavities in at. and solid state systems opens up possibilities to study optical nonlinearities on a single-photon level, which can be useful for future quantum information processing networks. However, these efforts have been hampered by unfavorable exptl. conditions, such as cryogenic temps. and ultrahigh vacuum, required to study such systems and phenomena. Although several attempts to realize strong light-matter interactions at room temp. using plasmon resonances have been made, successful realizations on the single-nanoparticle level are still lacking. Here, we demonstrate the strong coupling between plasmons confined within a single silver nanoprism and excitons in moleculari J aggregates at ambient conditions. Our findings show that deep subwavelength mode vols. V together with quality factors Q that are reasonably high for plasmonic nanostructures result in a strong-coupling figure of merit- Q/√V as high as ∼6 × 103 μm-3/2, a value comparable to state-of-the-art photonic crystal and microring resonator cavities. This suggests that plasmonic nanocavities, and specifically silver nanoprisms, can be used for room temp. quantum optics.
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    Rodriguez, S. R. K.; Feist, J.; Verschuuren, M. A.; García Vidal, F. J.; Gómez Rivas, J. Thermalization and Cooling of Plasmon-Exciton Polaritons: Towards Quantum Condensation. Phys. Rev. Lett. 2013, 111, 166802,  DOI: 10.1103/PhysRevLett.111.166802
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    Thermalization and cooling of plasmon-exciton polaritons: towards quantum condensation
    Rodriguez, S. R. K.; Feist, J.; Verschuuren, M. A.; Vidal, F. J. Garcia; Rivas, J. Gomez
    Physical Review Letters (2013), 111 (16), 166802/1-166802/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We present indications of thermalization and cooling of quasiparticles, a precursor for quantum condensation, in a plasmonic nanoparticle array. We investigate a periodic array of metallic nanorods covered by a polymer layer doped with an org. dye at room temp. Surface lattice resonances of the array-hybridized plasmonic-photonic modes-couple strongly to excitons in the dye, and bosonic quasiparticles which we call plasmon-exciton polaritons (PEPs) are formed. By increasing the PEP d. through optical pumping, we observe thermalization and cooling of the strongly coupled PEP band in the light emission dispersion diagram. For increased pumping, we observe satn. of the strong coupling and emission in a new weakly coupled band, which again shows signatures of thermalization and cooling.
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    Frisk Kockum, A.; Miranowicz, A.; De Liberato, S.; Savasta, S.; Nori, F. Ultrastrong Coupling between Light and Matter. Nat. Rev. Phys. 2019, 1, 19,  DOI: 10.1038/s42254-018-0006-2
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    Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Reversible Switching of Ultrastrong Light-Molecule Coupling. Phys. Rev. Lett. 2011, 106, 196405,  DOI: 10.1103/PhysRevLett.106.196405
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    Reversible switching of ultrastrong light-molecule coupling
    Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W.
    Physical Review Letters (2011), 106 (19), 196405/1-196405/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The authors demonstrate that photochromic mols. enable switching from the weak- to ultrastrong-coupling regime reversibly, by using all-optical control. This switch is achieved by photochem. induced conformational changes in the mol. Remarkably, a Rabi splitting of 700 meV is measured at room temp., corresponding to 32% of the mol. transition energy. A similar coupling strength is demonstrated in a plasmonic structure. Such systems present a unique combination of coupling strength and functional capacities.
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    Gambino, S.; Mazzeo, M.; Genco, A.; Di Stefano, O.; Savasta, S.; Patanè, S.; Ballarini, D.; Mangione, F.; Lerario, G.; Sanvitto, D.; Gigli, G. Exploring Light–Matter Interaction Phenomena under Ultrastrong Coupling Regime. ACS Photonics 2014, 1, 1042,  DOI: 10.1021/ph500266d
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    Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime
    Gambino, Salvatore; Mazzeo, Marco; Genco, Armando; Di Stefano, Omar; Savasta, Salvatore; Patane, Salvatore; Ballarini, Dario; Mangione, Federica; Lerario, Giovanni; Sanvitto, Daniele; Gigli, Giuseppe
    ACS Photonics (2014), 1 (10), 1042-1048CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Exciton-polaritons are bosonic quasiparticles that arise from the normal mode splitting of photons in a microcavity and excitons in a semiconductor material. One of the most intriguing extensions of such a light-matter interaction is the so-called ultrastrong coupling regime. It is achieved when the Rabi frequency (ΩR, the energy exchange rate between the emitter and the resonant photonic mode) reaches a considerable fraction of the emitter transition frequency, ω0. A Rabi energy splitting (2ℏΩR) of 1.12 eV is reported, and values of the coupling ratio (2ΩR/ω0) ≤0.6-fold the material band gap in org. semiconductor microcavities and ≤0.5-fold in monolithic heterostructure org. light-emitting diodes working at room temp. are recorded. With such a large coupling strength it is possible to undress the exciton homogeneous linewidth from its inhomogeneous broadening, which allows for an unprecedented narrow emission line (below the cavity finesse) for such org. LEDs. The latter can be exploited for the realization of novel monochromatic sources and near-IR org. emitting devices.
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    Eizner, E.; Brodeur, J.; Barachati, F.; Sridharan, A.; Kéna-Cohen, S. Organic Photodiodes with an Extended Responsivity Using Ultrastrong Light–Matter Coupling. ACS Photonics 2018, 5, 2921,  DOI: 10.1021/acsphotonics.8b00254
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    Organic Photodiodes with an Extended Responsivity Using Ultrastrong Light-Matter Coupling
    Eizner, Elad; Brodeur, Julien; Barachati, Fabio; Sridharan, Aravindan; Kena-Cohen, Stephane
    ACS Photonics (2018), 5 (7), 2921-2927CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    In org. photodiodes (OPDs), light is absorbed by excitons that dissoc. to generate photocurrent. Here, we demonstrate a novel type of OPD in which light is absorbed by polaritons, hybrid light-matter states. We demonstrate polariton OPDs operating in the ultrastrong coupling regime at visible and IR wavelengths. These devices can be engineered to show narrow responsivity with a very weak angle-dependence. More importantly, they can be tuned to operate in a spectral range outside that of the bare exciton absorption. Remarkably, we show that the responsivity of a polariton OPD can be pushed to near-IR wavelengths, where few org. absorbers are available, with external quantum efficiencies exceeding those of our control OPD.
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    Le Roux, F.; Taylor, R. A.; Bradley, D. D. C. Enhanced and Polarization-Dependent Coupling for Photoaligned Liquid Crystalline Conjugated Polymer Microcavities. ACS Photonics 2020, 7, 746,  DOI: 10.1021/acsphotonics.9b01596
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    Enhanced and Polarization-Dependent Coupling for Photoaligned Liquid Crystalline Conjugated Polymer Microcavities
    Le Roux, Florian; Taylor, Robert A.; Bradley, Donal D. C.
    ACS Photonics (2020), 7 (3), 746-758CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    The fabrication and optical characterization of org. microcavities contg. liq. cryst. conjugated polymers (LCCPs)-poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT), poly(9,9-dioctylfluorene) (PFO), and poly(9,9-dihexylfluorene-co-bithiophene) (F6T2)-aligned on top of a thin transparent sulfuric dye 1 (SD1) photoalignment layer are reported. The optical consts. of the aligned films were extd. using variable-angle ellipsometry, and metallic microcavities in which the ultrastrong coupling regime is manifest both for the aligned and nonaligned LCCPs were fabricated. Transition dipole moment alignment enables a systematic increase in the interaction strength, with unprecedented solid-state Rabi splittings of up to 1.80 eV, the 1st to reach energies comparable to those in the visible spectrum. With an optical gap of 2.79 eV for F6T2 this gives the highest-to-date org. microcavity coupling ratio, 65%. The coupling strength is polarization-dependent with bright polariton luminescence for TE polarization parallel to the polymer chains and either no emission or weakly coupled emission from the corresponding TM polarization.
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    Litinskaya, M.; Reineker, P.; Agranovich, V. M. Fast Polariton Relaxation in Strongly Coupled Organic Microcavities. J. Lumin. 2004, 110, 364,  DOI: 10.1016/j.jlumin.2004.08.033
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    Fast polariton relaxation in strongly coupled organic microcavities
    Litinskaya, M.; Reineker, P.; Agranovich, V. M.
    Journal of Luminescence (2004), 110 (4), 364-372CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
    The authors consider the regime of strong light-matter coupling in an org. microcavity, where large Rabi splitting can be achieved. As was shown, the excitation spectrum of such a structure, besides coherent polaritonic states, contains a no. of strongly spatially localized incoherent excited states. These states form the majority of the excited states of the microcavity and probably play the decisive role in the relaxation dynamics of the excitations in the microcavity. The authors consider the nonradiative transition from an incoherent excited state into one of the coherent states of the lower polaritonic branch accompanied by emission of a high-energy intramol. phonon. This process may det. the lifetime of incoherent excited states in the microcavity. This observation may be important in the discussion of pump-probe expts. with short pulses. This process may also play an important role for the population of the lowest energy states in org. microcavities, and hence in the problem of condensation of cavity polaritons.
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    Coles, D. M.; Michetti, P.; Clark, C.; Tsoi, W. C.; Adawi, A. M.; Kim, J.-S.; Lidzey, D. G. Vibrationally Assisted Polariton-Relaxation Processes in Strongly Coupled Organic-Semiconductor Microcavities. Adv. Funct. Mater. 2011, 21, 3691,  DOI: 10.1002/adfm.201100756
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    Vibrationally Assisted Polariton-Relaxation Processes in Strongly Coupled Organic-Semiconductor Microcavities
    Coles, David M.; Michetti, Paolo; Clark, Caspar; Tsoi, Wing Chung; Adawi, Ali M.; Kim, Ji-Seon; Lidzey, David G.
    Advanced Functional Materials (2011), 21 (19), 3691-3696CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
    If a semiconductor with an electronic transition that approximates a 2-level system is placed within an optical cavity, strong coupling can occur between the confined photons and the semiconductor excitons. This coupling can gave cavity polariton states that are a coherent superposition of light and matter. If the material in the cavity is an org. semiconductor, it was predicted that interactions between Frenkel excitons, polaritons, and mol. vibrational modes will have a profound role in defining the overall relaxation dynamics of the system. Here, using temp.-dependent spectroscopy on a microcavity contg. a J-aggregated cyanine dye, a spectrum of localized vibrational modes (identified by Raman scattering) enhances the population of certain polaritonic modes by acting as an energy-loss channel to the excitons as they undergo scattering. Work demonstrates that simultaneous control of the optical properties of a cavity and the vibrational structure of a mol. dye could promote the efficient population of k = 0 polariton states, from which lasing and other cooperative phenomena may occur.
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    Ramezani, M.; Halpin, A.; Fernández-Domínguez, A. I.; Feist, J.; Rodriguez, S. R.-K.; Garcia-Vidal, F. J.; Gómez Rivas, J. Plasmon-Exciton-Polariton Lasing. Optica 2017, 4, 31,  DOI: 10.1364/OPTICA.4.000031
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    Plasmon-exciton-polariton lasing
    Ramezani, Mohammad; Halpin, Alexei; Fernandez-Dominguez, Antonio I.; Feist, Johannes; Rodriguez, Rahimzadeh-Kalaleh; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez
    Optica (2017), 4 (1), 31-37CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
    Metallic nanostructures provide a toolkit for the generation of coherent light below the diffraction limit. Plasmonic-based lasing relies on the population inversion of emitters (such as org. fluorophores) along with feedback provided by plasmonic resonances. In this regime, known as weak light-matter coupling, the radiative characteristics of the system can be described by the Purcell effect. Strong light-matter coupling between the mol. excitons and electromagnetic field generated by the plasmonic structures leads to the formation of hybrid quasi-particles known as plasmon-exciton-polaritons (PEPs). Due to the bosonic character of these quasi-particles, exciton-polariton condensation can lead to laser-like emission at much lower threshold powers than in conventional photon lasers. Here, we observe PEP lasing through a dark plasmonic mode in an array of metallic nanoparticles with a low threshold in an optically pumped org. system. Interestingly, the threshold power of the lasing is reduced by increasing the degree of light - matter coupling in spite of the degrdn. of the quantum efficiency of the active material, highlighting the ultrafast dynamic responsible for the lasing, i.e., stimulated scattering. These results demonstrate a unique room-temp. platform for exploring the physics of exciton-polaritons in an open-cavity architecture and pave the road toward the integration of this on-chip lasing device with the current photonics and active metamaterial planar technologies.
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    Keeling, J.; Kéna-Cohen, S. Bose–Einstein Condensation of Exciton-Polaritons in Organic Microcavities. Annu. Rev. Phys. Chem. 2020, 71, 435,  DOI: 10.1146/annurev-physchem-010920-102509
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    Bose-Einstein Condensation of Exciton-Polaritons in Organic Microcavities
    Keeling, Jonathan; Kena-Cohen, Stephane
    Annual Review of Physical Chemistry (2020), 71 (), 435-459CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
    A review. Bose-Einstein condensation describes the macroscopic occupation of a single-particle mode: the condensate. This state can in principle be realized for any particles obeying Bose-Einstein statistics; this includes hybrid light-matter excitations known as polaritons. Some of the unique optoelectronic properties of org. mols. make them esp. well suited for the realization of polariton condensates. Exciton-polaritons form in optical cavities when electronic excitations couple collectively to the optical mode supported by the cavity. These polaritons obey bosonic statistics at moderate densities, are stable at room temp., and have been obsd. to form a condensed or lasing state. Understanding the optimal conditions for polariton condensation requires careful modeling of the complex photophysics of org. mols. In this article, we introduce the basic physics of exciton-polaritons and condensation and review expts. demonstrating polariton condensation in mol. materials.
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    Garcia-Vidal, F. J.; Feist, J. Long-Distance Operator for Energy Transfer. Science 2017, 357, 1357,  DOI: 10.1126/science.aao4268
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    Long-distance operator for energy transfer
    Garcia-Vidal, Francisco J.; Feist, Johannes
    Science (Washington, DC, United States) (2017), 357 (6358), 1357-1358CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    There is no expanded citation for this reference.
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    Du, M.; Martínez-Martínez, L.; Ribeiro, R.; Hu, Z.; Menon, V.; Yuen-Zhou, J. Theory for Polariton-Assisted Remote Energy Transfer. Chem. Sci. 2018, 9, 6659,  DOI: 10.1039/C8SC00171E
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    Theory for polariton-assisted remote energy transfer
    Du, Matthew; Martinez-Martinez, Luis A.; Ribeiro, Raphael F.; Hu, Zixuan; Menon, Vinod M.; Yuen-Zhou, Joel
    Chemical Science (2018), 9 (32), 6659-6669CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chem. reactivity of mol. systems. Recent expts. have demonstrated remarkable distance-independent long-range energy transfer between mols. strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect". This theor. study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between mol. systems.
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    Sáez-Blázquez, R.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Organic Polaritons Enable Local Vibrations to Drive Long-Range Energy Transfer. Phys. Rev. B 2018, 97, 241407R
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    Organic polaritons enable local vibrations to drive long-range energy transfer
    Saez-Blazquez, R.; Feist, J.; Fernandez-Dominguez, A. I.; Garcia-Vidal, F. J.
    Physical Review B (2018), 97 (24), 241407/1-241407/5CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    Long -range energy transfer in org. mols. has been exptl. obtained by strongly coupling their electronic excitations to a confined electromagnetic cavity mode. Here, we shed light into the polariton-mediated mechanism behind this process for different configurations: donor and acceptor mols. either intermixed or phys. sepd.We numerically address the phenomenon by means of Bloch-Redfield theory, which allows us to reproduce the effect of complex vibrational reservoirs characteristic of org. mols. Our findings reveal the key role played by the middle polariton as the nonlocal intermediary in the transmission of excitations from donor to acceptor mols. We also provide anal. insights on the key phys. magnitudes that help to optimize the efficiency of the long-range energy transfer.
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    Georgiou, K.; Jayaprakash, R.; Othonos, A.; Lidzey, D. G. Ultralong-Range Polariton-Assisted Energy Transfer in Organic Microcavities. Angew. Chem., Int. Ed. 2021, 60, 16661,  DOI: 10.1002/anie.202105442
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    Ultralong-Range Polariton-Assisted Energy Transfer in Organic Microcavities
    Georgiou, Kyriacos; Jayaprakash, Rahul; Othonos, Andreas; Lidzey, David G.
    Angewandte Chemie, International Edition (2021), 60 (30), 16661-16667CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Non-radiative energy transfer between spatially-sepd. mols. in a microcavity can occur when an excitonic state on both mols. are strongly-coupled to the same optical mode, forming so-called "hybrid" polaritons. Such energy transfer has previously been explored when thin-films of different mols. are relatively closely spaced (≈100 nm). In this manuscript, we explore strong-coupled microcavities in which thin-films of two J-aggregated mol. dyes were sepd. by a spacer layer having a thickness of up to 2μm. Here, strong light-matter coupling and hybridization between the excitonic transition is identified using white-light reflectivity and photoluminescence emission. We use steady-state spectroscopy to demonstrate polariton-mediated energy transfer between such coupled states over "mesoscopic distances", with this process being enhanced compared to non-cavity control structures.
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    Satapathy, S.; Khatoniar, M.; Parappuram, D. K.; Liu, B.; John, G.; Feist, J.; Garcia-Vidal, F. J.; Menon, V. M. Selective Isomer Emission via Funneling of Exciton Polaritons. Sci. Adv. 2021, 7, eabj0997,  DOI: 10.1126/sciadv.abj0997
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    Sáez-Blázquez, R.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Enhancing Photon Correlations through Plasmonic Strong Coupling. Optica 2017, 4, 1363,  DOI: 10.1364/OPTICA.4.001363
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    Enhancing photon correlations through plasmonic strong coupling
    Saez-Blazquez, R.; Feist, J.; Fernandez-Dominguez, A. I.; Garcia-Vidal, F. J.
    Optica (2017), 4 (11), 1363-1367CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
    There is an increasing scientific and technol. interest in the design and implementation of nanoscale sources of quantum light. Here, we investigate the quantum statistics of the light scattered from a plasmonic nanocavity coupled to a mesoscopic ensemble of emitters under low coherent pumping. We present an anal. description of the intensity correlations taking place in these systems and unveil the fingerprint of plasmon-exciton-polaritons in them. Our findings reveal that plasmonic cavities are able to retain and enhance excitonic nonlinearities, even when the no. of emitters is large. This makes plasmonic strong coupling a promising route for generating nonclassical light beyond the single-emitter level.
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    Sáez-Blázquez, R.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Photon Statistics in Collective Strong Coupling: Nanocavities and Microcavities. Phys. Rev. A 2018, 98, 013839,  DOI: 10.1103/PhysRevA.98.013839
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    Photon statistics in collective strong coupling: nanocavities and microcavities
    Saez-Blazquez, R.; Feist, J.; Garcia-Vidal, F. J.; Fernandez-Dominguez, A. I.
    Physical Review A (2018), 98 (1), 013839CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
    There exists a growing interest in the properties of the light generated by hybrid systems involving a mesoscopic no. of emitters as a means of providing macroscopic quantum light sources. In this work, the quantum correlations of the light emitted by a collection of emitters coupled to a generic optical cavity are studied theor. using an effective Hamiltonian approach. Starting from the single-emitter level, we analyze the persistence of photon antibunching as the ensemble size increases. Not only is the photon blockade effect identifiable, but photon antibunching originated from destructive interference processes, the so-called unconventional antibunching, is also present. We study the dependence of these two types of neg. correlations on the spectral detuning between cavity and emitters, as well as its evolution as the time delay between photon detections increases. Throughout this work, the performance of plasmonic nanocavities and dielec. microcavities is compared: despite the distinct energy scales and the differences introduced by their resp. open and closed character, the bunching and antibunching phenomenol. presents remarkable similarities in both types of cavities.
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    Li, R.-Q.; Hernángomez-Pérez, D.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Transformation Optics Approach to Plasmon-Exciton Strong Coupling in Nanocavities. Phys. Rev. Lett. 2016, 117, 107401,  DOI: 10.1103/PhysRevLett.117.107401
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    Transformation optics approach to plasmon-exciton strong coupling in nanocavities
    Li, Rui-Qi; Hernangomez-Perez, D.; Garcia-Vidal, F. J.; Fernandez-Dorninguez, A. I.
    Physical Review Letters (2016), 117 (10), 107401/1-107401/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We investigate the conditions yielding plasmon-exciton strong coupling at the single emitter level in the gap between two metal nanoparticles. Inspired by transformation optics ideas, a quasianal. approach is developed that makes possible a thorough exploration of this hybrid system incorporating the full richness of its plasmonic spectrum. This allows us to reveal that by placing the emitter away from the cavity center, its coupling to multipolar dark modes of both even and odd parity increases remarkably. This way, reversible dynamics in the population of the quantum emitter takes place in feasible implementations of this archetypal nanocavity.
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    Li, R.-Q.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Plasmon-Exciton Coupling in Symmetry-Broken Nanocavities. ACS Photonics 2018, 5, 177,  DOI: 10.1021/acsphotonics.7b00616
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    Plasmon-Exciton Coupling in Symmetry-Broken Nanocavities
    Li, Rui-Qi; Garcia-Vidal, F. J.; Fernandez-Dominguez, A. I.
    ACS Photonics (2018), 5 (1), 177-185CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    The onset of strong coupling in the temporal dynamics of the exciton population at a single emitter interacting with symmetry-broken plasmonic nanocavities was studied. These structures consist in pairs of metallodielec. elements sepd. by a nanometric gap, with different degrees of asymmetry imposed on their geometric or material characteristics. To describe the emergence of plasmon-exciton-polaritons in these systems, the authors extend and generalize a transformation optics method previously applied to dimers of identical particles. This approach provides a natural decompn. of the spectral d. in terms of a well-defined set of plasmonic resonances, as well as an insightful description of the coupling strength dependence on the emitter position. On the 1 hand, the authors shed light into the low sensitivity of plasmon-exciton interactions to geometric asymmetry in cavities such as nanoparticle-on-a-mirror configurations. A more complex spatial and spectral dependence of the strong-coupling phenomenol. takes place in systems with material asymmetry, such as 2-metal and metal-dielec. dimers.
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    Huidobro, P. A.; Fernández-Domínguez, A. I. Transformation Optics for Plasmonics: From Metasurfaces to Excitonic Strong Coupling. Comptes Rendus Phys. 2020, 21, 389,  DOI: 10.5802/crphys.22
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    Transformation optics for plasmonics: from metasurfaces to excitonic strong coupling
    Huidobro, Paloma A.; Fernandez-Dominguez, Antonio I.
    Comptes Rendus Physique (2020), 21 (4-5), 389-408CODEN: CRPOBN; ISSN:1878-1535. (Academie des Sciences)
    A review. We review the latest theor. advances in the application of the framework of Transformation Optics for the anal. description of deeply sub-wavelength electromagnetic phenomena. First, we present a general description of the technique, together with its usual exploitation for metamaterial conception and optimization in different areas of wave physics. Next, we discuss in detail the design of plasmonic metasurfaces, including the description of singular geometries which allow for broadband absorption in ultrathin platforms. Finally, we discuss the quasi-anal. treatment of plasmon-exciton strong coupling in nanocavities at the single emitter level.
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    Cuartero-González, A.; Fernández-Domínguez, A. I. Light-Forbidden Transitions in Plasmon-Emitter Interactions beyond the Weak Coupling Regime. ACS Photonics 2018, 5, 3415,  DOI: 10.1021/acsphotonics.8b00678
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    Light-Forbidden Transitions in Plasmon-Emitter Interactions beyond the Weak Coupling Regime
    Cuartero-Gonzalez, A.; Fernandez-Dominguez, A. I.
    ACS Photonics (2018), 5 (8), 3415-3420CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    We investigate the impact of light-forbidden exciton transitions in plasmon-emitter interactions beyond the weak coupling regime. We consider a V-type quantum emitter, with dipolar and quadrupolar excited states, placed at the subnanometric gap of a particle-on-a-mirror metallic cavity. We present a fully anal. description of the near-field population dynamics and far-field scattering spectrum of the hybrid system. Our approach enables us to reveal two realistic system configurations in which the dipole-inactive exciton alters significantly and in completely opposite ways the Purcell enhancement and Rabi splitting phenomenol., effectively enlarging or reducing the emitter lifetime and generating or removing spectral features in the cavity cross section.
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    Neuman, T.; Esteban, R.; Casanova, D.; García-Vidal, F. J.; Aizpurua, J. Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation. Nano Lett. 2018, 18, 2358,  DOI: 10.1021/acs.nanolett.7b05297
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    Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation
    Neuman, Tomas; Esteban, Ruben; Casanova, David; Garcia-Vidal, Francisco J.; Aizpurua, Javier
    Nano Letters (2018), 18 (4), 2358-2364CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    As the size of a mol. emitter becomes comparable to the dimensions of a nearby optical resonator, the std. approach that considers the emitter to be a point-like dipole breaks down. By adoption of a quantum description of the electronic transitions of org. mol. emitters, coupled to a plasmonic electromagnetic field, we are able to accurately calc. the position-dependent coupling strength between a plasmon and an emitter. The spatial distribution of excitonic and photonic quantum states is found to be a key aspect in detg. the dynamics of mol. emission in ultrasmall cavities both in the weak and strong coupling regimes. Moreover, we show that the extreme localization of plasmonic fields leads to the selection rule breaking of mol. excitations.
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    Fregoni, J.; Haugland, T. S.; Pipolo, S.; Giovannini, T.; Koch, H.; Corni, S. Strong Coupling between Localized Surface Plasmons and Molecules by Coupled Cluster Theory. Nano Lett. 2021, 21, 6664,  DOI: 10.1021/acs.nanolett.1c02162
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    Strong Coupling between Localized Surface Plasmons and Molecules by Coupled Cluster Theory
    Fregoni, Jacopo; Haugland, Tor S.; Pipolo, Silvio; Giovannini, Tommaso; Koch, Henrik; Corni, Stefano
    Nano Letters (2021), 21 (15), 6664-6670CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Plasmonic nanocavities enable the confinement of mols. and electromagnetic fields within nanometric vols. As a consequence, the mols. experience a remarkably strong interaction with the electromagnetic field to such an extent that the quantum states of the system become hybrids between light and matter: polaritons. Here, we present a nonperturbative method to simulate the emerging properties of such polaritons: it combines a high-level quantum chem. description of the mol. with a quantized description of the localized surface plasmons in the nanocavity. We apply the method to mols. of realistic complexity in a typical plasmonic nanocavity, featuring also a subnanometric asperity (picocavity). Our results disclose the effects of the mutual polarization and correlation of plasmons and mol. excitations, disregarded so far. They also quantify to what extent the mol. charge d. can be manipulated by nanocavities and stand as benchmarks to guide the development of methods for mol. polaritonics.
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    Cuartero-González, A.; Manjavacas, A.; Fernández-Domínguez, A. I. Distortion of the Local Density of States in a Plasmonic Cavity by a Quantum Emitter. New J. Phys. 2021, 23, 073011,  DOI: 10.1088/1367-2630/ac0199
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    Distortion of the local density of states in a plasmonic cavity by a quantum emitter
    Cuartero-Gonzalez, Alvaro; Manjavacas, Alejandro; Fernandez-Dominguez, Antonio I.
    New Journal of Physics (2021), 23 (July), 073011CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
    We investigate how the local d. of states in a plasmonic cavity changes due to the presence of a distorting quantum emitter. To this end, we use first-order scattering theory involving electromagnetic Green's function tensors for the bare cavity connecting the positions of the emitter that distorts the d. of states and the one that probes it. The confined, quasistatic character of the plasmonic modes enables us to write the d. of states as a Lorentzian sum. This way, we identify three different mechanisms behind the asym. spectral features emerging due to the emitter distortion: the modification of the plasmonic coupling to the probing emitter, the emergence of modal-like quadratic contributions and the absorption by the distorting emitter. We apply our theory to the study of two different systems (nanoparticle-on-mirror and asym. bow-tie-like geometries) to show the generality of our approach, whose validity is tested against numerical simulations. Finally, we provide an interpretation of our results in terms of a Hamiltonian model describing the distorted cavity.
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    Cuartero-González, A.; Fernández-Domínguez, A. I. Dipolar and Quadrupolar Excitons Coupled to a Nanoparticle-on-Mirror Cavity. Phys. Rev. B 2020, 101, 035403,  DOI: 10.1103/PhysRevB.101.035403
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    Dipolar and quadrupolar excitons coupled to a nanoparticle-on-mirror cavity
    Cuartero-Gonzalez, A.; Fernandez-Dominguez, A. I.
    Physical Review B (2020), 101 (3), 035403CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    We investigate plasmon-emitter interactions in a nanoparticle-on-mirror cavity. We consider two different sorts of emitters: Those that sustain dipolar transitions and those hosting only quadrupolar, dipole-inactive excitons. By means of a fully anal. two-dimensional transformation optics approach, we calc. the light-matter coupling strengths for the full plasmonic spectrum supported by the nanocavity. We reveal the impact of finite-size effects in the exciton charge distribution and describe the population dynamics in a spontaneous emission configuration. Pushing our model beyond the quasistatic approxn., we ext. the plasmonic dipole moments, which enables us to calc. the far-field scattering spectrum of the hybrid plasmon-emitter system. Our findings, tested against fully numerical simulations, reveal the similarities and differences between the light-matter coupling phenomenol. for bright and dark excitons in nanocavities.
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    Sáez-Blázquez, R.; Cuartero-González, Á.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities. Nano Lett. 2022, 22, 2365,  DOI: 10.1021/acs.nanolett.1c04872
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    Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities
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    Nano Letters (2022), 22 (6), 2365-2373CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    We investigate the quantum-optical properties of the light emitted by a nanoparticle-on-mirror cavity filled with a single quantum emitter. Inspired by recent expts., we model a dark-field setup and explore the photon statistics of the scattered light under grazing laser illumination. Exploiting anal. solns. to Maxwell's equations, we quantize the nanophotonic cavity fields and describe the formation of plasmon-exciton polaritons (or plexcitons) in the system. This way, we reveal that the rich plasmonic spectrum of the nanocavity offers unexplored mechanisms for nonclassical light generation that are more efficient than the resonant interaction between the emitter natural transition and the brightest optical mode. Specifically, we find three different sample configurations in which strongly antibunched light is produced. Finally, we illustrate the power of our approach by showing that the introduction of a second emitter in the platform can enhance photon correlations further.
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    Kulkarni, V.; Manjavacas, A. Quantum Effects in Charge Transfer Plasmons. ACS Photonics 2015, 2, 987,  DOI: 10.1021/acsphotonics.5b00246
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    Quantum Effects in Charge Transfer Plasmons
    Kulkarni, Vikram; Manjavacas, Alejandro
    ACS Photonics (2015), 2 (7), 987-992CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Metallic nanoparticles placed in close proximity support strong localized surface plasmon resonances. One such resonance, known as the charge transfer plasmon, involves the phys. transfer of electrons between the nanoparticles and, thus, exists only in dimers bridged with conductive junctions. Here we analyze the quantum effects assocd. with these type of plasmon modes by studying the optical response of a metallic dimer bridged with a two-level system. We find that the charge transfer plasmons are obsd. in the absorption spectrum only when one of the energy levels of the two-level system is resonant with the Fermi level of the nanoparticles. Furthermore, we explicitly show that, for the resonant configuration, the conductance of the junction reaches a value equal to one quantum of conductance, 2e2/h. Our results establish a connection between the optical response of plasmonic nanostructures and quantum transport phenomena, thus bringing a new perspective to quantum plasmonics.
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    Babaze, A.; Esteban, R.; Borisov, A. G.; Aizpurua, J. Electronic Exciton–Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture. Nano Lett. 2021, 21, 8466,  DOI: 10.1021/acs.nanolett.1c03202
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    Electronic Exciton-Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture
    Babaze, Antton; Esteban, Ruben; Borisov, Andrei G.; Aizpurua, Javier
    Nano Letters (2021), 21 (19), 8466-8473CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theor. addressed within the frameworks of classical electrodynamics and the time-dependent d. functional theory (TDDFT). A fully quantum many-body description of the electron dynamics within TDDFT allows for analyzing the effect of electronic coupling between the emitter and the nanoantenna, usually ignored in classical descriptions of the optical response. We show that the hybridization between the electronic states of the quantum emitter and those of the metallic nanoparticles strongly modifies the energy, the width, and the very existence of the optical resonances of the coupled system. We thus conclude that the application of a quantum many-body treatment that correctly addresses charge-transfer processes between the emitter and the nanoantenna is crucial to address complex electronic processes involving plasmon-exciton interactions directly impacting optoelectronic applications.
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    Sánchez-Barquilla, M.; García-Vidal, F. J.; Fernández-Domínguez, A. I.; Feist, J. Few-Mode Field Quantization for Multiple Emitters. arXiv [physics.optics] 2112.10581, (accessed 2021–12–20).
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    Dung, H. T.; Knöll, L.; Welsch, D.-G. Resonant Dipole-Dipole Interaction in the Presence of Dispersing and Absorbing Surroundings. Phys. Rev. A 2002, 66, 063810,  DOI: 10.1103/PhysRevA.66.063810
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    Resonant dipole-dipole interaction in the presence of dispersing and absorbing surroundings
    Dung, Ho Trung; Knoll, Ludwig; Welsch, Dirk-Gunnar
    Physical Review A: Atomic, Molecular, and Optical Physics (2002), 66 (6), 063810/1-063810/16CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
    Within the framework of quantization of the macroscopic electromagnetic field, equations of motion and an effective Hamiltonian for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual- and real-photon exchange in the energy transfer between the atoms. In particular, for weak atom-field interaction there is a time window, where the energy transfer follows a rate regime of the type obtained by ordinary 2nd-order perturbation theory. Finally, the resonant dipole-dipole interaction can change the singlet line of the emitted light to a doublet spectrum for weak atom-field interaction and the doublet spectrum to a triplet spectrum for strong atom-field interaction.
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    Sánchez-Barquilla, M.; Feist, J. Accurate Truncations of Chain Mapping Models for Open Quantum Systems. Nanomaterials 2021, 11, 2104,  DOI: 10.3390/nano11082104
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    Accurate Truncations of Chain Mapping Models for Open Quantum Systems
    Sanchez-Barquilla, Monica; Feist, Johannes
    Nanomaterials (2021), 11 (8), 2104CODEN: NANOKO; ISSN:2079-4991. (MDPI AG)
    The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a no. of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reprodn. of an arbitrary environment, and adding longer-range interactions does not further increase the effective no. of degrees of freedom in the environment.
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    Medina, I.; García-Vidal, F. J.; Fernández-Domínguez, A. I.; Feist, J. Few-Mode Field Quantization of Arbitrary Electromagnetic Spectral Densities. Phys. Rev. Lett. 2021, 126, 093601,  DOI: 10.1103/PhysRevLett.126.093601
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    Few-Mode Field Quantization of Arbitrary Electromagnetic Spectral Densities
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    Physical Review Letters (2021), 126 (9), 093601CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral d., obtained through classical electromagnetic simulations, to a model system involving a small no. of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and elec. field spatial dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.
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    Cluster-expansion representation in quantum optics
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    Physical Review A: Atomic, Molecular, and Optical Physics (2008), 78 (2, Pt. A), 022102/1-022102/26CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
    A theor. framework is developed that combines the systematic many-body cluster-expansion approach with the std. quantum-optical representations. A cluster-expansion transformation is derived to obtain a flexible 1-to-one mapping between correlated clusters and the usual phase-space and marginal distributions discussed in quantum optics. The convergence and correlation properties of this transformation are explored through several quantum-field examples including coherent, thermal, squeezed, Fock, and Schrodinger cat states. The resulting correlation properties can be used as a basis to characterize and control many-body correlations when quantum light interacts with matter. As an application, a cluster-expansion-restoration scheme is developed that allows for the retrieval of the true quantum statistics of light from realistic measurements that are deteriorated by the reduced quantum efficiency of the detectors.
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    Sánchez-Barquilla, M.; Silva, R. E. F.; Feist, J. Cumulant Expansion for the Treatment of Light-Matter Interactions in Arbitrary Material Structures. J. Chem. Phys. 2020, 152, 034108,  DOI: 10.1063/1.5138937
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    Cumulant expansion for the treatment of light-matter interactions in arbitrary material structures
    Sanchez-Barquilla, M.; Silva, R. E. F.; Feist, J.
    Journal of Chemical Physics (2020), 152 (3), 034108CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chem., and transport properties of materials, with significant theor. effort invested toward a better understanding of this phenomenon. A full theor. description of both matter and light is an extremely challenging task. Typical theor. approaches simplify the description of the photonic environment by describing it as a single mode or few modes. While this approxn. is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. The authors here study a compromise where the quantum character of light is taken into account at modest computational cost. To do so, the authors focus on a quantum emitter that interacts with an arbitrary photonic spectral d. and employ the cumulant, or cluster, expansion method to the Heisenberg equations of motion up to 1st, 2nd, and 3rd order. The authors benchmark the method by comparing it with exact solns. for specific situations and show that it can accurately represent dynamics for many parameter ranges. (c) 2020 American Institute of Physics.
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    Arnardottir, K. B.; Moilanen, A. J.; Strashko, A.; Törmä, P.; Keeling, J. Multimode Organic Polariton Lasing. Phys. Rev. Lett. 2020, 125, 233603,  DOI: 10.1103/PhysRevLett.125.233603
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    Multimode Organic Polariton Lasing
    Arnardottir, Kristin B.; Moilanen, Antti J.; Strashko, Artem; Torma, Paivi; Keeling, Jonathan
    Physical Review Letters (2020), 125 (23), 233603CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We present a beyond-mean-field approach to predict the nature of org. polariton lasing, accounting for all relevant photon modes in a planar microcavity. Starting from a microscopic picture, we show how lasing can switch between polaritonic states resonant with the maximal gain, and those at the bottom of the polariton dispersion. We show how the population of nonlasing modes can be found, and by using two-time correlations, we show how the photoluminescence spectrum (of both lasing and nonlasing modes) evolves with pumping and coupling strength, confirming recent exptl. work on the origin of blueshift for polariton lasing.
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    Chin, A. W.; Rivas, Á.; Huelga, S. F.; Plenio, M. B. Exact Mapping between System-Reservoir Quantum Models and Semi-Infinite Discrete Chains Using Orthogonal Polynomials. J. Math. Phys. 2010, 51, 092109,  DOI: 10.1063/1.3490188
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    Prior, J.; Chin, A. W.; Huelga, S. F.; Plenio, M. B. Efficient Simulation of Strong System-Environment Interactions. Phys. Rev. Lett. 2010, 105, 050404,  DOI: 10.1103/PhysRevLett.105.050404
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    Efficient Simulation of Strong System-Environment Interactions
    Prior, Javier; Chin, Alex W.; Huelga, Susana F.; Plenio, Martin B.
    Physical Review Letters (2010), 105 (5), 050404/1-050404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Multicomponent quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum dynamics of biomol. aggregates. Unfortunately, these systems are difficult to simulate as the system-bath interactions cannot be treated perturbatively and std. approaches are invalid or inefficient. Here we combine the time-dependent d. matrix renormalization group with techniques from the theory of orthogonal polynomials to provide an efficient method for simulating open quantum systems, including spin-boson models and their generalizations to multicomponent systems.
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    Woods, M. P.; Groux, R.; Chin, A. W.; Huelga, S. F.; Plenio, M. B. Mappings of Open Quantum Systems onto Chain Representations and Markovian Embeddings. Journal of Mathematical Physics 2014, 55, 032101,  DOI: 10.1063/1.4866769
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    del Pino, J.; Schröder, F. A. Y. N.; Chin, A. W.; Feist, J.; Garcia-Vidal, F. J. Tensor Network Simulation of Polaron-Polaritons in Organic Microcavities. Phys. Rev. B 2018, 98, 165416,  DOI: 10.1103/PhysRevB.98.165416
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    Tensor network simulation of polaron-polaritons in organic microcavities
    del Pino, Javier; Schroder, Florian A. Y. N.; Chin, Alex W.; Feist, Johannes; Garcia-Vidal, Francisco J.
    Physical Review B (2018), 98 (16), 165416CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    In the regime of strong coupling between mol. excitons and confined optical modes, the intramol. degrees of freedom are profoundly affected, leading to a reduced vibrational dressing of polaritons compared to bare electronically excited states. However, existing models only describe a single vibrational mode in each mol., while actual mols. possess a large no. of vibrational degrees of freedom and addnl. interact with a continuous bath of phononic modes in the host medium in typical expts. In this work, we investigate a small ensemble of mols. with an arbitrary no. of vibrational degrees of freedom under strong coupling to a microcavity mode. We demonstrate that reduced vibrational dressing is still present in this case, and show that the influence of the phononic environment on most electronic and photonic observables in the lowest excited state can be predicted from just two collective parameters of the vibrational modes. Besides, we explore vibrational features that can be addressed exclusively by our extended model and could be exptl. tested. Our findings indicate that vibronic coupling is more efficiently suppressed for environments characterized by low-frequency (sub-Ohmic) modes.
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    (a) del Pino, J.; Schröder, F. A. Y. N.; Chin, A. W.; Feist, J.; Garcia-Vidal, F. J. Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons. Phys. Rev. Lett. 2018, 121, 227401,  DOI: 10.1103/PhysRevLett.121.227401
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    Tensor network simulation of non-markovian dynamics in organic polaritons
    del Pino, Javier; Schroder, Florian A. Y. N.; Chin, Alex W.; Feist, Johannes; Garcia-Vidal, Francisco J.
    Physical Review Letters (2018), 121 (22), 227401/1-227401/7CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We calc. the exact many-body time dynamics of polaritonic states supported by an optical cavity filled with org. mols. Optical, vibrational, and radiative processes are treated on an equal footing employing the time-dependent variational matrix product states algorithm. We demonstrate signatures of non-Markovian vibronic dynamics and its fingerprints in the far-field photon emission spectrum at arbitrary light-matter interaction scales, ranging from the weak to the strong coupling regimes. We analyze both the single- and many-mol. cases, showing the crucial role played by the collective motion of mol. nuclei and dark states in detg. the polariton dynamics and the subsequent photon emission.
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    (b) del Pino, J.; Schröder, F. A. Y. N.; Chin, A. W.; Feist, J.; Garcia-Vidal, F. J. Erratum: Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons. Phys. Rev. Lett. 2019, 122, 159902,  DOI: 10.1103/PhysRevLett.122.159902
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    Erratum: Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons [Erratum to document cited in CA171:268059]
    del Pino, Javier; Schroder, Florian A. Y. N.; Chin, Alex W.; Feist, Johannes; Garcia-Vidal, Francisco J.
    Physical Review Letters (2019), 122 (15), 159902/1CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    There is no expanded citation for this reference.
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    Zhao, D.; Silva, R. E. F.; Climent, C.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Impact of Vibrational Modes in the Plasmonic Purcell Effect of Organic Molecules. ACS Photonics 2020, 7, 3369,  DOI: 10.1021/acsphotonics.0c01095
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    Impact of Vibrational Modes in the Plasmonic Purcell Effect of Organic Molecules
    Zhao, Dongxing; Silva, Rui E. F.; Climent, Claudia; Feist, Johannes; Fernandez-Dominguez, Antonio I.; Garcia-Vidal, Francisco J.
    ACS Photonics (2020), 7 (12), 3369-3375CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    By quantum tensor network calcns., the large Purcell effect experienced by an org. mol. placed in the vicinity of a plasmonic nanostructure was studied. In particular, a donor-π bridge-acceptor dye at the gap of 2 Ag nanospheres are considered. The theor. approach allows for a realistic description of the continua of both mol. vibrations and optical nanocavity modes. The ultrafast exciton dynamics in the large Purcell enhancement regime and the corresponding emission spectrum were analyzed, showing that these magnitudes are not accurately represented by the simplified models used up to date. Both the 2-level system model and the single vibrational mode model can only reproduce the dynamics over short time scales, whereas the Fermi's golden rule approach accounts only for the behavior at very long times. Including the whole set of vibrational modes is necessary to capture most of the dynamics and the corresponding spectrum. By disentangling the coupling of the mol. to radiative and nonradiative plasmonic modes, the authors also shed light into the quenching phenomenol. taking place in the system.
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    Rosenbach, R.; Cerrillo, J.; Huelga, S. F.; Cao, J.; Plenio, M. B. Efficient Simulation of Non-Markovian System-Environment Interaction. New J. Phys. 2016, 18, 23035,  DOI: 10.1088/1367-2630/18/2/023035
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    Efficient simulation of non-Markovian system-environment interaction
    Rosenbach, Robert; Cerrillo, Javier; Huelga, Susana F.; Cao, Jianshu; Plenio, Martin B.
    New Journal of Physics (2016), 18 (Feb.), 023035/1-023035/11CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
    A review. In this work, we combine an established method for open quantum systems-the time evolving d. matrix using orthogonal polynomials algorithm-with the transfer tensors formalism, a new tool for the anal., compression and propagation of non-Markovian processes. A compact propagator is generated out of sample trajectories covering the correlation time of the bath. This enables the investigation of previously inaccessible long-time dynamics with linear effort, such as those ensuing from low temp. regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our anal. by highlighting possible further applications of our method.
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    Cygorek, M.; Cosacchi, M.; Vagov, A.; Axt, V. M.; Lovett, B. W.; Keeling, J.; Gauger, E. M. Simulation of Open Quantum Systems by Automated Compression of Arbitrary Environments. Nat. Phys. 2022,  DOI: 10.1038/s41567-022-01544-9
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    Ge, R.-C.; Kristensen, P. T.; Young, J. F.; Hughes, S. Quasinormal Mode Approach to Modelling Light-Emission and Propagation in Nanoplasmonics. New J. Phys. 2014, 16, 113048,  DOI: 10.1088/1367-2630/16/11/113048
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    Sauvan, C.; Wu, T.; Zarouf, R.; Muljarov, E. A.; Lalanne, P. Normalization, Orthogonality, and Completeness of Quasinormal Modes of Open Systems: The Case of Electromagnetism [Invited]. Opt. Express, OE 2022, 30, 6846,  DOI: 10.1364/OE.443656
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    Yang, J.; Perrin, M.; Lalanne, P. Analytical Formalism for the Interaction of Two-Level Quantum Systems with Metal Nanoresonators. Phys. Rev. X 2015, 5, 021008
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    Analytical formalism for the interaction of two-level quantum systems with metal nanoresonators
    Yang, Jianji; Perrin, Mathias; Lalanne, Philippe
    Physical Review X (2015), 5 (2), 021008/1-021008/9CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    Hybrid systems made of quantum emitters and plasmonic nanoresonators offer a unique platform to implement artificial atoms with completely novel optical responses that are not available otherwise. However, their theor. anal. is difficult, and since many degrees of freedom have to be explored, engineering their optical properties remains challenging. Here, we propose a new formalism that removes most limitations encountered in previous anal. treatments and allows a flexible and efficient study of complex nanoresonators with arbitrary shapes in an almost fully anal. way. The formalism brings accurate closed-form expressions for the hybrid-system optical response and provides an intuitive description based on the coupling between the quantum emitters and the resonance modes of the nanoresonator. The ability to quickly predict light-scattering properties of hybrid systems paves the way to a deep exploration of their fascinating properties and may enable rapid optimization of quantum plasmonic metamaterials or quantum information devices.
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    Franke, S.; Hughes, S.; Kamandar Dezfouli, M.; Kristensen, P. T.; Busch, K.; Knorr, A.; Richter, M. Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics. Phys. Rev. Lett. 2019, 122, 213901,  DOI: 10.1103/PhysRevLett.122.213901
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    117
    Quantization of quasinormal modes for open cavities and plasmonic cavity quantum electrodynamics
    Franke, Sebastian; Hughes, Stephen; Dezfouli, Mohsen Kamandar; Kristensen, Philip Trost; Busch, Kurt; Knorr, Andreas; Richter, Marten
    Physical Review Letters (2019), 122 (21), 213901CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenol. dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielec.-metal cavity structure.
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    Franke, S.; Ren, J.; Hughes, S. Quantized Quasinormal-Mode Theory of Coupled Lossy and Amplifying Resonators. Phys. Rev. A 2022, 105, 023702,  DOI: 10.1103/PhysRevA.105.023702
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    118
    Quantized quasinormal-mode theory of coupled lossy and amplifying resonators
    Franke, Sebastian; Ren, Juanjuan; Hughes, Stephen
    Physical Review A (2022), 105 (2), 023702CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
    In the presence of arbitrary three-dimensional linear media with material loss and amplification, we present an electromagnetic field quantization scheme for quasinormal modes (QNMs), extending previous work for lossy media [S. Franke, Phys. Lett.122, 213901 (2019)0031-900710.1103/PhysRevLett.122.213901]. Applying a symmetrization transformation, we show two fundamentally different ways for constructing a QNM photon Fock space, including (i) where there is a sep. operator basis for both gain and loss, and (ii) where the loss and gain degrees of freedom are combined into a single basis. These QNM operator bases are subsequently used to derive the assocd. QNM master equations, including the interaction with a quantum emitter, modeled as a quantized two-level system (TLS). We then compare the two different quantization approaches, and also show how commonly used phenomenol. methods to quantize light in gain-loss resonators are cor. by several important aspects, such as a loss-induced and gain-induced intermode coupling, which appears through the rigorous treatment of loss and amplification on a dissipative mode level. For specific resonator designs, modeled in a fully consistent way with the classical Maxwell equations with open boundary conditions, we then present numerical results for the quantum parameters and observables of a TLS weakly interacting with the medium-assisted field in a gain-loss microdisk resonator system, and discuss the validity of the different quantization approaches for several gain-loss parameter regimes.
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    Wang, D.; Kelkar, H.; Martin-Cano, D.; Rattenbacher, D.; Shkarin, A.; Utikal, T.; Götzinger, S.; Sandoghdar, V. Turning a Molecule into a Coherent Two-Level Quantum System. Nat. Phys. 2019, 15, 483,  DOI: 10.1038/s41567-019-0436-5
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    119
    Turning a molecule into a coherent two-level quantum system
    Wang, Daqing; Kelkar, Hrishikesh; Martin-Cano, Diego; Rattenbacher, Dominik; Shkarin, Alexey; Utikal, Tobias; Goetzinger, Stephan; Sandoghdar, Vahid
    Nature Physics (2019), 15 (5), 483-489CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)
    The use of mols. in quantum optical applications has been hampered by incoherent internal vibrations and other phononic interactions with their environment. Here we show that an org. mol. placed into an optical microcavity behaves as a coherent two-level quantum system. This allows the observation of 99% extinction of a laser beam by a single mol., satn. with less than 0.5 photons and non-classical generation of few-photons super-bunched light. Furthermore, we demonstrate efficient interaction of the mol.-microcavity system with single photons generated by a second mol. in a distant lab. Our achievements represent an important step towards linear and nonlinear quantum photonic circuits based on org. platforms.
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    Feist, J.; Garcia-Vidal, F. J. Extraordinary Exciton Conductance Induced by Strong Coupling. Phys. Rev. Lett. 2015, 114, 196402,  DOI: 10.1103/PhysRevLett.114.196402
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    120
    Extraordinary exciton conductance induced by strong coupling
    Feist, Johannes; Garcia-Vidal, Francisco J.
    Physical Review Letters (2015), 114 (19), 196402/1-196402/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We demonstrate that exciton conductance in org. materials can be enhanced by several orders of magnitude when the mols. are strongly coupled to an electromagnetic mode. Using a 1D model system, we show how the formation of a collective polaritonic mode allows excitons to bypass the disordered array of mols. and jump directly from one end of the structure to the other. This finding could have important implications in the fields of exciton transistors, heat transport, photosynthesis, and biol. systems in which exciton transport plays a key role.
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    Schachenmayer, J.; Genes, C.; Tignone, E.; Pupillo, G. Cavity-Enhanced Transport of Excitons. Phys. Rev. Lett. 2015, 114, 196403,  DOI: 10.1103/PhysRevLett.114.196403
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    Cavity-enhanced transport of excitons
    Schachenmayer, Johannes; Genes, Claudiu; Tignone, Edoardo; Pupillo, Guido
    Physical Review Letters (2015), 114 (19), 196403/1-196403/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We show that exciton-type transport in certain materials can be dramatically modified by their inclusion in an optical cavity: the modification of the electromagnetic vacuum mode structure introduced by the cavity leads to transport via delocalized polariton modes rather than through tunneling processes in the material itself. This can help overcome exponential suppression of transmission properties as a function of the system size in the case of disorder and other imperfections. We exemplify massive improvement of transmission for excitonic wave packets through a cavity, as well as enhancement of steady-state exciton currents under incoherent pumping. These results may have implications for expts. of exciton transport in disordered org. materials. We propose that the basic phenomena can be obsd. in quantum simulators made of Rydberg atoms, cold mols. in optical lattices, as well as in expts. with trapped ions.
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    Carmichael, H. J.; Walls, D. F. Master Equation for Strongly Interacting Systems. J. Phys. Math. Nucl. Gen. 1973, 6, 1552,  DOI: 10.1088/0305-4470/6/10/014
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    del Pino, J.; Feist, J.; Garcia-Vidal, F. J. Quantum Theory of Collective Strong Coupling of Molecular Vibrations with a Microcavity Mode. New J. Phys. 2015, 17, 053040,  DOI: 10.1088/1367-2630/17/5/053040
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    Sáez-Blázquez, R.; Feist, J.; Romero, E.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Cavity-Modified Exciton Dynamics in Photosynthetic Units. J. Phys. Chem. Lett. 2019, 10, 4252,  DOI: 10.1021/acs.jpclett.9b01495
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    Cavity-Modified Exciton Dynamics in Photosynthetic Units
    Saez-Blazquez, Rocio; Feist, Johannes; Romero, Elisabet; Fernandez-Dominguez, Antonio I.; Garcia-Vidal, Francisco J.
    Journal of Physical Chemistry Letters (2019), 10 (15), 4252-4258CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Recently, exciton-photon strong coupling has been proposed as a means to control and enhance energy transfer in ensembles of org. mols. Here, we demonstrate that the exciton dynamics in an archetypal purple bacterial photosynthetic unit, composed of six LH2 antennas surrounding a single LH1 complex, is greatly modified by its interaction with an optical cavity. We develop a Bloch-Redfield master equation approach that accounts for the interplay between the B800 and B850 bacteriochlorophyll mols. within each LH2 antenna, as well as their interactions with the central LH1 complex. Using a realistic parametrization of both the photosynthetic unit and optical cavity, we investigate the formation of polaritons in the system, revealing that these can be tuned to accelerate its exciton dynamics by 3 orders of magnitude. This yields a significant occupation of the LH1 complex, the stage immediately prior to the reaction center, with only a few-femtosecond delay after the initial excitation of the LH2 B800 pigments. Our theor. findings unveil polaritonic phenomena as a promising route for the characterization, tailoring, and optimization of light-harvesting mechanisms in natural and artificial photosynthetic processes.
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    Kirton, P.; Keeling, J. Nonequilibrium Model of Photon Condensation. Phys. Rev. Lett. 2013, 111, 100404,  DOI: 10.1103/PhysRevLett.111.100404
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    Nonequilibrium model of photon condensation
    Kirton, Peter; Keeling, Jonathan
    Physical Review Letters (2013), 111 (10), 100404/1-100404/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We develop a nonequil. model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye mols., and investigate when the photons are able to reach a thermal equil. Bose-Einstein distribution. At low temps., or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equil. and the behavior becomes more like that of a conventional laser.
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    Herrera, F.; Spano, F. C. Cavity-Controlled Chemistry in Molecular Ensembles. Phys. Rev. Lett. 2016, 116, 238301,  DOI: 10.1103/PhysRevLett.116.238301
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    Cavity-controlled chemistry in molecular ensembles
    Herrera, Felipe; Spano, Frank C.
    Physical Review Letters (2016), 116 (23), 238301/1-238301/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    A review. The demonstration of strong and ultrastrong coupling regimes of cavity QED with polyat. mols. has opened new routes to control chem. dynamics at the nanoscale. We show that strong resonant coupling of a cavity field with an electronic transition can effectively decouple collective electronic and nuclear degrees of freedom in a disordered mol. ensemble, even for mols. with high-frequency quantum vibrational modes having strong electron-vibration interactions. This type of polaron decoupling can be used to control chem. reactions. We show that the rate of electron transfer reactions in a cavity can be orders of magnitude larger than in free space for a wide class of org. mol. species.
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    Kasha, M. Energy Transfer Mechanisms and the Molecular Exciton Model for Molecular Aggregates. Radiat. Res. 1963, 20, 55,  DOI: 10.2307/3571331
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    Energy transfer mechanisms and the molecular exciton model for molecular aggregates
    Kasha, Michael
    Radiation Research (1963), 20 (), 55-70CODEN: RAREAE; ISSN:0033-7587.
    A review with 21 references.
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    Herrera, F.; Spano, F. C. Dark Vibronic Polaritons and the Spectroscopy of Organic Microcavities. Phys. Rev. Lett. 2017, 118, 223601,  DOI: 10.1103/PhysRevLett.118.223601
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    Dark vibronic polaritons and the spectroscopy of organic microcavities
    Herrera, Felipe; Spano, Frank C.
    Physical Review Letters (2017), 118 (22), 223601/1-223601/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Org. microcavities are photonic nanostructures that strongly confine the electromagnetic field, allowing exotic quantum regimes of light-matter interaction with disordered org. semiconductors. The unambiguous interpretation of the spectra of org. microcavities has been a long-standing challenge due to several competing effects involving electrons, vibrations, and cavity photons. Here we present a theor. framework that is able to describe the main spectroscopic features of org. microcavities consistently.We introduce a class of light-matter excitations called dark vibronic polaritons, which strongly emit but only weakly absorb light in the same frequency region of the bare electronic transition. A successful comparison with exptl. data demonstrates the applicability of our theory. The proposed microscopic understanding of org. microcavities paves the way for the development of optoelectronic devices enhanced by quantum optics.
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    Herrera, F.; Spano, F. C. Absorption and Photoluminescence in Organic Cavity QED. Phys. Rev. A 2017, 95, 053867,  DOI: 10.1103/PhysRevA.95.053867
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    129
    Absorption and photoluminescence in organic cavity QED
    Herrera, Felipe; Spano, Frank C.
    Physical Review A (2017), 95 (5), 053867/1-053867/24CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
    Org. microcavities can be engineered to reach exotic quantum regimes of strong and ultrastrong light-matter coupling. However, the microscopic interpretation of their spectroscopic signals can be challenging due to the competition between coherent and dissipative processes involving electrons, vibrations, and cavity photons. We develop here a theor. framework based on the Holstein-Tavis-Cummings model and a Markovian treatment of dissipation to account for previously unexplained spectroscopic features of org. microcavities consistently. We identify conditions for the formation of dark vibronic polaritons, a class of light-matter excitations that are not visible in absorption but lead to strong photoluminescence lines. We show that photon leakage from dark vibronic polaritons can be responsible for enhancing photoluminescence at the lower polariton frequency, and also can explain the apparent breakdown of reciprocity between absorption and emission in the vicinity of the bare mol. transition frequency. Successful comparison with exptl. data demonstrates the applicability of our theory.
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    Herrera, F.; Spano, F. C. Theory of Nanoscale Organic Cavities: The Essential Role of Vibration-Photon Dressed States. ACS Photonics 2018, 5, 65,  DOI: 10.1021/acsphotonics.7b00728
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    Theory of Nanoscale Organic Cavities: The Essential Role of Vibration-Photon Dressed States
    Herrera, Felipe; Spano, Frank C.
    ACS Photonics (2018), 5 (1), 65-79CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    A review. The interaction of org. mols. and mol. aggregates with electromagnetic fields that are strongly confined in nanoscale optical cavities has allowed the observation of exotic quantum regimes of light-matter interaction at room temp., for a wide variety of cavity materials and geometries. Understanding the universal features of such org. cavities represents a significant challenge for theor. modeling, as expts. show that these systems are characterized by an intricate competition between coherent and dissipative processes involving entangled nuclear, electronic and photonic degrees of freedom. A new theor. framework that can describe org. cavities under strong light-matter coupling is discussed. The theory combines std. concepts in chem. physics and quantum optics to provide a microscopic description of vibronic org. polaritons that is fully consistent with available expts., and yet is profoundly different from the common view of org. polaritons. By introducing a new class of vibronic polariton wave functions with a photonic component that is dressed by intramol. vibrations, the new theory can offer a consistent soln. to some of the long-standing puzzles in the interpretation of org. cavity luminescence. The predictions of the model with spectroscopic observations are confronted, and the conditions under which the theory reduces to previous approaches are described. Possible extensions of the theory to account for realistic complexities of org. cavities such spatial inhomogeneities and the multimode nature of confined electromagnetic fields are discussed.
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    Zeb, M. A.; Kirton, P. G.; Keeling, J. Exact States and Spectra of Vibrationally Dressed Polaritons. ACS Photonics 2018, 5, 249,  DOI: 10.1021/acsphotonics.7b00916
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    Exact States and Spectra of Vibrationally Dressed Polaritons
    Zeb, M. Ahsan; Kirton, Peter G.; Keeling, Jonathan
    ACS Photonics (2018), 5 (1), 249-257CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Strong coupling between light and matter is possible with a variety of org. materials. In contrast to the simpler inorg. case, org. materials often have a complicated spectrum, with vibrationally dressed electronic transitions. Strong coupling to light competes with this vibrational dressing and, if strong enough, can suppress the entanglement between electronic and vibrational degrees of freedom. By exploiting symmetries, the authors can perform exact numerical diagonalization to find the polaritonic states for intermediate nos. of mols. and use these to define and validate accurate expressions for the lower polariton states and strong-coupling spectrum in the thermodn. limit. Using this approach, vibrational decoupling occurs as a sharp transition above a crit. matter-light coupling strength. Also the polariton spectrum evolves with the no. of mols., recovering classical linear optics results only at large N.
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    Strashko, A.; Kirton, P.; Keeling, J. Organic Polariton Lasing and the Weak to Strong Coupling Crossover. Phys. Rev. Lett. 2018, 121, 193601,  DOI: 10.1103/PhysRevLett.121.193601
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    Organic Polariton Lasing and the Weak to Strong Coupling Crossover
    Strashko, Artem; Kirton, Peter; Keeling, Jonathan
    Physical Review Letters (2018), 121 (19), 193601CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Following exptl. realizations of room temp. polariton lasing with org. mols., we present a microscopic model that allows us to explore the crossover from weak to strong matter-light coupling. We consider a nonequil. Dicke-Holstein model, including both strong coupling to vibrational modes and strong matter-light coupling, providing the phase diagram of this model in the thermodn. limit. We discuss the mechanism of polariton lasing, uncovering a process of self-tuning, and identify the relation and distinction between regular dye lasers and org. polariton lasers.
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    Galego, J.; Garcia-Vidal, F. J.; Feist, J. Cavity-Induced Modifications of Molecular Structure in the Strong-Coupling Regime. Phys. Rev. X 2015, 5, 041022
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    Cavity-induced modifications of molecular structure in the strong-coupling regime
    Galego, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
    Physical Review X (2015), 5 (4), 041022/1-041022/14CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    In most theor. descriptions of collective strong coupling of org. mols. to a cavity mode, the mols. are modeled as simple two-level systems. This picture fails to describe the rich structure provided by their internal rovibrational (nuclear) degrees of freedom. We investigate a first-principles model that fully takes into account both electronic and nuclear degrees of freedom, allowing an exploration of the phenomenon of strong coupling from an entirely new perspective. First, we demonstrate the limitations of applicability of the Born-Oppenheimer approxn. in strongly coupled mol.-cavity structures. For the case of two mols., we also show how dark states, which within the two-level picture are effectively decoupled from the cavity, are indeed affected by the formation of collective strong coupling. Finally, we discuss ground-state modifications in the ultrastrong-coupling regime and show that some mol. observables are affected by the collective coupling strength, while others depend only on the single-mol. coupling const.
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    Galego, J.; Garcia-Vidal, F. J.; Feist, J. Suppressing Photochemical Reactions with Quantized Light Fields. Nat. Commun. 2016, 7, 13841,  DOI: 10.1038/ncomms13841
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    Suppressing photochemical reactions with quantized light fields
    Galego, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
    Nature Communications (2016), 7 (), 13841CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    Photoisomerization, i.e., a photochem. reaction leading to a change of mol. structure after absorption of a photon, can have detrimental effects such as leading to DNA damage under solar irradn., or as a limiting factor for the efficiency of solar cells. Here, we show that strong coupling of org. mols. to a confined light mode can be used to strongly suppress photoisomerization, as well as other photochem. reactions, and thus convert mols. that normally show fast photodegrdn. into photostable forms. We find this to be esp. efficient in the case of collective strong coupling, where the distribution of a single excitation over many mols. and the light mode leads to a collective protection effect that almost completely suppresses the photochem. reaction.
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    Silva, R. E. F.; del Pino, J.; García-Vidal, F. J.; Feist, J. Polaritonic Molecular Clock for All-Optical Ultrafast Imaging of Wavepacket Dynamics without Probe Pulses. Nat. Commun. 2020, 11, 1423,  DOI: 10.1038/s41467-020-15196-x
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    Polaritonic molecular clock for all-optical ultrafast imaging of wavepacket dynamics without probe pulses
    Silva, R. E. F.; del Pino, Javier; Garcia-Vidal, Francisco J.; Feist, Johannes
    Nature Communications (2020), 11 (1), 1423CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Conventional approaches to probing ultrafast mol. dynamics rely on the use of synchronized laser pulses with a well-defined time delay. Typically, a pump pulse excites a mol. wavepacket. A subsequent probe pulse can then dissoc. or ionize the mol., and measurement of the mol. fragments provides information about where the wavepacket was for each time delay. Here, we propose to exploit the ultrafast nuclear-position-dependent emission obtained due to large light-matter coupling in plasmonic nanocavities to image wavepacket dynamics using only a single pump pulse. We show that the time-resolved emission from the cavity provides information about when the wavepacket passes a given region in nuclear configuration space. This approach can image both cavity-modified dynamics on polaritonic (hybrid light-matter) potentials in the strong light-matter coupling regime and bare-mol. dynamics in the intermediate coupling regime of large Purcell enhancements, and provides a route towards ultrafast mol. spectroscopy with plasmonic nanocavities.
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    Strathearn, A.; Kirton, P.; Kilda, D.; Keeling, J.; Lovett, B. W. Efficient Non-Markovian Quantum Dynamics Using Time-Evolving Matrix Product Operators. Nat. Commun. 2018, 9, 3322,  DOI: 10.1038/s41467-018-05617-3
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    Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
    Strathearn A; Kirton P; Kilda D; Keeling J; Lovett B W
    Nature communications (2018), 9 (1), 3322 ISSN:.
    In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian harmonic environment. Our method relies on expressing the system state and its propagator as a matrix product state and operator, respectively, and using a singular value decomposition to compress the description of the state as time evolves. We demonstrate the power and flexibility of our approach by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.
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  • Abstract

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    Figure 1

    Figure 1. Schematic representations of typical situations in molecular polaritonics. (a) Molecular ensemble inside a photonic microcavity and (b) single emitter coupled to a plasmonic nanoantenna.

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    Figure 2

    Figure 2. (a) Scheme of the hybridization of one EM mode (purple) and one quantum emitter (yellow). In the strong-coupling regime, an upper (UP) and lower (LP) polariton are formed and are separated by the Rabi splitting ΩR. (b) Energies of the polaritons under nonzero detuning. The dashed lines show the uncoupled frequencies.

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    Figure 3

    Figure 3. (a) Sketch of the chain mapping model: (i) quantum system coupled to a discrete set of environment modes; (ii) quantum system coupled to the (collective) reaction mode, with this mode coupled to a residual bath of modes; (iii) chain mapping for the environment modes after n steps, with a residual bath of N – n modes at the end of the chain. (b) Sketch of the few-mode quantization model for one quantum emitter. The spectral density of the model can be fitted to the one obtained classically from the Green’s function. Therefore, the couplings to the interacting modes gi, their frequencies and coupling ωij, and the dissipative terms κi can be known. Panel (a) is reprinted from ref (98) under the terms of the Creative Commons Attribution 4.0 International license. Copyright 2021 MDPI. Panel (b) is reprinted from ref (99) under the terms of the Creative Commons Attribution 4.0 International license. Copyright 2021 American Physical Society.

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    Figure 4

    Figure 4. Conceptual potential energy surfaces for one cavity mode and one molecule at different coupling strengths: (a) weak coupling; (b, c) strong coupling. The color represents the fraction of each constituent. Reprinted with permission from ref (51). Copyright 2017 American Chemical Society.

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  • References

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      Strong coupling between surface plasmon polaritons and emitters: a review
      Torma P; Barnes W L
      Reports on progress in physics. Physical Society (Great Britain) (2015), 78 (1), 013901 ISSN:.
      In this review we look at the concepts and state-of-the-art concerning the strong coupling of surface plasmon-polariton modes to states associated with quantum emitters such as excitons in J-aggregates, dye molecules and quantum dots. We explore the phenomenon of strong coupling with reference to a number of examples involving electromagnetic fields and matter. We then provide a concise description of the relevant background physics of surface plasmon polaritons. An extensive overview of the historical background and a detailed discussion of more recent relevant experimental advances concerning strong coupling between surface plasmon polaritons and quantum emitters is then presented. Three conceptual frameworks are then discussed and compared in depth: classical, semi-classical and fully quantum mechanical; these theoretical frameworks will have relevance to strong coupling beyond that involving surface plasmon polaritons. We conclude our review with a perspective on the future of this rapidly emerging field, one we are sure will grow to encompass more intriguing physics and will develop in scope to be of relevance to other areas of science.
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    11. 11
      Hopfield, J. J.; Thomas, D. G. Polariton Absorption Lines. Phys. Rev. Lett. 1965, 15, 22,  DOI: 10.1103/PhysRevLett.15.22
      11
      Polariton absorption lines
      Hopfield, J. J.; Thomas, D. G.
      Physical Review Letters (1965), 15 (1), 22-5CODEN: PRLTAO; ISSN:0031-9007.
      The observation and interpretation in ZnO of sharp weak absorption lines with energies which cannot be calcd. from a many-bodied Hamiltonian where the electron-electron interaction is the simple Coulomb potential are reported. The existence of polariton absorption lines with H‖.vector.q is a classic effect in anisotropic crystals.
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    12. 12
      Morris, G. C.; Sceats, M. G. The 4000 Å Transition of Crystal Anthracene. Chem. Phys. 1974, 3, 164,  DOI: 10.1016/0301-0104(74)80058-3
      There is no corresponding record for this reference.
    13. 13
      Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Macroscopic QED for Quantum Nanophotonics: Emitter-Centered Modes as a Minimal Basis for Multiemitter Problems. Nanophotonics 2020, 10, 477,  DOI: 10.1515/nanoph-2020-0451
      There is no corresponding record for this reference.
    14. 14
      Fano, U. Atomic Theory of Electromagnetic Interactions in Dense Materials. Phys. Rev. 1956, 103, 1202,  DOI: 10.1103/PhysRev.103.1202
      14
      Atomic theory of electromagnetic interactions in dense materials
      Fano, U.
      Physical Review (1956), 103 (), 1202-18CODEN: PHRVAO; ISSN:0031-899X.
      cf. ibid. 102, 385(1956). A quantum analog of the classical electron oscillator model is developed. The Hamiltonian of long-wave excitations of matter is equiv. to that of an assembly of oscillators under very general assumptions. These oscillators are coupled with the electromagnetic field oscillators and the normal modes of the coupled system are analyzed. The normal modes of longitudinal and transverse excitation have different spectra; the transverse frequencies depend strongly on the wave length but the longitudinal ones do not. If the "longitudinal photons" are eliminated after the transformation to normal modes, the resulting Coulomb law has the dielec. const. in the denominator. The dielec. response law is expressed as a series of oscillations and also in terms of Van Hove's correlation function (C.A. 48, 9803a). Born approximation theory of the collisions of fast charged particles with the assembly of normal mode (longitudinal and transverse) oscillators yields the same total cross section as does Fermi's macroscopic theory (C.A. 34, 3977.8). The transverse excitations include the Cherenkov radiation.
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    15. 15
      Huttner, B.; Barnett, S. M. Quantization of the Electromagnetic Field in Dielectrics. Phys. Rev. A 1992, 46, 4306,  DOI: 10.1103/PhysRevA.46.4306
      15
      Quantization of the electromagnetic field in dielectrics
      Huttner; Barnett
      Physical review. A, Atomic, molecular, and optical physics (1992), 46 (7), 4306-4322 ISSN:1050-2947.
      There is no expanded citation for this reference.
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    16. 16
      Scheel, S.; Knöll, L.; Welsch, D.-G. QED Commutation Relations for Inhomogeneous Kramers-Kronig Dielectrics. Phys. Rev. A 1998, 58, 700,  DOI: 10.1103/PhysRevA.58.700
      16
      QED commutation relations for inhomogeneous Kramers-Kronig dielectrics
      Scheel, Stefan; Knoll, Ludwig; Welsch, Dirk-Gunnar
      Physical Review A: Atomic, Molecular, and Optical Physics (1998), 58 (1), 700-706CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
      Recently a quantization scheme for the phenomenol. Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielec. medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface. Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commutation relations of QED are preserved for an arbitrarily space-dependent, Kramers-Kronig consistent permittivity. Further, an extension of the quantization scheme to linear media with bounded regions of amplification is given, and the problem of anisotropic media is briefly addressed.
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    17. 17
      Knöll, L.; Scheel, S.; Welsch, D.-G. In Coherence and Statistics of Photons and Atoms, 1st ed.; Peřina, J., Ed.; Wiley-VCH Verlag: New York, 2001.
      There is no corresponding record for this reference.
    18. 18
      Wubs, M.; Suttorp, L. G.; Lagendijk, A. Multipole Interaction between Atoms and Their Photonic Environment. Phys. Rev. A 2003, 68, 013822,  DOI: 10.1103/PhysRevA.68.013822
      18
      Multipole interaction between atoms and their photonic environment
      Wubs, Martijn; Suttorp, L. G.; Lagendijk, A.
      Physical Review A: Atomic, Molecular, and Optical Physics (2003), 68 (1), 013822/1-013822/16CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)
      Macroscopic field quantization is presented for a nondispersive photonic dielec. environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivs. shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are detd. and in particular, the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielec. a dipole couples to a field that is neither the (transverse) elec. nor the macroscopic displacement field. The dielec. function is different from the bulk dielec. function at the position of the dipole, so that local-field effects must be taken into account.
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    19. 19
      Scheel, S.; Buhmann, S. Y. Macroscopic Quantum Electrodynamics - Concepts and Applications. Acta Phys. Slovaca 2008, 58, 675,  DOI: 10.2478/v10155-010-0092-x
      19
      Macroscopic quantum electrodynamics - concepts and applications
      Scheel, Stefan; Buhmann, Stefan Yoshi
      Acta Physica Slovaca (2008), 58 (5), 675-809CODEN: APSVCO; ISSN:0323-0465. (Institute of Physics, Slovak Academy of Sciences)
      In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the std. mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated at. systems and magnetoelec. bodies, and serves as an important tool for the understanding of surface-assisted at. relaxation effects and the intimately connected position-dependent energy shifts which give rise to Casimir-Polder and van der Waals forces.
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    20. 20
      Buhmann, S. Y. Dispersion Forces I; Springer Tracts in Modern Physics; Springer Berlin Heidelberg: Berlin, Heidelberg, 2012; Vol. 247.
      There is no corresponding record for this reference.
    21. 21
      Buhmann, S. Y. Dispersion Forces II; Springer Tracts in Modern Physics; Springer Berlin Heidelberg: Berlin, Heidelberg, 2012; Vol. 248.
      There is no corresponding record for this reference.
    22. 22
      Gérard, J. M.; Barrier, D.; Marzin, J. Y.; Kuszelewicz, R.; Manin, L.; Costard, E.; Thierry-Mieg, V.; Rivera, T. Quantum Boxes as Active Probes for Photonic Microstructures: The Pillar Microcavity Case. Appl. Phys. Lett. 1996, 69, 449,  DOI: 10.1063/1.118135
      22
      Quantum boxes as active probes for photonic microstructures: the pillar microcavity case
      Gerard, J. M.; Barrier, D.; Marzin, J. Y.; Kuszelewicz, R.; Manin, L.; Costard, E.; Thierry-Mieg, V.; Rivera, T.
      Applied Physics Letters (1996), 69 (4), 449-451CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      A Ga/As/AlAs planar cavity contg. a collection in InAs quantum boxes in its core region was grown in a single step by mol. beam epitaxy, and processed by electron-beam lithog. and reactive ion etching into pillar microresonators. The optical study by photoluminescence of these localized light emitters allows a systematic and precise detn. of the energies of the 1st confined photon modes of such microstructures, in a good agreement with theor. ests. More generally, such probes facilitate the exptl. study of the modes of complex photonic microstructures and of the spontaneous emission alteration they entail on a quasimonochromatic light emitter.
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    23. 23
      Hood, C. J.; Lynn, T. W.; Doherty, A. C.; Parkins, A. S.; Kimble, H. J. Atom-Cavity Microscope: Single Atoms Bound in Orbit by Single Photons. Science 2000, 287, 1447,  DOI: 10.1126/science.287.5457.1447
      23
      The atom-cavity microscope. Single atoms bound in orbit by single photons
      Hood, C. J.; Lynn, T. W.; Doherty, A. C.; Parkins, A. S.; Kimble, H. J.
      Science (Washington, D. C.) (2000), 287 (5457), 1447-1453CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The motion of individual Cs atoms trapped inside an optical resonator is revealed with the atom-cavity microscope (ACM). A single atom moving within the resonator generates large variations in the transmission of a weak probe laser, which are recorded in real time. An inversion algorithm then allows individual atom trajectories to be reconstructed from the record of cavity transmission and reveals single atoms bound in orbit by the mech. forces assocd. with single photons. In these initial expts., the ACM yields 2-μm spatial resoln. in a 10-μs time interval. Over the duration of the observation, the sensitivity is near the std. quantum limit for sensing the motion of a Cs atom.
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    24. 24
      Painter, O.; Lee, R. K.; Scherer, A.; Yariv, A.; O’Brien, J. D.; Dapkus, P. D.; Kim, I. Two-Dimensional Photonic Band-Gap Defect Mode Laser. Science 1999, 284, 1819,  DOI: 10.1126/science.284.5421.1819
      24
      Two-dimensional photonic band-gap defect mode laser
      Painter, O.; Lee, R. K.; Scherer, A.; Yariv, A.; O'Brien, J. D.; Dapkus, P. D.; Kim, I.
      Science (Washington, D. C.) (1999), 284 (5421), 1819-1821CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      A laser cavity formed from a single defect in a two-dimensional photonic crystal is demonstrated. The optical microcavity consists of a half wavelength-thick waveguide for vertical confinement and a two-dimensional photonic crystal mirror for lateral localization. A defect in the photonic crystal is introduced to trap photons inside a vol. of 2.5 cubic half-wavelengths, approx. 0.03 cubic micrometers. The laser is fabricated in the indium gallium arsenic phosphide material system, and optical gain is provided by strained quantum wells designed for a peak emission wavelength of 1.55 μm at room temp. Pulsed lasing action has been obsd. at a wavelength of 1.5 μm from optically pumped devices with a substrate temp. of 143 K.
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    25. 25
      Lodahl, P.; Mahmoodian, S.; Stobbe, S. Interfacing Single Photons and Single Quantum Dots with Photonic Nanostructures. Rev. Mod. Phys. 2015, 87, 347,  DOI: 10.1103/RevModPhys.87.347
      25
      Interfacing single photons and single quantum dots with photonic nanostructures
      Lodahl, Peter; Mahmoodian, Sahand; Stobbe, Soren
      Reviews of Modern Physics (2015), 87 (2), 347-400CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
      Photonic nanostructures provide a means of tailoring the interaction between light and matter and the past decade has witnessed tremendous exptl. and theor. progress on this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics expts. on, e.g.. spontaneous- emission control, modified Lamb shifts, and enhanced dipole-dipole interaction. Furthermore, highly efficient single-photon sources and giant photon nonlinearities may be implemented with immediate applications for photonic quantum-information processing. This review summarizes the general theor. framework of photon emission including the role of dephasing processes and applies it to photonic nanostructures of current interest, such as photonic-crystal cavities and waveguides, dielec. nanowires, and plasmonic waveguides. The introduced concepts are generally applicable in quantum nanophotonics and apply to a large extent also to other quantum emitters, such as mols., nitrogen vacancy centers, or atoms. Finally, the progress and future prospects of applications in quantum-information processing are considered.
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    26. 26
      Fernández-Domínguez, A. I.; García-Vidal, F. J.; Martín-Moreno, L. Unrelenting Plasmons. Nat. Photonics 2017, 11, 8,  DOI: 10.1038/nphoton.2016.258
      26
      Unrelenting plasmons
      Fernandez-Dominguez, Antonio I.; Garcia-Vidal, Francisco J.; Martin-Moreno, Luis
      Nature Photonics (2017), 11 (1), 8-10CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
      Worldwide research efforts on plasmonics and metamaterials have been growing exponentially for the past ten years. Will this course hold true over the next decade.
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    27. 27
      Fernández-Domínguez, A. I.; Bozhevolnyi, S. I.; Mortensen, N. A. Plasmon-Enhanced Generation of Nonclassical Light. ACS Photonics 2018, 5, 3447,  DOI: 10.1021/acsphotonics.8b00852
      27
      Plasmon-Enhanced Generation of Nonclassical Light
      Fernandez-Dominguez, Antonio I.; Bozhevolnyi, Sergey I.; Mortensen, N. Asger
      ACS Photonics (2018), 5 (9), 3447-3451CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      A review. Strong light-matter interactions enabled by surface plasmons have given rise to a wide range of photonic, optoelectronic, and chem. functionalities. In recent years, the interest in this research area has focused on the quantum regime, aiming to developing ultracompact nanoscale instruments operating at the single (few) photon(s) level. In this perspective, we provide a general overview of recent exptl. and theor. advances as well as near-future challenges toward the design and implementation of plasmon-empowered quantum optical and photoemitting devices based on the building blocks of nanophotonics technol.: metallo-dielec. nanostructures and microscopic light sources.
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    28. 28
      Baumberg, J. J.; Aizpurua, J.; Mikkelsen, M. H.; Smith, D. R. Extreme Nanophotonics from Ultrathin Metallic Gaps. Nat. Mater. 2019, 18, 668,  DOI: 10.1038/s41563-019-0290-y
      28
      Extreme nanophotonics from ultrathin metallic gaps
      Baumberg, Jeremy J.; Aizpurua, Javier; Mikkelsen, Maiken H.; Smith, David R.
      Nature Materials (2019), 18 (7), 668-678CODEN: NMAACR; ISSN:1476-1122. (Nature Research)
      A review. Ultrathin dielec. gaps between metals can trap plasmonic optical modes with surprisingly low loss and with vols. below 1 nm3. We review the origin and subtle properties of these modes, and show how they can be well accounted for by simple models. Particularly important is the mixing between radiating antennas and confined nanogap modes, which is extremely sensitive to precise nanogeometry, right down to the single-atom level. Coupling nanogap plasmons to electronic and vibronic transitions yields a host of phenomena including single-mol. strong coupling and mol. optomechanics, opening access to at.-scale chem. and materials science, as well as quantum metamaterials. Ultimate low-energy devices such as robust bottom-up assembled single-atom switches are thus in prospect.
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    29. 29
      Khurgin, J. B. How to Deal with the Loss in Plasmonics and Metamaterials. Nat. Nanotechnol. 2015, 10, 2,  DOI: 10.1038/nnano.2014.310
      29
      How to deal with the loss in plasmonics and metamaterials
      Khurgin, Jacob B.
      Nature Nanotechnology (2015), 10 (1), 2-6CODEN: NNAABX; ISSN:1748-3387. (Nature Publishing Group)
      A review with commentary. Metal losses affect the performance of every plasmonic or metamaterial structure; dealing with them will det. the degree to which these structures will find practical applications.
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    30. 30
      Galego, J.; Climent, C.; Garcia-Vidal, F. J.; Feist, J. Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity. Phys. Rev. X 2019, 9, 021057
      30
      Cavity Casimir-Polder Forces and Their Effects in Ground-State Chemical Reactivity
      Galego, Javier; Climent, Claudia; Garcia-Vidal, Francisco J.; Feist, Johannes
      Physical Review X (2019), 9 (2), 021057CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      A review. Here, we present a fundamental study on how the ground-state chem. reactivity of a single mol. can be modified in a QED scenario, i.e., when it is placed inside a nanoscale cavity and there is strong coupling between the cavity field and vibrational modes within the mol. We work with a model system for the mol. (Shin-Metiu model) in which nuclear, electronic, and photonic degrees of freedom are treated on the same footing. This simplified model allows the comparison of exact quantum reaction rate calcns. with predictions emerging from transition state theory based on the cavity Born-Oppenheimer approach. We demonstrate that QED effects are indeed able to significantly modify activation barriers in chem. reactions and, as a consequence, reaction rates. The crit. phys. parameter controlling this effect is the permanent dipole of the mol. and how this magnitude changes along the reaction coordinate. We show that the effective coupling can lead to significant single-mol. energy shifts in an exptl. available nanoparticle-on-mirror cavity. We then apply the validated theory to a realistic case (internal rotation in the 1,2-dichloroethane mol.), showing how reactions can be inhibited or catalyzed depending on the profile of the mol. dipole. Furthermore, we discuss the absence of resonance effects in the present scenario, which can be understood through its connection to Casimir-Polder forces. Finally, we treat the case of many-mol. strong coupling and find collective modifications of reaction rates if the mol. permanent dipole moments are oriented with respect to the cavity field.
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    31. 31
      Zhang, Y.; He, S.; Guo, W.; Hu, Y.; Huang, J.; Mulcahy, J. R.; Wei, W. D. Surface-Plasmon-Driven Hot Electron Photochemistry. Chem. Rev. 2018, 118, 2927,  DOI: 10.1021/acs.chemrev.7b00430
      31
      Surface-plasmon-driven hot electron photochemistry
      Zhang, Yuchao; He, Shuai; Guo, Wenxiao; Hu, Yue; Huang, Jiawei; Mulcahy, Justin R.; Wei, Wei David
      Chemical Reviews (Washington, DC, United States) (2018), 118 (6), 2927-2954CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
      A review. Visible-light-driven photochem. has continued to attract heightened interest due to its capacity to efficiently harvest solar energy and its potential to solve the global energy crisis. Plasmonic nanostructures boast broadly tunable optical properties coupled with catalytically active surfaces that offer a unique opportunity for solar photochem. Resonant optical excitation of surface plasmons produces energetic hot electrons that can be collected to facilitate chem. reactions. This review sums up recent theor. and exptl. approaches for understanding the underlying photophys. processes in hot electron generation and discusses various electron-transfer models on both plasmonic metal nanostructures and plasmonic metal/semiconductor heterostructures. Following that are highlights of recent examples of plasmon-driven hot electron photochem. reactions within the context of both cases. The review concludes with a discussion about the remaining challenges in the field and future opportunities for addressing the low reaction efficiencies in hot-electron-induced photochem.
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    32. 32
      Zhou, L.; Swearer, D. F.; Zhang, C.; Robatjazi, H.; Zhao, H.; Henderson, L.; Dong, L.; Christopher, P.; Carter, E. A.; Nordlander, P.; Halas, N. J. Quantifying Hot Carrier and Thermal Contributions in Plasmonic Photocatalysis. Science 2018, 362, 69,  DOI: 10.1126/science.aat6967
      32
      Quantifying hot carrier and thermal contributions in plasmonic photocatalysis
      Zhou, Linan; Swearer, Dayne F.; Zhang, Chao; Robatjazi, Hossein; Zhao, Hangqi; Henderson, Luke; Dong, Liangliang; Christopher, Phillip; Carter, Emily A.; Nordlander, Peter; Halas, Naomi J.
      Science (Washington, DC, United States) (2018), 362 (6410), 69-72CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Photocatalysis based on optically active, "plasmonic" metal nanoparticles has emerged as a promising approach to facilitate light-driven chem. conversions under far milder conditions than thermal catalysis. However, an understanding of the relation between thermal and electronic excitations has been lacking. We report the substantial light-induced redn. of the thermal activation barrier for ammonia decompn. on a plasmonic photocatalyst. We introduce the concept of a light-dependent activation barrier to account for the effect of light illumination on electronic and thermal excitations in a single unified picture. This framework provides insight into the specific role of hot carriers in plasmon-mediated photochem., which is critically important for designing energy-efficient plasmonic photocatalysts.
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    33. 33
      Tanji-Suzuki, H.; Leroux, I. D.; Schleier-Smith, M. H.; Cetina, M.; Grier, A.; Simon, J.; Vuletić, V. Interaction between Atomic Ensembles and Optical Resonators: Classical Description. Adv. At. Mol. Opt. Phys. 2011, 60, 201,  DOI: 10.1016/B978-0-12-385508-4.00004-8
      33
      Interaction between atomic ensembles and optical resonators: classical description
      Tanji-Suzuki, Haruka; Leroux, Ian D.; Schleier-Smith, Monika H.; Cetina, Marko; Grier, Andrew T.; Simon, Jonathan; Vuletic, Vladan
      Advances in Atomic, Molecular, and Optical Physics (2011), 60 (), 201-237CODEN: AAMPE9; ISSN:1049-250X. (Elsevier Inc.)
      Many effects in the interaction between atoms and a cavity that are usually described in quantum mech. terms (cavity quantum electrodynamics, cavity QED) can be understood and quant. analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit expressions for the coupling of single atoms and at. ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role and is given a geometrical interpretation. The classical anal. yields transparent, intuitive results that are useful for analyzing applications of cavity QED such as atom detection and counting, cavity cooling, cavity spin squeezing, cavity spin optomechanics, or phase transitions assocd. with the self-organization of the ensemble-light system.
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    34. 34
      Kewes, G.; Binkowski, F.; Burger, S.; Zschiedrich, L.; Benson, O. Heuristic Modeling of Strong Coupling in Plasmonic Resonators. ACS Photonics 2018, 5, 4089,  DOI: 10.1021/acsphotonics.8b00766
      34
      Heuristic Modeling of Strong Coupling in Plasmonic Resonators
      Kewes, Guenter; Binkowski, Felix; Burger, Sven; Zschiedrich, Lin; Benson, Oliver
      ACS Photonics (2018), 5 (10), 4089-4097CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      A heuristic modeling approach is presented for strongly coupled systems based on plasmonic nanoparticles and dipolar emitters that accounts for such broadening and elucidates on recent expts. with single emitters. The focus is explicitly on a clear and intuitive classical description that uses established methods, easy to use within typical Maxwell solvers. The heuristic model (i) provides exptl. relevant nos. such as emitter densities, and spectra, (ii) allows discrimination of systems which can reach the strong coupling regime from those which cannot, (iii) allows identification of optimization routes and (iv) nicely matches with exptl. findings. An approach related to quasi normal modes and extinction simulations where the excitonic system is represented by a frequency dependent permittivity is used. Two configurations with many but also single emitters which were studied in recent expts. are examples.
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    35. 35
      Sáez-Blázquez, R.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Theory of Energy Transfer in Organic Nanocrystals. Adv. Opt. Mater. 2020, 8, 2001447,  DOI: 10.1002/adom.202001447
      35
      Theory of Energy Transfer in Organic Nanocrystals
      Saez-Blazquez, Rocio; Feist, Johannes; Garcia-Vidal, Francisco J.; Fernandez-Dominguez, Antonio I.
      Advanced Optical Materials (2020), 8 (23), 2001447CODEN: AOMDAX; ISSN:2195-1071. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Recent expts. have shown that highly efficient energy transfer can take place in org. nanocrystals at extremely low acceptor densities. This striking phenomenon has been ascribed to the formation of exciton polaritons thanks to the photon confinement provided by the crystal itself. An alternative theor. model that accurately reproduces fluorescence lifetime and spectrum measurements in these systems without such an assumption is proposed. The approach treats mol.-photon interactions in the weak-coupling regime, and describes the donor and acceptor population dynamics by means of rate equations with parameters extd. from electromagnetic simulations. The phys. insight and predictive value of this model also enables the authors to propose nanocrystal configurations in which acceptor emission dominates the fluorescence spectrum at densities orders of magnitude lower than the exptl. ones.
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    36. 36
      Jaynes, E. T.; Cummings, F. W. Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser. Proc. IEEE 1963, 51, 89,  DOI: 10.1109/PROC.1963.1664
      There is no corresponding record for this reference.
    37. 37
      Kristensen, P. T.; Van Vlack, C.; Hughes, S. Generalized Effective Mode Volume for Leaky Optical Cavities. Opt. Lett. 2012, 37, 1649,  DOI: 10.1364/OL.37.001649
      37
      Generalized effective mode volume for leaky optical cavities
      Kristensen P T; Van Vlack C; Hughes S
      Optics letters (2012), 37 (10), 1649-51 ISSN:.
      We show explicitly how the commonly adopted prescription for calculating effective mode volumes is wrong and leads to uncontrolled errors. Instead, we introduce a generalized mode volume that can be easily evaluated based on the mode calculation methods typically applied in the literature, and which allows one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.
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    38. 38
      Cognée, K. G.; Yan, W.; China, F. L.; Balestri, D.; Intonti, F.; Gurioli, M.; Koenderink, A. F.; Lalanne, P. Mapping Complex Mode Volumes with Cavity Perturbation Theory. Optica, OPTICA 2019, 6, 269,  DOI: 10.1364/OPTICA.6.000269
      There is no corresponding record for this reference.
    39. 39
      Tserkezis, C.; Fernández-Domínguez, A. I.; Gonçalves, P. A. D.; Todisco, F.; Cox, J. D.; Busch, K.; Stenger, N.; Bozhevolnyi, S. I.; Mortensen, N. A.; Wolff, C. On the Applicability of Quantum-Optical Concepts in Strong-Coupling Nanophotonics. Rep. Prog. Phys. 2020, 83, 082401,  DOI: 10.1088/1361-6633/aba348
      39
      On the applicability of quantum-optical concepts in strong-coupling nanophotonics
      Tserkezis, Christos; Fernandez-Dominguez, Antonio I.; Goncalves, P. A. D.; Todisco, Francesco; Cox, Joel D.; Busch, Kurt; Stenger, Nicolas; Bozhevolnyi, Sergey I.; Mortensen, N. Asger; Wolff, Christian
      Reports on Progress in Physics (2020), 83 (8), 082401CODEN: RPPHAG; ISSN:1361-6633. (IOP Publishing Ltd.)
      Rooted in quantum optics and benefiting from its well-established foundations, strong coupling in nanophotonics has experienced increasing popularity in recent years. With nanophotonics being an expt.-driven field, the absence of appropriate theor. methods to describe ground-breaking advances has often emerged as an important issue. To address this problem, the temptation to directly transfer and extend concepts already available from quantum optics is strong, even if a rigorous justification is not always available. In this review we discuss situations where, in our view, this strategy has indeed overstepped its bounds. We focus on exciton-plasmon interactions, and particularly on the idea of calcg. the no. of excitons involved in the coupling. We analyze how, starting from an unfounded interpretation of the term N/V that appears in theor. descriptions at different levels of complexity, one might be tempted to make independent assumptions for what the no. N and the vol. V are, and attempt to calc. them sep. Such an approach can lead to different, often contradictory results, depending on the initial assumptions (e.g. through different treatments of V as the-ambiguous in plasmonics-mode vol.). We argue that the source of such contradictions is the question itself-How many excitons are coupled, which disregards the true nature of the coupled components of the system, has no meaning and often not even any practical importance. If one is interested in validating the quantum nature of the system-which appears to be the motivation driving the pursuit of strong coupling with small N-one could instead focus on quantities such as the photon emission rate or the second-order correlation function. While many of the issues discussed here may appear straightforward to specialists, our target audience is predominantly newcomers to the field, either students or scientists specialised in different disciplines. We have thus tried to minimise the occurrence of proofs and overly-tech. details, and instead provide a qual. discussion of analyses that should be avoided, hoping to facilitate further growth of this promising area.
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    40. 40
      Garraway, B. M. The Dicke Model in Quantum Optics: Dicke Model Revisited. Philos. Trans. R. Soc. A 2011, 369, 1137,  DOI: 10.1098/rsta.2010.0333
      There is no corresponding record for this reference.
    41. 41
      Meschede, D.; Walther, H.; Müller, G. One-Atom Maser. Phys. Rev. Lett. 1985, 54, 551,  DOI: 10.1103/PhysRevLett.54.551
      41
      One-atom maser
      Meschede, D.; Walther, H.; Mueller, G.
      Physical Review Letters (1985), 54 (6), 551-4CODEN: PRLTAO; ISSN:0031-9007.
      The exchange of photons between single Rydberg atoms and a single mode of a superconducting cavity with a quality factor Q = 8 × 108 at 2 K was obsd. Signals could still be detected with an av. no. of only 0.06 atom simultaneously in the cavity. With 1 Rydberg atom, the linewidth of the maser transition at ∼21 GHz was power broadened and at higher densities asymmetry of the transition was obsd., which is ascribed to an a.c. Stark effect.
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    42. 42
      Rempe, G.; Walther, H.; Klein, N. Observation of Quantum Collapse and Revival in a One-Atom Maser. Phys. Rev. Lett. 1987, 58, 353,  DOI: 10.1103/PhysRevLett.58.353
      42
      Observation of quantum collapse and revival in a one-atom maser
      Rempe, Gerhard; Walther, Herbert; Klein, Norbert
      Physical Review Letters (1987), 58 (4), 353-6CODEN: PRLTAO; ISSN:0031-9007.
      The dynamics of the interaction of a single Rydberg atom with a single mode of an electromagnetic field in a superconducting cavity was investigated. Velocity-selected atoms were used, and the evolution of the at. inversion as atom and field exchange energy was obsd. The quantum collapse and revival predicted by the E.T. Jaynes-F.W. Cummings (1963) model were demonstrated exptl. The evaluation of the dynamic behavior of the atoms allows detg. the statistics of the few photons in the cavity.
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    43. 43
      Reithmaier, J. P.; Sȩk, G.; Löffler, A.; Hofmann, C.; Kuhn, S.; Reitzenstein, S.; Keldysh, L. V.; Kulakovskii, V. D.; Reinecke, T. L.; Forchel, A. Strong Coupling in a Single Quantum Dot–Semiconductor Microcavity System. Nature 2004, 432, 197,  DOI: 10.1038/nature02969
      43
      Strong coupling in a single quantum dot-semiconductor microcavity system
      Reithmaier, J. P.; Sek, G.; Loeffler, A.; Hofmann, C.; Kuhn, S.; Reitzenstein, S.; Keldysh, L. V.; Kulakovskii, V. D.; Reinecke, T. L.; Forchel, A.
      Nature (London, United Kingdom) (2004), 432 (7014), 197-200CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      The authors report the observation of strong coupling of a single 2-level solid-state system with a photon, as realized by a single quantum dot in a semiconductor microcavity. The strong coupling is manifest in photoluminescence data that display anti-crossings between the quantum dot exciton and cavity-mode dispersion relations, characterized by a vacuum Rabi splitting of ∼140 μeV.
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    44. 44
      Santhosh, K.; Bitton, O.; Chuntonov, L.; Haran, G. Vacuum Rabi Splitting in a Plasmonic Cavity at the Single Quantum Emitter Limit. Nat. Commun. 2016, 7, 11823,  DOI: 10.1038/ncomms11823
      44
      Vacuum Rabi splitting in a plasmonic cavity at the single quantum emitter limit
      Santhosh, Kotni; Bitton, Ora; Chuntonov, Lev; Haran, Gilad
      Nature Communications (2016), 7 (), ncomms11823CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The strong interaction of individual quantum emitters with resonant cavities is of fundamental interest for understanding light-matter interactions. Plasmonic cavities hold the promise of attaining the strong coupling regime even under ambient conditions and within subdiffraction vols. Recent expts. revealed strong coupling between individual plasmonic structures and multiple org. mols.; however, strong coupling at the limit of a single quantum emitter has not been reported so far. Here we demonstrate vacuum Rabi splitting, a manifestation of strong coupling, using silver bowtie plasmonic cavities loaded with semiconductor quantum dots (QDs). A transparency dip is obsd. in the scattering spectra of individual bowties with one to a few QDs, which are directly counted in their gaps. A coupling rate as high as 120 meV is registered even with a single QD, placing the bowtie-QD constructs close to the strong coupling regime. These observations are verified by polarization-dependent expts. and validated by electromagnetic calcns.
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    45. 45
      Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S. J.; Scherman, O. A.; Rosta, E.; Demetriadou, A.; Fox, P.; Hess, O.; Baumberg, J. J. Single-Molecule Strong Coupling at Room Temperature in Plasmonic Nanocavities. Nature 2016, 535, 127,  DOI: 10.1038/nature17974
      45
      Single-molecule strong coupling at room temperature in plasmonic nanocavities
      Chikkaraddy, Rohit; de Nijs, Bart; Benz, Felix; Barrow, Steven J.; Scherman, Oren A.; Rosta, Edina; Demetriadou, Angela; Fox, Peter; Hess, Ortwin; Baumberg, Jeremy J.
      Nature (London, United Kingdom) (2016), 535 (7610), 127-130CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Photon emitters placed in an optical cavity experience an environment that changes how they are coupled to the surrounding light field. In the weak-coupling regime, the extn. of light from the emitter is enhanced. But more profound effects emerge when single-emitter strong coupling occurs: mixed states are produced that are part light, part matter, forming building blocks for quantum information systems and for ultralow-power switches and lasers. Such cavity quantum electrodynamics has until now been the preserve of low temps. and complicated fabrication methods, compromising its use. Here, by scaling the cavity vol. to less than 40 cubic nanometers and using host-guest chem. to align one to ten protectively isolated methylene-blue mols., we reach the strong-coupling regime at room temp. and in ambient conditions. Dispersion curves from more than 50 such plasmonic nanocavities display characteristic light-matter mixing, with Rabi frequencies of 300 millielectronvolts for ten methylene-blue mols., decreasing to 90 millielectronvolts for single mols.-matching quant. models. Statistical anal. of vibrational spectroscopy time series and dark-field scattering spectra provides evidence of single-mol. strong coupling. This dressing of mols. with light can modify photochem., opening up the exploration of complex natural processes such as photosynthesis and the possibility of manipulating chem. bonds.
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    46. 46
      Liu, R.; Zhou, Z.-K.; Yu, Y.-C.; Zhang, T.; Wang, H.; Liu, G.; Wei, Y.; Chen, H.; Wang, X.-H. Strong Light-Matter Interactions in Single Open Plasmonic Nanocavities at the Quantum Optics Limit. Phys. Rev. Lett. 2017, 118, 237401,  DOI: 10.1103/PhysRevLett.118.237401
      46
      Strong light-matter interactions in single open plasmonic nanocavities at the quantum optics limit
      Liu, Renming; Zhou, Zhang-Kai; Yu, Yi-Cong; Zhang, Tengwei; Wang, Hao; Liu, Guanghui; Wei, Yuming; Chen, Huanjun; Wang, Xue-Hua
      Physical Review Letters (2017), 118 (23), 237401/1-237401/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Reaching the quantum optics limit of strong light-matter interactions between a single exciton and a plasmon mode is highly desirable, because it opens up possibilities to explore room-temp. quantum devices operating at the single-photon level. However, two challenges severely hinder the realization of this limit: the integration of single-exciton emitters with plasmonic nanostructures and making the coupling strength at the single-exciton level overcome the large damping of the plasmon mode. Here, we demonstrate that these two hindrances can be overcome by attaching individual J aggregates to single cuboid Au@Ag nanorods. In such hybrid nanosystems, both the ultrasmall mode vol. of ∼71 nm3 and the ultrashort interaction distance of less than 0.9 nm make the coupling coeff. between a single J-aggregate exciton and the cuboid nanorod as high as ∼41.6 meV, enabling strong light-matter interactions to be achieved at the quantum optics limit in single open plasmonic nanocavities.
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    47. 47
      Li, W.; Zhou, Q.; Zhang, P.; Chen, X.-W. Bright Optical Eigenmode of 1 nm3 Mode Volume. Phys. Rev. Lett. 2021, 126, 257401,  DOI: 10.1103/PhysRevLett.126.257401
      47
      Bright Optical Eigenmode of 1 nm3 Mode Volume
      Li, Wancong; Zhou, Qiang; Zhang, Pu; Chen, Xue-Wen
      Physical Review Letters (2021), 126 (25), 257401CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode vols. of about 1 nm3. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4x107 times intensity enhancement.
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    48. 48
      Wu, T.; Yan, W.; Lalanne, P. Bright Plasmons with Cubic Nanometer Mode Volumes through Mode Hybridization. ACS Photonics 2021, 8, 307,  DOI: 10.1021/acsphotonics.0c01569
      48
      Bright Plasmons with Cubic Nanometer Mode Volumes through Mode Hybridization
      Wu, Tong; Yan, Wei; Lalanne, Philippe
      ACS Photonics (2021), 8 (1), 307-314CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      We propose a new interpretation for light confinement in picocavities formed by ultrasmall metallic protuberances inside the gap of metal-insulator-metal nanoresonators. We demonstrate that the protuberances support dark resonances with mode vols. comparable to their geometric vols. and that their brightness can be enhanced by several orders of magnitude when they are strongly coupled with the modes of nanoresonators with nanometric dielec. spacers. With a simple and accurate closed-form expression, we clarify the role of gap plasmons in this coupling. Based on this understanding, we propose a general strategy, exploiting strong coupling to design extremely localized modes with cubic nanometer vols. and so-far unreached brightness.
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    49. 49
      Pscherer, A.; Meierhofer, M.; Wang, D.; Kelkar, H.; Martín-Cano, D.; Utikal, T.; Götzinger, S.; Sandoghdar, V. Single-Molecule Vacuum Rabi Splitting: Four-Wave Mixing and Optical Switching at the Single-Photon Level. Phys. Rev. Lett. 2021, 127, 133603,  DOI: 10.1103/PhysRevLett.127.133603
      49
      Single-Molecule Vacuum Rabi Splitting: Four-Wave Mixing and Optical Switching at the Single-Photon Level
      Pscherer, Andre; Meierhofer, Manuel; Wang, Daqing; Kelkar, Hrishikesh; Martin-Cano, Diego; Utikal, Tobias; Goetzinger, Stephan; Sandoghdar, Vahid
      Physical Review Letters (2021), 127 (13), 133603CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      A single quantum emitter can possess a very strong intrinsic nonlinearity, but its overall promise for nonlinear effects is hampered by the challenge of efficient coupling to incident photons. Common nonlinear optical materials, on the other hand, are easy to couple to but are bulky, imposing a severe limitation on the miniaturization of photonic systems. In this Letter, we show that a single org. mol. acts as an extremely efficient nonlinear optical element in the strong coupling regime of cavity quantum electrodynamics. We report on single-photon sensitivity in nonlinear signal generation and all-optical switching. Our work promotes the use of mols. for applications such as integrated photonic circuits operating at very low powers.
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    50. 50
      Tavis, M.; Cummings, F. W. Exact Solution for an N-molecule-radiation-field Hamiltonian. Phys. Rev. 1968, 170, 379,  DOI: 10.1103/PhysRev.170.379
      There is no corresponding record for this reference.
    51. 51
      Feist, J.; Galego, J.; Garcia-Vidal, F. J. Polaritonic Chemistry with Organic Molecules. ACS Photonics 2018, 5, 205,  DOI: 10.1021/acsphotonics.7b00680
      51
      Polaritonic Chemistry with Organic Molecules
      Feist, Johannes; Galego, Javier; Garcia-Vidal, Francisco J.
      ACS Photonics (2018), 5 (1), 205-216CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      A review. The authors present an overview of the general concepts of polaritonic chem. with org. mols., i.e., the manipulation of chem. structure that can be achieved through strong coupling between confined light modes and org. mols. Strong coupling and the assocd. formation of polaritons, hybrid light-matter excitations, lead to energy shifts in such systems that can amt. to a large fraction of the uncoupled transition energy. This has recently been shown to significantly alter the chem. structure of the coupled mols., which opens the possibility to manipulate and control reactions. The authors discuss the current state of theory for describing these changes and present several applications, with a particular focus on the collective effects obsd. when many mols. are involved in strong coupling.
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    52. 52
      Ribeiro, R. F.; Martínez-Martínez, L. A.; Du, M.; Campos-Gonzalez-Angulo, J.; Yuen-Zhou, J. Polariton Chemistry: Controlling Molecular Dynamics with Optical Cavities. Chem. Sci. 2018, 9, 6325,  DOI: 10.1039/C8SC01043A
      52
      Polariton chemistry: controlling molecular dynamics with optical cavities
      Ribeiro, Raphael F.; Martinez-Martinez, Luis A.; Du, Matthew; Campos-Gonzalez-Angulo, Jorge; Yuen-Zhou, Joel
      Chemical Science (2018), 9 (30), 6325-6339CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Mol. polaritons are the optical excitations which emerge when mol. transitions interact strongly with confined electromagnetic fields. Increasing interest in the hybrid mol.-photonic materials that host these excitations stems from recent observations of their novel and tunable chem. Some of the remarkable functionalities exhibited by polaritons include the ability to induce long-range excitation energy transfer, enhance charge cond., and inhibit or accelerate chem. reactions. In this review, we explain the effective theories of mol. polaritons which form a basis for the interpretation and guidance of expts. at the strong coupling limit. The theor. discussion is illustrated with the anal. of innovative applications of strongly coupled mol.-photonic systems to chem. phenomena of fundamental importance to future technologies.
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    53. 53
      Yakovlev, V. A.; Nazin, V. G.; Zhizhin, G. N. The Surface Polariton Splitting Due to Thin Surface Film LO Vibrations. Opt. Commun. 1975, 15, 293,  DOI: 10.1016/0030-4018(75)90306-5
      53
      Surface polariton splitting due to thin surface film LO [longitudinal optical] vibrations
      Yakovlev, V. A.; Nazin, V. G.; Zhizhin, G. N.
      Optics Communications (1975), 15 (2), 293-5CODEN: OPCOB8; ISSN:0030-4018.
      A study of the influence of thin dielec. (LiF) films on the sapphire and rutile surface polaritons was carried out by the attenuated total reflection (ATR) technique and the results indicated that the LO oscillation of the 100-Å LiF film causes a splitting in the min. of the surface polariton ATR reflectivity. The splitting increases with increasing film thickness. In all cases the splitting was obsd. around a frequency lower than the LO frequency of bulk LiF indicating that the LO film frequency may be lower than the LO bulk frequency due to a film structure different from the structure of bulk LiF.
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    54. 54
      Pockrand, I.; Brillante, A.; Möbius, D. Exciton–Surface Plasmon Coupling: An Experimental Investigation. J. Chem. Phys. 1982, 77, 6289,  DOI: 10.1063/1.443834
      54
      Exciton-surface plasmon coupling: an experimental investigation
      Pockrand, I.; Brillante, A.; Moebius, D.
      Journal of Chemical Physics (1982), 77 (12), 6289-95CODEN: JCPSA6; ISSN:0021-9606.
      Langmuir-Blodgett monolayer assemblies, which contained dye mols., were deposited on Ag films. Exciton-surface plasmon interactions were studied by attenuated total reflection (ATR) spectroscopy. Reflectivity and dispersion curves for plasmon surface polaritons (PSP's) at the metal interface are reported for both angular and wavelength scans. In agreement with theory, dispersion curves from angle scans exhibit a double back bending at the transverse exciton frequency ωT (due to PSP interaction with the in plane component of the dye transition dipole moment) and at the longitudinal frequency ωL (due to PSP interaction with a perpendicular component). Correspondingly, dispersion curves from wavelength scans break into sep. branches at these frequencies.
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    55. 55
      Kaluzny, Y.; Goy, P.; Gross, M.; Raimond, J.; Haroche, S. Observation of Self-Induced Rabi Oscillations in Two-Level Atoms Excited Inside a Resonant Cavity: The Ringing Regime of Superradiance. Phys. Rev. Lett. 1983, 51, 1175,  DOI: 10.1103/PhysRevLett.51.1175
      55
      Observation of self-induced Rabi oscillations in two-level atoms excited inside a resonant cavity: the ringing regime of superradiance
      Kaluzny, Y.; Goy, P.; Gross, M.; Raimond, J. M.; Haroche, S.
      Physical Review Letters (1983), 51 (13), 1175-8CODEN: PRLTAO; ISSN:0031-9007.
      A collection of N Rydberg atoms and a resonant millimeter-wave cavity exchange energy back and forth at a rate 2(d/ℏ)E0√N, where d is the elec. dipole matrix element of the at. transition and E0 the field photon in the cavity. This expt. is a demonstration of self-induced Rabi oscillations in a 2-level atom system coupled to a single electromagnetic field mode and can also be considered as a very simple illustration of ringings in superradiant emission.
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    56. 56
      Thompson, R. J.; Rempe, G.; Kimble, H. J. Observation of Normal-Mode Splitting for an Atom in an Optical Cavity. Phys. Rev. Lett. 1992, 68, 1132,  DOI: 10.1103/PhysRevLett.68.1132
      56
      Observation of normal-mode splitting for an atom in an optical cavity
      Thompson, R. J.; Rempe, G.; Kimble, H. J.
      Physical Review Letters (1992), 68 (8), 1132-5CODEN: PRLTAO; ISSN:0031-9007.
      An investigation of the spectral response of a small collection of two-state atoms strongly coupled to the field of a high-finesse optical resonator is described for mean no. ‾N ≤ 10 atoms. For weak excitation, a coupling-induced normal-mode splitting is obsd. even for one intracavity atom, representing a direct spectroscopic measurement of the so-called vacuum Rabi splitting for the atom-cavity system.
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    57. 57
      Weisbuch, C.; Nishioka, M.; Ishikawa, A.; Arakawa, Y. Observation of the Coupled Exciton-Photon Mode Splitting in a Semiconductor Quantum Microcavity. Phys. Rev. Lett. 1992, 69, 3314,  DOI: 10.1103/PhysRevLett.69.3314
      57
      Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity
      Weisbuch, C.; Nishioka, M.; Ishikawa, A.; Arakawa, Y.
      Physical Review Letters (1992), 69 (23), 3314-17CODEN: PRLTAO; ISSN:0031-9007.
      The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splittings when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons and the electromagnetic field of the microcavity. An exciton oscillator strength of 4 × 1012 cm-2 is deduced for 76-Å quantum wells.
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    58. 58
      Houdré, R.; Weisbuch, C.; Stanley, R. P.; Oesterle, U.; Pellandini, P.; Ilegems, M. Measurement of Cavity-Polariton Dispersion Curve from Angle-Resolved Photoluminescence Experiments. Phys. Rev. Lett. 1994, 73, 2043,  DOI: 10.1103/PhysRevLett.73.2043
      58
      Measurement of cavity-polariton dispersion curve from angle-resolved photoluminescence experiments
      Houdre, R.; Weisbuch, C.; Stanley, R. P.; Eesterle, U.; Pellandini, P.; Ilegems, M.
      Physical Review Letters (1994), 73 (15), 2043-6CODEN: PRLTAO; ISSN:0031-9007.
      We study the photoluminescence of quantum well excitons imbedded in monolithic microcavities. In the strong coupling regime, a coupled-mode situation develops, the cavity polariton. We describe a model of the photoluminescence phenomenon in this regime, which by comparison with expts. enables us to det. the cavity-polariton dispersion curve. An excellent agreement with a theor. model is found.
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    59. 59
      Kelkar, P.; Kozlov, V.; Jeon, H.; Nurmikko, A. V.; Chu, C.-C.; Grillo, D. C.; Han, J.; Hua, C. G.; Gunshor, R. L. Excitons in a II-VI Semiconductor Microcavity in the Strong-Coupling Regime. Phys. Rev. B 1995, 52, R5491,  DOI: 10.1103/PhysRevB.52.R5491
      59
      Excitons in a II-VI semiconductor microcavity in the strong-coupling regime
      Kelkar, P.; Kozlov, V.; Jeon, H.; Nurmikko, A. V.; Chu, C. C.; Grillo, D. C.; Han, J.; Hua, C. G.; Gunshor, R. L.
      Physical Review B: Condensed Matter (1995), 52 (8), R5491-R5494CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      Microcavities which contained Zn-Cd-Se quantum wells as the resonant medium were fabricated and tested at blue-green wavelengths. The authors saw clear evidence of coupled-mode behavior at the n=1 heavy-hole exciton in both angle and temp. tuning expts., with anticrossing (vacuum-Rabi) splittings approaching 20 meV. The exciton-cavity interaction was consistent with predictions by theory in the strong-coupling regime, and illustrated the impact of the large oscillator strength available in II-VI compds.
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    60. 60
      Lidzey, D. G.; Bradley, D. D. C.; Skolnick, M. S.; Virgili, T.; Walker, S.; Whittaker, D. M. Strong Exciton-Photon Coupling in an Organic Semiconductor Microcavity. Nature 1998, 395, 53,  DOI: 10.1038/25692
      60
      Strong exciton-photon coupling in an organic semiconductor microcavity
      Lidzey, D. G.; Gradley, D. D. C.; Skolnick, M. S.; Virgili, T.; Walker, S.; Whittaker, D. M.
      Nature (London) (1998), 395 (6697), 53-55CODEN: NATUAS; ISSN:0028-0836. (Macmillan Magazines)
      The modification and control of exciton-photon interactions in semiconductors is of both fundamental and practical interest, being of direct relevance to the design of improved light-emitting diodes, photodetectors and lasers. In a semiconductor microcavity, the confined electromagnetic field modifies the optical transitions of the material. Two distinct types of interaction are possible: weak and strong coupling. In the former perturbative regime, the spectral and spatial distribution of the emission is modified but exciton dynamics are little altered. In the latter case, however, mixing of exciton and photon states occurs leading to strongly modified dynamics. Both types of effect were obsd. in planar microcavity structures in inorg. semiconductor quantum wells and bulk layers. But org. semiconductor microcavities were studied only in the weak-coupling regime. An org. semiconductor microcavity that operates in the strong-coupling regime is reported. Characteristic mixing is seen of the exciton and photon modes (anti-crossing), and a room-temp. vacuum Rabi splitting (an indicator of interaction strength) that is an order of magnitude larger than the previously reported highest values for inorg. semiconductors. The results may lead to new structures and device concepts incorporating hybrid states of org. and inorg. excitons, and suggest that polariton lasing may be possible.
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    61. 61
      (a) Abujetas, D. R.; Feist, J.; García-Vidal, F. J.; Gómez Rivas, J.; Sánchez-Gil, J. A. Strong Coupling between Weakly Guided Semiconductor Nanowire Modes and an Organic Dye. Phys. Rev. B 2019, 99, 205409,  DOI: 10.1103/PhysRevB.99.205409
      61a
      Strong coupling between weakly guided semiconductor nanowire modes and an organic dye
      Abujetas, Diego R.; Feist, Johannes; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez; Sanchez-Gil, Jose A.
      Physical Review B (2019), 99 (20), 205409CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      The light-matter coupling between electromagnetic modes guided by a semiconductor nanowire and excitonic states of mols. localized in its surrounding media is studied from both classical and quantum perspectives, with the aim of describing the strong-coupling regime. Weakly guided modes (bare photonic modes) are found through a classical anal., identifying those lowest-order modes presenting large electromagnetic fields spreading outside the nanowire while preserving their robust guided behavior. Exptl. fits of the dielec. permittivity of an org. dye that exhibits excitonic states are used for realistic scenarios. A quantum model properly confirms through an avoided mode crossing that the strong-coupling regime can be achieved for this configuration, leading to Rabi splitting values above 100 meV. In addn., it is shown that the coupling strength depends on the fraction of energy spread outside the nanowire, rather than on the mode field localization. These results open up a new avenue towards strong-coupling phenomenol. involving propagating modes in nonabsorbing media.
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      (b) Abujetas, D. R.; Feist, J.; García-Vidal, F. J.; Rivas, J. G.; Sánchez-Gil, J. A. Erratum: Strong Coupling between Weakly Guided Semiconductor Nanowire Modes and an Organic Dye. Phys. Rev. B 2020, 102, 239901,  DOI: 10.1103/PhysRevB.102.239901
      61b
      Erratum: Strong coupling between weakly guided semiconductor nanowire modesand an organic dye [Phys. Rev. B 99, 205409 (2019)]
      Abujetas, Diego R.; Feist, Johannes; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez; Sanchez-Gil, Jose A.
      Physical Review B (2020), 102 (23), 239901/1CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      There is no expanded citation for this reference.
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    62. 62
      Canales, A.; Baranov, D. G.; Antosiewicz, T. J.; Shegai, T. Abundance of Cavity-Free Polaritonic States in Resonant Materials and Nanostructures. J. Chem. Phys. 2021, 154, 024701,  DOI: 10.1063/5.0033352
      62
      Abundance of cavity-free polaritonic states in resonant materials and nanostructures
      Canales, Adriana; Baranov, Denis G.; Antosiewicz, Tomasz J.; Shegai, Timur
      Journal of Chemical Physics (2021), 154 (2), 024701CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Strong coupling between various kinds of material excitations and optical modes has recently shown potential to modify chem. reaction rates in both excited and ground states. The ground-state modification in chem. reaction rates has usually been reported by coupling a vibrational mode of an org. mol. to the vacuum field of an external optical cavity, such as a planar Fabry-Perot microcavity made of two metallic mirrors. However, using an external cavity to form polaritonic states might (i) limit the scope of possible applications of such systems and (ii) might be unnecessary. Here, we highlight the possibility of using optical modes sustained by materials themselves to self-couple to their own electronic or vibrational resonances. By tracing the roots of the corresponding dispersion relations in the complex frequency plane, we show that electronic and vibrational polaritons are natural eigenstates of bulk and nanostructured resonant materials that require no external cavity. Several concrete examples such as a slab of the excitonic material and a spherical water droplet in vacuum are shown to reach the regime of such cavity-free self-strong coupling. The abundance of cavity-free polaritons in simple and natural structures points at their relevance and potential practical importance for the emerging field of polaritonic chem., exciton transport, and modified material properties. (c) 2021 American Institute of Physics.
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    63. 63
      Barra-Burillo, M.; Muniain, U.; Catalano, S.; Autore, M.; Casanova, F.; Hueso, L. E.; Aizpurua, J.; Esteban, R.; Hillenbrand, R. Microcavity Phonon Polaritons from the Weak to the Ultrastrong Phonon–Photon Coupling Regime. Nat. Commun. 2021, 12, 6206,  DOI: 10.1038/s41467-021-26060-x
      63
      Microcavity phonon polaritons from the weak to the ultrastrong phonon-photon coupling regime
      Barra-Burillo Maria; Catalano Sara; Autore Marta; Casanova Felix; Hueso Luis E; Muniain Unai; Aizpurua Javier; Esteban Ruben; Casanova Felix; Hueso Luis E; Hillenbrand Rainer; Aizpurua Javier; Esteban Ruben; Hillenbrand Rainer
      Nature communications (2021), 12 (1), 6206 ISSN:.
      Strong coupling between molecular vibrations and microcavity modes has been demonstrated to modify physical and chemical properties of the molecular material. Here, we study the less explored coupling between lattice vibrations (phonons) and microcavity modes. Embedding thin layers of hexagonal boron nitride (hBN) into classical microcavities, we demonstrate the evolution from weak to ultrastrong phonon-photon coupling when the hBN thickness is increased from a few nanometers to a fully filled cavity. Remarkably, strong coupling is achieved for hBN layers as thin as 10 nm. Further, the ultrastrong coupling in fully filled cavities yields a polariton dispersion matching that of phonon polaritons in bulk hBN, highlighting that the maximum light-matter coupling in microcavities is limited to the coupling strength between photons and the bulk material. Tunable cavity phonon polaritons could become a versatile platform for studying how the coupling strength between photons and phonons may modify the properties of polar crystals.
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    64. 64
      Hopfield, J. Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals. Phys. Rev. 1958, 112, 1555,  DOI: 10.1103/PhysRev.112.1555
      64
      Theory of the contribution of excitons to the complex dielectric constant of crystals
      Hopfield, J. J.
      Physical Review (1958), 112 (), 1555-67CODEN: PHRVAO; ISSN:0031-899X.
      A more complete theory is developed which is better than the semi-classical theory which, while satisfactory for interband transition absorption, is inadequate for exciton state light absorption. Excitons are approx. bosons, and, in interaction with the electromagnetic field, their field assumes the role of the classical polarization field. The eigenstates of the crystal-field system are photon-exciton mixtures. The ordinary one-quantum optical lifetime of an excitation is infinite; absorption occurs only on introduction of 3-body processes. The theory includes local field effects, leading to Lorentz local field correction when it is applicable. A Smakula equation is derived for the oscillator strength in terms of the integrated absorption const.
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    65. 65
      Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J. Strong Coupling between Surface Plasmons and Excitons in an Organic Semiconductor. Phys. Rev. Lett. 2004, 93, 036404,  DOI: 10.1103/PhysRevLett.93.036404
      65
      Strong Coupling between Surface Plasmons and Excitons in an Organic Semiconductor
      Bellessa, J.; Bonnand, C.; Plenet, J. C.; Mugnier, J.
      Physical Review Letters (2004), 93 (3), 036404/1-036404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The authors report on the observation of a strong coupling between a surface plasmon and an exciton. Reflectometry expts. were performed on an org. semiconductor, namely, cyanide dye J aggregates, deposited on a Ag film. The dispersion lines present an anticrossing that is the signature of a strong plasmon-exciton coupling. Mixed states are formed in a similar way as microcavities polaritons. The Rabi splitting characteristic of this coupling reaches 180 meV at room temp. The emission of the low energy plasmon-exciton mixed state was obsd. and is largely shifted from the uncoupled emission.
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    66. 66
      Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W. Strong Coupling between Surface Plasmon-Polaritons and Organic Molecules in Subwavelength Hole Arrays. Phys. Rev. B 2005, 71, 035424,  DOI: 10.1103/PhysRevB.71.035424
      66
      Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays
      Dintinger, J.; Klein, S.; Bustos, F.; Barnes, W. L.; Ebbesen, T. W.
      Physical Review B: Condensed Matter and Materials Physics (2005), 71 (3), 035424/1-035424/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      The interaction of a J-aggregate and surface plasmon polariton modes of a subwavelength hole array were studied. By measuring the effects of hole array period, angular dispersion and concn. of the J-aggregate on the transmission of the array, the existence of a strong coupling regime is demonstrated with a Rabi splitting of 250 meV. This large splitting is explained by the high oscillator strength of the dye and by the high local field amplitudes generated by surface plasmons of the metallic structure.
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    67. 67
      Zengin, G.; Wersäll, M.; Nilsson, S.; Antosiewicz, T. J.; Käll, M.; Shegai, T. Realizing Strong Light-Matter Interactions between Single-Nanoparticle Plasmons and Molecular Excitons at Ambient Conditions. Phys. Rev. Lett. 2015, 114, 157401,  DOI: 10.1103/PhysRevLett.114.157401
      67
      Realizing strong light-matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions
      Zengin, Gulis; Wersaell, Martin; Nilsson, Sara; Antosiewicz, Tomasz J.; Kaell, Mikael; Shegai, Timur
      Physical Review Letters (2015), 114 (15), 157401/1-157401/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Realizing strong light-matter interactions between individual two-level systems and resonating cavities in at. and solid state systems opens up possibilities to study optical nonlinearities on a single-photon level, which can be useful for future quantum information processing networks. However, these efforts have been hampered by unfavorable exptl. conditions, such as cryogenic temps. and ultrahigh vacuum, required to study such systems and phenomena. Although several attempts to realize strong light-matter interactions at room temp. using plasmon resonances have been made, successful realizations on the single-nanoparticle level are still lacking. Here, we demonstrate the strong coupling between plasmons confined within a single silver nanoprism and excitons in moleculari J aggregates at ambient conditions. Our findings show that deep subwavelength mode vols. V together with quality factors Q that are reasonably high for plasmonic nanostructures result in a strong-coupling figure of merit- Q/√V as high as ∼6 × 103 μm-3/2, a value comparable to state-of-the-art photonic crystal and microring resonator cavities. This suggests that plasmonic nanocavities, and specifically silver nanoprisms, can be used for room temp. quantum optics.
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    68. 68
      Rodriguez, S. R. K.; Feist, J.; Verschuuren, M. A.; García Vidal, F. J.; Gómez Rivas, J. Thermalization and Cooling of Plasmon-Exciton Polaritons: Towards Quantum Condensation. Phys. Rev. Lett. 2013, 111, 166802,  DOI: 10.1103/PhysRevLett.111.166802
      68
      Thermalization and cooling of plasmon-exciton polaritons: towards quantum condensation
      Rodriguez, S. R. K.; Feist, J.; Verschuuren, M. A.; Vidal, F. J. Garcia; Rivas, J. Gomez
      Physical Review Letters (2013), 111 (16), 166802/1-166802/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We present indications of thermalization and cooling of quasiparticles, a precursor for quantum condensation, in a plasmonic nanoparticle array. We investigate a periodic array of metallic nanorods covered by a polymer layer doped with an org. dye at room temp. Surface lattice resonances of the array-hybridized plasmonic-photonic modes-couple strongly to excitons in the dye, and bosonic quasiparticles which we call plasmon-exciton polaritons (PEPs) are formed. By increasing the PEP d. through optical pumping, we observe thermalization and cooling of the strongly coupled PEP band in the light emission dispersion diagram. For increased pumping, we observe satn. of the strong coupling and emission in a new weakly coupled band, which again shows signatures of thermalization and cooling.
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    69. 69
      Frisk Kockum, A.; Miranowicz, A.; De Liberato, S.; Savasta, S.; Nori, F. Ultrastrong Coupling between Light and Matter. Nat. Rev. Phys. 2019, 1, 19,  DOI: 10.1038/s42254-018-0006-2
      There is no corresponding record for this reference.
    70. 70
      Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W. Reversible Switching of Ultrastrong Light-Molecule Coupling. Phys. Rev. Lett. 2011, 106, 196405,  DOI: 10.1103/PhysRevLett.106.196405
      70
      Reversible switching of ultrastrong light-molecule coupling
      Schwartz, T.; Hutchison, J. A.; Genet, C.; Ebbesen, T. W.
      Physical Review Letters (2011), 106 (19), 196405/1-196405/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The authors demonstrate that photochromic mols. enable switching from the weak- to ultrastrong-coupling regime reversibly, by using all-optical control. This switch is achieved by photochem. induced conformational changes in the mol. Remarkably, a Rabi splitting of 700 meV is measured at room temp., corresponding to 32% of the mol. transition energy. A similar coupling strength is demonstrated in a plasmonic structure. Such systems present a unique combination of coupling strength and functional capacities.
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    71. 71
      Gambino, S.; Mazzeo, M.; Genco, A.; Di Stefano, O.; Savasta, S.; Patanè, S.; Ballarini, D.; Mangione, F.; Lerario, G.; Sanvitto, D.; Gigli, G. Exploring Light–Matter Interaction Phenomena under Ultrastrong Coupling Regime. ACS Photonics 2014, 1, 1042,  DOI: 10.1021/ph500266d
      71
      Exploring Light-Matter Interaction Phenomena under Ultrastrong Coupling Regime
      Gambino, Salvatore; Mazzeo, Marco; Genco, Armando; Di Stefano, Omar; Savasta, Salvatore; Patane, Salvatore; Ballarini, Dario; Mangione, Federica; Lerario, Giovanni; Sanvitto, Daniele; Gigli, Giuseppe
      ACS Photonics (2014), 1 (10), 1042-1048CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Exciton-polaritons are bosonic quasiparticles that arise from the normal mode splitting of photons in a microcavity and excitons in a semiconductor material. One of the most intriguing extensions of such a light-matter interaction is the so-called ultrastrong coupling regime. It is achieved when the Rabi frequency (ΩR, the energy exchange rate between the emitter and the resonant photonic mode) reaches a considerable fraction of the emitter transition frequency, ω0. A Rabi energy splitting (2ℏΩR) of 1.12 eV is reported, and values of the coupling ratio (2ΩR/ω0) ≤0.6-fold the material band gap in org. semiconductor microcavities and ≤0.5-fold in monolithic heterostructure org. light-emitting diodes working at room temp. are recorded. With such a large coupling strength it is possible to undress the exciton homogeneous linewidth from its inhomogeneous broadening, which allows for an unprecedented narrow emission line (below the cavity finesse) for such org. LEDs. The latter can be exploited for the realization of novel monochromatic sources and near-IR org. emitting devices.
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    72. 72
      Eizner, E.; Brodeur, J.; Barachati, F.; Sridharan, A.; Kéna-Cohen, S. Organic Photodiodes with an Extended Responsivity Using Ultrastrong Light–Matter Coupling. ACS Photonics 2018, 5, 2921,  DOI: 10.1021/acsphotonics.8b00254
      72
      Organic Photodiodes with an Extended Responsivity Using Ultrastrong Light-Matter Coupling
      Eizner, Elad; Brodeur, Julien; Barachati, Fabio; Sridharan, Aravindan; Kena-Cohen, Stephane
      ACS Photonics (2018), 5 (7), 2921-2927CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      In org. photodiodes (OPDs), light is absorbed by excitons that dissoc. to generate photocurrent. Here, we demonstrate a novel type of OPD in which light is absorbed by polaritons, hybrid light-matter states. We demonstrate polariton OPDs operating in the ultrastrong coupling regime at visible and IR wavelengths. These devices can be engineered to show narrow responsivity with a very weak angle-dependence. More importantly, they can be tuned to operate in a spectral range outside that of the bare exciton absorption. Remarkably, we show that the responsivity of a polariton OPD can be pushed to near-IR wavelengths, where few org. absorbers are available, with external quantum efficiencies exceeding those of our control OPD.
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    73. 73
      Le Roux, F.; Taylor, R. A.; Bradley, D. D. C. Enhanced and Polarization-Dependent Coupling for Photoaligned Liquid Crystalline Conjugated Polymer Microcavities. ACS Photonics 2020, 7, 746,  DOI: 10.1021/acsphotonics.9b01596
      73
      Enhanced and Polarization-Dependent Coupling for Photoaligned Liquid Crystalline Conjugated Polymer Microcavities
      Le Roux, Florian; Taylor, Robert A.; Bradley, Donal D. C.
      ACS Photonics (2020), 7 (3), 746-758CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      The fabrication and optical characterization of org. microcavities contg. liq. cryst. conjugated polymers (LCCPs)-poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT), poly(9,9-dioctylfluorene) (PFO), and poly(9,9-dihexylfluorene-co-bithiophene) (F6T2)-aligned on top of a thin transparent sulfuric dye 1 (SD1) photoalignment layer are reported. The optical consts. of the aligned films were extd. using variable-angle ellipsometry, and metallic microcavities in which the ultrastrong coupling regime is manifest both for the aligned and nonaligned LCCPs were fabricated. Transition dipole moment alignment enables a systematic increase in the interaction strength, with unprecedented solid-state Rabi splittings of up to 1.80 eV, the 1st to reach energies comparable to those in the visible spectrum. With an optical gap of 2.79 eV for F6T2 this gives the highest-to-date org. microcavity coupling ratio, 65%. The coupling strength is polarization-dependent with bright polariton luminescence for TE polarization parallel to the polymer chains and either no emission or weakly coupled emission from the corresponding TM polarization.
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    74. 74
      Litinskaya, M.; Reineker, P.; Agranovich, V. M. Fast Polariton Relaxation in Strongly Coupled Organic Microcavities. J. Lumin. 2004, 110, 364,  DOI: 10.1016/j.jlumin.2004.08.033
      74
      Fast polariton relaxation in strongly coupled organic microcavities
      Litinskaya, M.; Reineker, P.; Agranovich, V. M.
      Journal of Luminescence (2004), 110 (4), 364-372CODEN: JLUMA8; ISSN:0022-2313. (Elsevier B.V.)
      The authors consider the regime of strong light-matter coupling in an org. microcavity, where large Rabi splitting can be achieved. As was shown, the excitation spectrum of such a structure, besides coherent polaritonic states, contains a no. of strongly spatially localized incoherent excited states. These states form the majority of the excited states of the microcavity and probably play the decisive role in the relaxation dynamics of the excitations in the microcavity. The authors consider the nonradiative transition from an incoherent excited state into one of the coherent states of the lower polaritonic branch accompanied by emission of a high-energy intramol. phonon. This process may det. the lifetime of incoherent excited states in the microcavity. This observation may be important in the discussion of pump-probe expts. with short pulses. This process may also play an important role for the population of the lowest energy states in org. microcavities, and hence in the problem of condensation of cavity polaritons.
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    75. 75
      Coles, D. M.; Michetti, P.; Clark, C.; Tsoi, W. C.; Adawi, A. M.; Kim, J.-S.; Lidzey, D. G. Vibrationally Assisted Polariton-Relaxation Processes in Strongly Coupled Organic-Semiconductor Microcavities. Adv. Funct. Mater. 2011, 21, 3691,  DOI: 10.1002/adfm.201100756
      75
      Vibrationally Assisted Polariton-Relaxation Processes in Strongly Coupled Organic-Semiconductor Microcavities
      Coles, David M.; Michetti, Paolo; Clark, Caspar; Tsoi, Wing Chung; Adawi, Ali M.; Kim, Ji-Seon; Lidzey, David G.
      Advanced Functional Materials (2011), 21 (19), 3691-3696CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
      If a semiconductor with an electronic transition that approximates a 2-level system is placed within an optical cavity, strong coupling can occur between the confined photons and the semiconductor excitons. This coupling can gave cavity polariton states that are a coherent superposition of light and matter. If the material in the cavity is an org. semiconductor, it was predicted that interactions between Frenkel excitons, polaritons, and mol. vibrational modes will have a profound role in defining the overall relaxation dynamics of the system. Here, using temp.-dependent spectroscopy on a microcavity contg. a J-aggregated cyanine dye, a spectrum of localized vibrational modes (identified by Raman scattering) enhances the population of certain polaritonic modes by acting as an energy-loss channel to the excitons as they undergo scattering. Work demonstrates that simultaneous control of the optical properties of a cavity and the vibrational structure of a mol. dye could promote the efficient population of k = 0 polariton states, from which lasing and other cooperative phenomena may occur.
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    76. 76
      Ramezani, M.; Halpin, A.; Fernández-Domínguez, A. I.; Feist, J.; Rodriguez, S. R.-K.; Garcia-Vidal, F. J.; Gómez Rivas, J. Plasmon-Exciton-Polariton Lasing. Optica 2017, 4, 31,  DOI: 10.1364/OPTICA.4.000031
      76
      Plasmon-exciton-polariton lasing
      Ramezani, Mohammad; Halpin, Alexei; Fernandez-Dominguez, Antonio I.; Feist, Johannes; Rodriguez, Rahimzadeh-Kalaleh; Garcia-Vidal, Francisco J.; Rivas, Jaime Gomez
      Optica (2017), 4 (1), 31-37CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
      Metallic nanostructures provide a toolkit for the generation of coherent light below the diffraction limit. Plasmonic-based lasing relies on the population inversion of emitters (such as org. fluorophores) along with feedback provided by plasmonic resonances. In this regime, known as weak light-matter coupling, the radiative characteristics of the system can be described by the Purcell effect. Strong light-matter coupling between the mol. excitons and electromagnetic field generated by the plasmonic structures leads to the formation of hybrid quasi-particles known as plasmon-exciton-polaritons (PEPs). Due to the bosonic character of these quasi-particles, exciton-polariton condensation can lead to laser-like emission at much lower threshold powers than in conventional photon lasers. Here, we observe PEP lasing through a dark plasmonic mode in an array of metallic nanoparticles with a low threshold in an optically pumped org. system. Interestingly, the threshold power of the lasing is reduced by increasing the degree of light - matter coupling in spite of the degrdn. of the quantum efficiency of the active material, highlighting the ultrafast dynamic responsible for the lasing, i.e., stimulated scattering. These results demonstrate a unique room-temp. platform for exploring the physics of exciton-polaritons in an open-cavity architecture and pave the road toward the integration of this on-chip lasing device with the current photonics and active metamaterial planar technologies.
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    77. 77
      Keeling, J.; Kéna-Cohen, S. Bose–Einstein Condensation of Exciton-Polaritons in Organic Microcavities. Annu. Rev. Phys. Chem. 2020, 71, 435,  DOI: 10.1146/annurev-physchem-010920-102509
      77
      Bose-Einstein Condensation of Exciton-Polaritons in Organic Microcavities
      Keeling, Jonathan; Kena-Cohen, Stephane
      Annual Review of Physical Chemistry (2020), 71 (), 435-459CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
      A review. Bose-Einstein condensation describes the macroscopic occupation of a single-particle mode: the condensate. This state can in principle be realized for any particles obeying Bose-Einstein statistics; this includes hybrid light-matter excitations known as polaritons. Some of the unique optoelectronic properties of org. mols. make them esp. well suited for the realization of polariton condensates. Exciton-polaritons form in optical cavities when electronic excitations couple collectively to the optical mode supported by the cavity. These polaritons obey bosonic statistics at moderate densities, are stable at room temp., and have been obsd. to form a condensed or lasing state. Understanding the optimal conditions for polariton condensation requires careful modeling of the complex photophysics of org. mols. In this article, we introduce the basic physics of exciton-polaritons and condensation and review expts. demonstrating polariton condensation in mol. materials.
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    78. 78
      Garcia-Vidal, F. J.; Feist, J. Long-Distance Operator for Energy Transfer. Science 2017, 357, 1357,  DOI: 10.1126/science.aao4268
      78
      Long-distance operator for energy transfer
      Garcia-Vidal, Francisco J.; Feist, Johannes
      Science (Washington, DC, United States) (2017), 357 (6358), 1357-1358CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      There is no expanded citation for this reference.
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    79. 79
      Du, M.; Martínez-Martínez, L.; Ribeiro, R.; Hu, Z.; Menon, V.; Yuen-Zhou, J. Theory for Polariton-Assisted Remote Energy Transfer. Chem. Sci. 2018, 9, 6659,  DOI: 10.1039/C8SC00171E
      79
      Theory for polariton-assisted remote energy transfer
      Du, Matthew; Martinez-Martinez, Luis A.; Ribeiro, Raphael F.; Hu, Zixuan; Menon, Vinod M.; Yuen-Zhou, Joel
      Chemical Science (2018), 9 (32), 6659-6669CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chem. reactivity of mol. systems. Recent expts. have demonstrated remarkable distance-independent long-range energy transfer between mols. strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect". This theor. study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between mol. systems.
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    80. 80
      Sáez-Blázquez, R.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Organic Polaritons Enable Local Vibrations to Drive Long-Range Energy Transfer. Phys. Rev. B 2018, 97, 241407R
      80
      Organic polaritons enable local vibrations to drive long-range energy transfer
      Saez-Blazquez, R.; Feist, J.; Fernandez-Dominguez, A. I.; Garcia-Vidal, F. J.
      Physical Review B (2018), 97 (24), 241407/1-241407/5CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      Long -range energy transfer in org. mols. has been exptl. obtained by strongly coupling their electronic excitations to a confined electromagnetic cavity mode. Here, we shed light into the polariton-mediated mechanism behind this process for different configurations: donor and acceptor mols. either intermixed or phys. sepd.We numerically address the phenomenon by means of Bloch-Redfield theory, which allows us to reproduce the effect of complex vibrational reservoirs characteristic of org. mols. Our findings reveal the key role played by the middle polariton as the nonlocal intermediary in the transmission of excitations from donor to acceptor mols. We also provide anal. insights on the key phys. magnitudes that help to optimize the efficiency of the long-range energy transfer.
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    81. 81
      Georgiou, K.; Jayaprakash, R.; Othonos, A.; Lidzey, D. G. Ultralong-Range Polariton-Assisted Energy Transfer in Organic Microcavities. Angew. Chem., Int. Ed. 2021, 60, 16661,  DOI: 10.1002/anie.202105442
      81
      Ultralong-Range Polariton-Assisted Energy Transfer in Organic Microcavities
      Georgiou, Kyriacos; Jayaprakash, Rahul; Othonos, Andreas; Lidzey, David G.
      Angewandte Chemie, International Edition (2021), 60 (30), 16661-16667CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Non-radiative energy transfer between spatially-sepd. mols. in a microcavity can occur when an excitonic state on both mols. are strongly-coupled to the same optical mode, forming so-called "hybrid" polaritons. Such energy transfer has previously been explored when thin-films of different mols. are relatively closely spaced (≈100 nm). In this manuscript, we explore strong-coupled microcavities in which thin-films of two J-aggregated mol. dyes were sepd. by a spacer layer having a thickness of up to 2μm. Here, strong light-matter coupling and hybridization between the excitonic transition is identified using white-light reflectivity and photoluminescence emission. We use steady-state spectroscopy to demonstrate polariton-mediated energy transfer between such coupled states over "mesoscopic distances", with this process being enhanced compared to non-cavity control structures.
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    82. 82
      Satapathy, S.; Khatoniar, M.; Parappuram, D. K.; Liu, B.; John, G.; Feist, J.; Garcia-Vidal, F. J.; Menon, V. M. Selective Isomer Emission via Funneling of Exciton Polaritons. Sci. Adv. 2021, 7, eabj0997,  DOI: 10.1126/sciadv.abj0997
      There is no corresponding record for this reference.
    83. 83
      Sáez-Blázquez, R.; Feist, J.; Fernández-Domínguez, A. I.; García-Vidal, F. J. Enhancing Photon Correlations through Plasmonic Strong Coupling. Optica 2017, 4, 1363,  DOI: 10.1364/OPTICA.4.001363
      83
      Enhancing photon correlations through plasmonic strong coupling
      Saez-Blazquez, R.; Feist, J.; Fernandez-Dominguez, A. I.; Garcia-Vidal, F. J.
      Optica (2017), 4 (11), 1363-1367CODEN: OPTIC8; ISSN:2334-2536. (Optical Society of America)
      There is an increasing scientific and technol. interest in the design and implementation of nanoscale sources of quantum light. Here, we investigate the quantum statistics of the light scattered from a plasmonic nanocavity coupled to a mesoscopic ensemble of emitters under low coherent pumping. We present an anal. description of the intensity correlations taking place in these systems and unveil the fingerprint of plasmon-exciton-polaritons in them. Our findings reveal that plasmonic cavities are able to retain and enhance excitonic nonlinearities, even when the no. of emitters is large. This makes plasmonic strong coupling a promising route for generating nonclassical light beyond the single-emitter level.
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    84. 84
      Sáez-Blázquez, R.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Photon Statistics in Collective Strong Coupling: Nanocavities and Microcavities. Phys. Rev. A 2018, 98, 013839,  DOI: 10.1103/PhysRevA.98.013839
      84
      Photon statistics in collective strong coupling: nanocavities and microcavities
      Saez-Blazquez, R.; Feist, J.; Garcia-Vidal, F. J.; Fernandez-Dominguez, A. I.
      Physical Review A (2018), 98 (1), 013839CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)
      There exists a growing interest in the properties of the light generated by hybrid systems involving a mesoscopic no. of emitters as a means of providing macroscopic quantum light sources. In this work, the quantum correlations of the light emitted by a collection of emitters coupled to a generic optical cavity are studied theor. using an effective Hamiltonian approach. Starting from the single-emitter level, we analyze the persistence of photon antibunching as the ensemble size increases. Not only is the photon blockade effect identifiable, but photon antibunching originated from destructive interference processes, the so-called unconventional antibunching, is also present. We study the dependence of these two types of neg. correlations on the spectral detuning between cavity and emitters, as well as its evolution as the time delay between photon detections increases. Throughout this work, the performance of plasmonic nanocavities and dielec. microcavities is compared: despite the distinct energy scales and the differences introduced by their resp. open and closed character, the bunching and antibunching phenomenol. presents remarkable similarities in both types of cavities.
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    85. 85
      Li, R.-Q.; Hernángomez-Pérez, D.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Transformation Optics Approach to Plasmon-Exciton Strong Coupling in Nanocavities. Phys. Rev. Lett. 2016, 117, 107401,  DOI: 10.1103/PhysRevLett.117.107401
      85
      Transformation optics approach to plasmon-exciton strong coupling in nanocavities
      Li, Rui-Qi; Hernangomez-Perez, D.; Garcia-Vidal, F. J.; Fernandez-Dorninguez, A. I.
      Physical Review Letters (2016), 117 (10), 107401/1-107401/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We investigate the conditions yielding plasmon-exciton strong coupling at the single emitter level in the gap between two metal nanoparticles. Inspired by transformation optics ideas, a quasianal. approach is developed that makes possible a thorough exploration of this hybrid system incorporating the full richness of its plasmonic spectrum. This allows us to reveal that by placing the emitter away from the cavity center, its coupling to multipolar dark modes of both even and odd parity increases remarkably. This way, reversible dynamics in the population of the quantum emitter takes place in feasible implementations of this archetypal nanocavity.
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    86. 86
      Li, R.-Q.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Plasmon-Exciton Coupling in Symmetry-Broken Nanocavities. ACS Photonics 2018, 5, 177,  DOI: 10.1021/acsphotonics.7b00616
      86
      Plasmon-Exciton Coupling in Symmetry-Broken Nanocavities
      Li, Rui-Qi; Garcia-Vidal, F. J.; Fernandez-Dominguez, A. I.
      ACS Photonics (2018), 5 (1), 177-185CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      The onset of strong coupling in the temporal dynamics of the exciton population at a single emitter interacting with symmetry-broken plasmonic nanocavities was studied. These structures consist in pairs of metallodielec. elements sepd. by a nanometric gap, with different degrees of asymmetry imposed on their geometric or material characteristics. To describe the emergence of plasmon-exciton-polaritons in these systems, the authors extend and generalize a transformation optics method previously applied to dimers of identical particles. This approach provides a natural decompn. of the spectral d. in terms of a well-defined set of plasmonic resonances, as well as an insightful description of the coupling strength dependence on the emitter position. On the 1 hand, the authors shed light into the low sensitivity of plasmon-exciton interactions to geometric asymmetry in cavities such as nanoparticle-on-a-mirror configurations. A more complex spatial and spectral dependence of the strong-coupling phenomenol. takes place in systems with material asymmetry, such as 2-metal and metal-dielec. dimers.
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    87. 87
      Huidobro, P. A.; Fernández-Domínguez, A. I. Transformation Optics for Plasmonics: From Metasurfaces to Excitonic Strong Coupling. Comptes Rendus Phys. 2020, 21, 389,  DOI: 10.5802/crphys.22
      87
      Transformation optics for plasmonics: from metasurfaces to excitonic strong coupling
      Huidobro, Paloma A.; Fernandez-Dominguez, Antonio I.
      Comptes Rendus Physique (2020), 21 (4-5), 389-408CODEN: CRPOBN; ISSN:1878-1535. (Academie des Sciences)
      A review. We review the latest theor. advances in the application of the framework of Transformation Optics for the anal. description of deeply sub-wavelength electromagnetic phenomena. First, we present a general description of the technique, together with its usual exploitation for metamaterial conception and optimization in different areas of wave physics. Next, we discuss in detail the design of plasmonic metasurfaces, including the description of singular geometries which allow for broadband absorption in ultrathin platforms. Finally, we discuss the quasi-anal. treatment of plasmon-exciton strong coupling in nanocavities at the single emitter level.
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    88. 88
      Cuartero-González, A.; Fernández-Domínguez, A. I. Light-Forbidden Transitions in Plasmon-Emitter Interactions beyond the Weak Coupling Regime. ACS Photonics 2018, 5, 3415,  DOI: 10.1021/acsphotonics.8b00678
      88
      Light-Forbidden Transitions in Plasmon-Emitter Interactions beyond the Weak Coupling Regime
      Cuartero-Gonzalez, A.; Fernandez-Dominguez, A. I.
      ACS Photonics (2018), 5 (8), 3415-3420CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      We investigate the impact of light-forbidden exciton transitions in plasmon-emitter interactions beyond the weak coupling regime. We consider a V-type quantum emitter, with dipolar and quadrupolar excited states, placed at the subnanometric gap of a particle-on-a-mirror metallic cavity. We present a fully anal. description of the near-field population dynamics and far-field scattering spectrum of the hybrid system. Our approach enables us to reveal two realistic system configurations in which the dipole-inactive exciton alters significantly and in completely opposite ways the Purcell enhancement and Rabi splitting phenomenol., effectively enlarging or reducing the emitter lifetime and generating or removing spectral features in the cavity cross section.
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    89. 89
      Neuman, T.; Esteban, R.; Casanova, D.; García-Vidal, F. J.; Aizpurua, J. Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation. Nano Lett. 2018, 18, 2358,  DOI: 10.1021/acs.nanolett.7b05297
      89
      Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation
      Neuman, Tomas; Esteban, Ruben; Casanova, David; Garcia-Vidal, Francisco J.; Aizpurua, Javier
      Nano Letters (2018), 18 (4), 2358-2364CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      As the size of a mol. emitter becomes comparable to the dimensions of a nearby optical resonator, the std. approach that considers the emitter to be a point-like dipole breaks down. By adoption of a quantum description of the electronic transitions of org. mol. emitters, coupled to a plasmonic electromagnetic field, we are able to accurately calc. the position-dependent coupling strength between a plasmon and an emitter. The spatial distribution of excitonic and photonic quantum states is found to be a key aspect in detg. the dynamics of mol. emission in ultrasmall cavities both in the weak and strong coupling regimes. Moreover, we show that the extreme localization of plasmonic fields leads to the selection rule breaking of mol. excitations.
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    90. 90
      Fregoni, J.; Haugland, T. S.; Pipolo, S.; Giovannini, T.; Koch, H.; Corni, S. Strong Coupling between Localized Surface Plasmons and Molecules by Coupled Cluster Theory. Nano Lett. 2021, 21, 6664,  DOI: 10.1021/acs.nanolett.1c02162
      90
      Strong Coupling between Localized Surface Plasmons and Molecules by Coupled Cluster Theory
      Fregoni, Jacopo; Haugland, Tor S.; Pipolo, Silvio; Giovannini, Tommaso; Koch, Henrik; Corni, Stefano
      Nano Letters (2021), 21 (15), 6664-6670CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Plasmonic nanocavities enable the confinement of mols. and electromagnetic fields within nanometric vols. As a consequence, the mols. experience a remarkably strong interaction with the electromagnetic field to such an extent that the quantum states of the system become hybrids between light and matter: polaritons. Here, we present a nonperturbative method to simulate the emerging properties of such polaritons: it combines a high-level quantum chem. description of the mol. with a quantized description of the localized surface plasmons in the nanocavity. We apply the method to mols. of realistic complexity in a typical plasmonic nanocavity, featuring also a subnanometric asperity (picocavity). Our results disclose the effects of the mutual polarization and correlation of plasmons and mol. excitations, disregarded so far. They also quantify to what extent the mol. charge d. can be manipulated by nanocavities and stand as benchmarks to guide the development of methods for mol. polaritonics.
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    91. 91
      Cuartero-González, A.; Manjavacas, A.; Fernández-Domínguez, A. I. Distortion of the Local Density of States in a Plasmonic Cavity by a Quantum Emitter. New J. Phys. 2021, 23, 073011,  DOI: 10.1088/1367-2630/ac0199
      91
      Distortion of the local density of states in a plasmonic cavity by a quantum emitter
      Cuartero-Gonzalez, Alvaro; Manjavacas, Alejandro; Fernandez-Dominguez, Antonio I.
      New Journal of Physics (2021), 23 (July), 073011CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
      We investigate how the local d. of states in a plasmonic cavity changes due to the presence of a distorting quantum emitter. To this end, we use first-order scattering theory involving electromagnetic Green's function tensors for the bare cavity connecting the positions of the emitter that distorts the d. of states and the one that probes it. The confined, quasistatic character of the plasmonic modes enables us to write the d. of states as a Lorentzian sum. This way, we identify three different mechanisms behind the asym. spectral features emerging due to the emitter distortion: the modification of the plasmonic coupling to the probing emitter, the emergence of modal-like quadratic contributions and the absorption by the distorting emitter. We apply our theory to the study of two different systems (nanoparticle-on-mirror and asym. bow-tie-like geometries) to show the generality of our approach, whose validity is tested against numerical simulations. Finally, we provide an interpretation of our results in terms of a Hamiltonian model describing the distorted cavity.
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    92. 92
      Cuartero-González, A.; Fernández-Domínguez, A. I. Dipolar and Quadrupolar Excitons Coupled to a Nanoparticle-on-Mirror Cavity. Phys. Rev. B 2020, 101, 035403,  DOI: 10.1103/PhysRevB.101.035403
      92
      Dipolar and quadrupolar excitons coupled to a nanoparticle-on-mirror cavity
      Cuartero-Gonzalez, A.; Fernandez-Dominguez, A. I.
      Physical Review B (2020), 101 (3), 035403CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      We investigate plasmon-emitter interactions in a nanoparticle-on-mirror cavity. We consider two different sorts of emitters: Those that sustain dipolar transitions and those hosting only quadrupolar, dipole-inactive excitons. By means of a fully anal. two-dimensional transformation optics approach, we calc. the light-matter coupling strengths for the full plasmonic spectrum supported by the nanocavity. We reveal the impact of finite-size effects in the exciton charge distribution and describe the population dynamics in a spontaneous emission configuration. Pushing our model beyond the quasistatic approxn., we ext. the plasmonic dipole moments, which enables us to calc. the far-field scattering spectrum of the hybrid plasmon-emitter system. Our findings, tested against fully numerical simulations, reveal the similarities and differences between the light-matter coupling phenomenol. for bright and dark excitons in nanocavities.
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    93. 93
      Sáez-Blázquez, R.; Cuartero-González, Á.; Feist, J.; García-Vidal, F. J.; Fernández-Domínguez, A. I. Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities. Nano Lett. 2022, 22, 2365,  DOI: 10.1021/acs.nanolett.1c04872
      93
      Plexcitonic Quantum Light Emission from Nanoparticle-on-Mirror Cavities
      Saez-Blazquez, Rocio; Cuartero-Gonzalez, Alvaro; Feist, Johannes; Garcia-Vidal, Francisco J.; Fernandez-Dominguez, Antonio I.
      Nano Letters (2022), 22 (6), 2365-2373CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      We investigate the quantum-optical properties of the light emitted by a nanoparticle-on-mirror cavity filled with a single quantum emitter. Inspired by recent expts., we model a dark-field setup and explore the photon statistics of the scattered light under grazing laser illumination. Exploiting anal. solns. to Maxwell's equations, we quantize the nanophotonic cavity fields and describe the formation of plasmon-exciton polaritons (or plexcitons) in the system. This way, we reveal that the rich plasmonic spectrum of the nanocavity offers unexplored mechanisms for nonclassical light generation that are more efficient than the resonant interaction between the emitter natural transition and the brightest optical mode. Specifically, we find three different sample configurations in which strongly antibunched light is produced. Finally, we illustrate the power of our approach by showing that the introduction of a second emitter in the platform can enhance photon correlations further.
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    94. 94
      Kulkarni, V.; Manjavacas, A. Quantum Effects in Charge Transfer Plasmons. ACS Photonics 2015, 2, 987,  DOI: 10.1021/acsphotonics.5b00246
      94
      Quantum Effects in Charge Transfer Plasmons
      Kulkarni, Vikram; Manjavacas, Alejandro
      ACS Photonics (2015), 2 (7), 987-992CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Metallic nanoparticles placed in close proximity support strong localized surface plasmon resonances. One such resonance, known as the charge transfer plasmon, involves the phys. transfer of electrons between the nanoparticles and, thus, exists only in dimers bridged with conductive junctions. Here we analyze the quantum effects assocd. with these type of plasmon modes by studying the optical response of a metallic dimer bridged with a two-level system. We find that the charge transfer plasmons are obsd. in the absorption spectrum only when one of the energy levels of the two-level system is resonant with the Fermi level of the nanoparticles. Furthermore, we explicitly show that, for the resonant configuration, the conductance of the junction reaches a value equal to one quantum of conductance, 2e2/h. Our results establish a connection between the optical response of plasmonic nanostructures and quantum transport phenomena, thus bringing a new perspective to quantum plasmonics.
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    95. 95
      Babaze, A.; Esteban, R.; Borisov, A. G.; Aizpurua, J. Electronic Exciton–Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture. Nano Lett. 2021, 21, 8466,  DOI: 10.1021/acs.nanolett.1c03202
      95
      Electronic Exciton-Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture
      Babaze, Antton; Esteban, Ruben; Borisov, Andrei G.; Aizpurua, Javier
      Nano Letters (2021), 21 (19), 8466-8473CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theor. addressed within the frameworks of classical electrodynamics and the time-dependent d. functional theory (TDDFT). A ful