Atomic-Scale Dynamics Probed by Photon Correlations

Light absorption and emission have their origins in fast atomic-scale phenomena. To characterize these basic steps (e.g., in photosynthesis, luminescence, and quantum optics), it is necessary to access picosecond temporal and picometer spatial scales simultaneously. In this Perspective, we describe how state-of-the-art picosecond photon correlation spectroscopy combined with luminescence induced at the atomic scale with a scanning tunneling microscope (STM) enables such studies. We outline recent STM-induced luminescence work on single-photon emitters and the dynamics of excitons, charges, molecules, and atoms as well as several prospective experiments concerning light–matter interactions at the nanoscale. We also describe future strategies for measuring and rationalizing ultrafast phenomena at the nanoscale.

L ight−matter interactions at the atomic scale are crucial to many branches of science. They constitute the basis of quantum optics, determine the efficiency of electroluminescent or photovoltaic devices, or drive photochemical processes. Fundamental understanding of such mechanisms, which is necessary for both upscaling and improving several technologies, requires direct interrogation of individual events and entities, such as how single charge-transfer events and photons interconvert and how single molecules move and undergo chemical reactions. These processes can be very fast. Routine probes of such effects involve luminescence and ultrafast laser spectroscopy, with the latter reaching the subfemtosecond regime. 1,2 However, for free propagating beams, both probes are diffraction limited, so their spatial resolution is restricted to a few hundred nanometers. This scale is 2−3 orders of magnitude above the spatial dimensions of the molecular and atomic-scale emitters of interest in this Perspective. Alternatively, scanning probe and electron microscopies permit studying emitters with even picometer precision, albeit for relatively slow (millisecond) dynamics. Recently, these techniques have also been developed for ultrafast time scales, 3,4 especially in the field of scanning tunneling microscopy (STM), in which researchers have successfully combined atomic-scale studies with time-resolved optics-based methods. 5−10 In this Perspective, we focus on the combination of STM-induced luminescence (STML) with time-resolved light detection without employing laser pulses. This partnership provides experimentalists with unique access to the dynamics of important physical processes, such as the charge transport, molecular motion, or quantum properties of light, all achieved by studying photon correlations that originate from picosecond−picometer phenomena. We present recent advances in this rapidly developing field and describe possible experiments that may further broaden our understanding of light−matter interaction dynamics at the atomic scale.

PHOTON CORRELATIONS IN PRACTICE
Because of wave−particle duality, a light beam can be considered as a stream of photons. The temporal statistics of the photons Published: June 1, 2020 In this Perspective, we focus on the combination of scanning tunneling microscopy-induced luminescence with time-resolved light detection without employing laser pulses.
within such a beam provides information on the dynamical nature of the light source, which is captured by computing photon time correlations. Mathematically, they are described by the second-order correlation function g (2) (Δt) of the electromagnetic field, defined by the time-dependent light intensity P(t): where the g (2) (Δt) function describes the likelihood to emit a photon at time delay before (Δt < 0) or after (Δt > 0) a given emission process that occurred at time t. This function is normalized such that g (2) (Δt → ±∞) = 1 because the emitter "loses memory" of all previous emission events for long time delays. Typical regimes of g (2) (Δt) are shown in Figure 1. In the simplest case, g (2) (Δt) is unity for all Δt (third row in Figure 1) if photons are emitted in independent events (Poissonian statistics), as is the case for coherent light (e.g., from a singlemode laser). Next, let us consider nonunity values of the correlation function for short delay times. The g (2) (0) > 1 condition is evidence of photon bunching for classical chaotic light (1 < g (2) (0) ≤ 2, second row in Figure 1) and superbunching (g (2) (0) > 2, top row in Figure 1), which may occur for photon pair emission or an intensity-modulated light source. Finally, there is antibunching (g (2) (0) < 1) for which the simultaneous emission of two light quanta is reduced over a time interval τ > 0, which, in turn, can relate to the intrinsic lifetime of the emitting state or its refilling time. In the extreme case of a perfect single-photon emitter, g (2) (0) = 0 (bottom row in Figure 1), two photons are never emitted simultaneously. In practice, a source is often designated as a single-photon emitter if an experiment yields g (2) (0) < 0.5 because this condition already rules out the existence of two simultaneous emission processes having the same emission rate. Due to the intrinsic time-dependent character, photon correlations are an excellent tool to explore the dynamics of quantum emitters, their associated intrinsic lifetimes, and even mechanisms of bunched emission (e.g., beam chopping).
The experimental setup that we use for a wide variety of STMbased time-resolved studies is schematically presented in Figure  2. The setup comprises a low-temperature (4 K), ultrahigh  Schematic of a scanning tunneling microscope (STM) combined with a time-resolved optical detection system. The light emitted from the tunnel junction, for example from a quantum state (QS), is collected by three lenses located in the STM head (not shown) and guided through viewports toward detectors located in the ambient (single-photon avalanche photodiodes, SPADs, and a gated optical spectrometer). A time-correlated single-photon counting (TCSPC) module enables time-resolved STML (red shaded box) and Hanbury Brown−Twiss STM (gray shaded box) measurements. AWG, arbitrary wave generator. vacuum (UHV) STM with three independent free space optical access pathways 11 for time-resolved detection systems situated in the ambient. It is one of a few similar set-ups in the field. 6,12−18 In order to address ultrafast phenomena, the electroluminescence detection is performed by single-photon avalanche photodiodes (SPADs) with 30 ps time resolution (equal to the output pulse jitter with respect to photon arrival) and by an optical spectrometer coupled to an intensifier-gated chargecoupled device (CCD) camera with a minimum gate width of 5 ns. In the following, we distinguish between the Hanbury Brown−Twiss STM (HBT-STM, photon−photon correlation) and time-resolved STML (TR-STML, voltage pulse−photon correlation) modes of operation.
In the HBT-STM intensity interferometer mode (gray box, Figure 2), 5,6,19−22 the time-correlated single-photon counting (TCSPC) PC card measures the distribution of time intervals between registered start and stop photons with a 30 ps (detector-limited) time resolution, which enables determining g (2) (Δt) using eq 1. The number of measured correlations per time bin is N = Tν 1 ν 2 τ ch , where T is the integration time, ν 1 and ν 2 are the respective count rates of the two detectors, and τ ch is the width of each time bin. Alternatively, for a configuration with only one SPAD, 23 TCSPC time tagging records the absolute arrival time of each detected photon, enabling a subsequent or on-the-fly calculation of the correlation function (see the Supporting Information for more details). However, in this onedetector configuration, the time-resolution is limited to a few μs, because of after-pulsing artifacts 24 that lead to spurious g (2) (Δt) > 1 features for Δt < 1 μs. Ultimately, the SPAD dead time (∼100 ns) limits the time resolution of the one-detector approach.
An arbitrary wave generator (AWG) enables one to send tailored 25 voltage pulses to the tunnel junction with a time resolution of approximately 1 ns, which is a limitation that results from the wires connected to the STM junction. 25,26 The TR-STML technique (pink box, Figure 2) registers the time evolution of electroluminescence (P(Δt), yellow trace in Figure  2) upon application of a rectangular voltage pulse. It is used to perform experiments for which a time resolution of 1 ns is sufficient. In contrast to HBT-STM, the events per time slot scale linearly with the detector count rate, and, due to triggering by synchronization pulses with a high repetition rate (∼1 MHz) compared to typical photon count rate (10−100 kHz), the signal-to-noise ratio is significantly increased in TR-STML.
These different setups discussed above show how dynamical studies of quantum systems with discrete levels can be performed with relative ease at the atomic scale. In all cases, the method profits from the strong local field enhancement present in tip−surface nanocavities. 27 Concurrently, the picometer precise current injection by a STM tip enables studies of entities far smaller than the diffraction limit, such as the luminescence of a single molecule at the subnanometer scale. 28,29 In general, there are two principal emission mechanisms of STML: plasmonic and excitonic. In plasmonic emission, an inelastic electron tunneling process excites nanocavity plasmon modes that may couple to far-field photons with a broadband spectrum (ΔE > 100 meV). In excitonic emission, luminescence occurs due to electron−hole recombination in a decoupled system. Sufficient decoupling can be achieved by separating the emitting system from the metallic electrodes, prominently the substrate, with a thin (d ≈ 0.5 nm) insulating film, such that the nonradiative decay of the excitation via coupling to the metal is strongly reduced, while tunneling is still sufficiently efficient. 29 Under these conditions, the emission spectrum can exhibit spectrally sharp features (ΔE < 20 meV), which can be used to identify the emitter, by comparison with, for example, photoluminescence measurements. 28,30−32 We will next focus on examples of atomic-scale processes that lead to photon bunching and antibunching. We will discuss how to model their dynamics using rate equations, an approach commonly used for analyzing optical processes in quantum optics, such as spontaneous or stimulated emission or photo-or electron-induced luminescence, including single-photon emission. 27

CLASSICAL PHOTON CORRELATIONS AT THE ATOMIC SCALE
We will start with a simple model system: a telegraphic emitter ( Figure 3). It switches randomly between an "on" and an "off" state, thus providing data that resemble historic telegraphic The picometer precise current injection by a scanning tunneling microscope tip enables studies of entities far smaller than the diffraction limit, such as the luminescence of a single molecule at the subnanometer scale. Figure 3. Telegraphic modulation of scanning tunneling microscopy-induced luminescence. (a) Schematic of plasmonic luminescence intensity modulation due to adsorbate motion below the tip. The red shading symbolizes the tip-induced plasmon. Bottom-right: Schematic correlation function g (2) (Δt) showing photon bunching over a characteristic time τ move = (k 01 + k 10 ) −1 . (b) Two level system consisting of a bright (continuously emitting with a rate k 11 , gray rounded arrow) and a dark state that the system transitions between, with rates k 01 and k 10 . (c) Measured photon bunching g (2) (Δt) (black circles) fitted by a triple-exponential function (red line) yielding characteristic time constants of 8 ms, 1 ms, and 45 μs. The slowest time constant τ move = 8 ms is assigned to the lateral diffusion of a single hydrogen molecule below the scanning tunneling microscope tip. 23 ACS Nano www.acsnano.org Perspective signals. Such systems are often encountered in molecular physics as a result of molecular motion or an oscillating chemical reaction. 33−35 A telegraphic light emitter exhibits classical (intensity-based) photon bunching, as illustrated in Figure 3, by switching between a bright "on" and a dark "off" state with time-dependent populations n 1 (t) and n 0 (t), respectively. The transition rates k 10 and k 01 describe the probabilities of switching between the two states, thus determining the time evolution of the system according to the following Master equation For initial populations n 0 (0) = 0, n 1 (0) = 1 (that is assuming an emission event at t = 0): We define the light intensity to be P(t) = ηk 11 n 1 (t) for a continuous emission from a bright state, where η is the detection efficiency and k 11 is the emission rate in the bright state. Then, we obtain the following correlation function characterizing the luminescence fluctuations: The characteristic time of the dynamics is τ move = (k 01 + k 10 ) −1 .
Because g (2) (0) = 1 + k 10 /k 01 , the photons are bunched and both rates can be extracted from a fit to the measured correlation function. A detailed discussion on this topic can be found elsewhere. 36 Photon correlations that arise from luminescence fluctuations in time are a perfect means to infer the dynamics of an adsorbate. Importantly, this approach does not require intrinsic emission from the adsorbate but only from inelastic tunneling (plasmonic emission), an easily achieved condition, which enables studies on a broad range of systems. The phenomena can be tracked with picosecond resolution, greatly extending the temporal range of tunneling current correlations in STM (typically limited to ∼0.1 ms). The first studies employing this approach focused on a qualitative description of the nanoscale dynamics of adsorbates. 19−21 We have used the same approach to quantify the dynamics of a single H 2 molecule within a well-defined lowcoverage Fermi lattice on Au(111). 23 An example of photon bunching for that system in the millisecond to microsecond regime is shown in Figure 3c. The motion of the molecules in the STM junction modifies the intensity of the plasmonic luminescence creating bunches of photons. As demonstrated recently, photon correlations can be used to track the dynamics of single-molecule tautomerization. 37 We envision further studies on the dynamics of molecular devices such as motors 38,39 and related diffusive and catalytic processes at the single-atom level. 40,41 QUANTUM EMITTERS The next important class of systems is formed by quantum emitters that produce photons linked with each other by quantum mechanical relations originating at the atomic scale. Single photon or photon pair sources belong to this category and are one of the most promising routes for the implementation of quantum computing and cryptography. The simplest description of a single-photon emitter requires only two states (ground and excited states). A single photon is emitted upon transition from an excited to a ground state, as realized in the photoluminescence of a single molecule or quantum dot. The emitting state is excited with a rate k 01 and decays with a rate k 10 ( Figure 4b). Solving eq 2 (with initial conditions n 0 (0) = 1, n 1 (0) = 0, that is, assuming an emission event at t = 0) yields The light intensity is P t k n t ( ) ( ) 10 1 η = (6) and the correlation function is which becomes 0 for Δt = 0, demonstrating perfect antibunched emission. In addition to molecules or quantum dots, single-photon emitters can be realized by exploiting a Coulomb blockade (Figure 4a). 42 This effect is operative for a wide range of bias voltages and relies on tunneling through an electronic quantum state (QS), which can be occupied by only one electron at a time due to Coulomb repulsion. As a result, electrons flow one-byone, in an antibunched manner, exciting the tip-induced plasmon (Figure 4c) via the inelastic tunneling process ( Figure  4d,e) in a temporally antibunched way. When an individual tunneling event can only produce a single photon, this 1:1 relationship also ensures that the light emission that is plasmonic in nature can behave as a single-photon emitter. The Coulomb blockaded single-photon emitter may be used as a basis for constructing more sophisticated quantum light sources. Because single electron tunneling under specific conditions can emit more than one photon, 22,43 one may expect to observe single pair emission (Figure 4f,g), that is, each pair emission event is embedded in a time interval free of any other photon. In the future, such concepts could be applied, for instance, in optoelectronic devices based on inelastic tunneling. 44−47 So far, we have used a two-state kinetic model to analyze timeresolved plasmonic electroluminescence. Spectrally sharp intrinsic excitonic emission (Figure 5d) can also be described in this framework if the system is excited with incoming light or by a locally excited plasmon in the junction. However, exciton generation with direct charge injection requires at least a threestate kinetic model description. 5,26,48 An example is given in Figure 5b, where first the hole is created on the molecule or defect by extracting an electron with a rate k 01 , followed by the injection of an electron into a higher level with a rate k 12 . This sequence can also occur in reverse order. When both processes have occurred, an electron−hole pair (exciton) forms. Finally, this exciton decays with a rate k 20 , which can lead to light emission (radiative decay). The sequence is summarized in a diagram (Figure 5c) whose parameters satisfy: Ä Following the same approach as for the Coulomb blockade case, we obtain with S = k 01 + k 12 + k 20 and Q = (S 2 − 4(k 01 k 12 + k 12 k 20 + k 20 k 01 )) 0.5 . Here, g (2) (0) = 0, thus, the system is an electrically driven single-photon emitter. The width of the dip observed in correlation measurements in this case is modulated by two exponential functions in eq 9, which results in a broader parabolic rise of the antibunching dip compared to the linear single exponential rise that is observed for the same emitter if the excitation took place by photon absorption (photoluminescence). 49 Single-photon emission from individual defects 5 or molecules 6 reported by STML (Figure 5a) is described well by threestate models. Considering typical HBT-STM thin-film conditions (slow k 01 , fast k 12 ), 5,6 the recovery time of the measured dip in g (2) (Δt) is usually dominated by the exciton lifetime τ ex . We note that in eqs 8 and 9 the three time constants of the model may be permuted without changing the resulting correlation function. Thus, additional arguments that are separate from the model are required in order to assign the model rate constants to specific physical processes. If, for instance, a high Purcell factor reduces the exciton lifetime drastically, the charge transfer to, or from, the substrate may be dominating the measured correlation, albeit the tunneling current toward the tip remains low.
In addition to probing single photon emitters with atomic precision, scanning tunneling microscopy enables their lifetime manipulation. In Figure 5e we present an emission center in a thin C 60 film, the first single-photon emitter explored by STML. 5 The exciton lifetime can be increased by improving the ACS Nano www.acsnano.org Perspective decoupling from the metal substrate 6 or decreased by applying higher tunneling current. 5 Although an equivalent behavior in optically pumped quantum dots is usually attributed to exciton− exciton annihilation, 50 here, the dominance of charge carriers suggests that an entirely different mechanism is at work, which involves the tuning of nonradiative decay through charge− exciton annihilation. 5 This mechanism enables using the charge injection via tunneling current as an "internal clock", permitting one to monitor the picosecond dynamics of a single-photon emitter simply by investigating its emission efficiency as a function of tunneling current. 5,26,51 The P(τ tunnel ) dependency (equivalent to P(I/e)) can be obtained by calculating P(t → ∞) and then introducing charge−exciton annihilation as an additional quenching channel. 51 However, the mechanism may not be generalizable; it was reported that P(I) can also increase in a superlinear way for moderate tunneling currents, an effect that is attributed to an increase in the radiative rate with respect to the nonradiative decay. 6,52 Processes slower than exciton decay, like charge injection, can be more readily addressed using TR-STML. In this approach, a train of nanosecond voltage pulses drives the system periodically out of equilibrium and the transient light response is monitored and accumulated over millions of pulse repetitions. This standard transient electroluminescence technique, which is normally used in organic optoelectronics, 53,54 can now be implemented in STML, resulting in a methodology capable of spatially resolved scanning over an individual emitter, which opens new research avenues on the relation between molecular electronic structure and optical properties. 26

MODELING COMPLEX SYSTEMS NUMERICALLY
Although the analytical description presented above captures the peculiarities of simple emitters, many imaginable lightemitting systems and stochastic process networks are too complicated to have their dynamics treated analytically. Nevertheless, it has proven useful to simulate their behavior in combination with the performance of the photon detection and correlation hardware, which enables a quick assessment and exploration of features observed in correlation data. For this purpose, we use the Monte Carlo approach to simulate the evolution of a multistate system with rate-governed transitions between its states. We generate a random sequence of processes through which the system moves from state to state, which is based on ad-hoc-generated (pseudo) random numbers. If defined as radiative, a transition can result in a signal in an emulated detector. The final output of the simulation is the time correlation function after the system has undergone thousands to millions of transitions (see the Supporting Information for more details). Monte Carlo simulations make it possible to model correlation measurements (HBT-STM) or the evolution of a system driven by periodic voltage (TR-STML) or laser pulses in a simple manner. In this Perspective, we employ such simulations to predict the behavior of a single-pair emitter (Figure 4g), a combined singlet−triplet emitter (Figure 6c), and exciton−plasmon cross-correlations (Figure 7b), all of which are eagerly anticipated developments in the field.

FUTURE DIRECTIONS OF THE FIELD
The time evolution of the optical emission spectra after initial excitation can be monitored with gated optical spectroscopy. This method is particularly well suited for investigating singlet and triplet dynamics, because their time scales are very different. Fluorescence lifetimes (singlet decay) are usually on the order of a few nanoseconds, while phosphorescence lifetimes (triplet decay) can be as long as a few microseconds. State-of-the-art intensified CCD detectors have the requisite few nanosecond gate length and gate delay time scales for such a measurement. Gated measurements may be able to clarify how local energy transfer happens, such as the intersystem-crossing dynamics of room-temperature organic phosphors. 55 A sequence of short voltage pulses (Figure 6a) from an AWG is used to excite the quantum system. By synchronizing the pulses with the gating of the CCD intensifier and varying the gate delay, one can obtain the transient spectral response before, during, and after the voltage pulse.
Recently, the existence of bright 56 and dark 57 triplet states in molecules was reported in STML. A triplet state might manifest itself in HBT-STM measurements from a single molecule because it acts as a shelving state for singlet emission, resulting in singlet emission at short and long time scales that is antibunched and bunched, respectively (Figure 6c). The time constant of the bunching decay can be directly linked to the characteristic spin-In addition to probing single photon emitters with atomic precision, scanning tunneling microscopy enables their lifetime manipulation. ACS Nano www.acsnano.org Perspective triplet state lifetime. Moreover, electroluminescence, unlike photoluminescence, enables not only charge-induced annihilation but also up-conversion of a triplet excitonic state to the singlet state. 57 We expect that these detailed processes and their relative weights and conditions will be explored in the near future. Extended information on the dynamics of quantum systems can be gained by measuring photon time cross-correlations between different emission channels. A measurement on the bimodal excitonic−plasmonic emission from C 60 defects, 51 for example, can be realized by spectral filtering the excitonic line for one time-resolved detector and blocking this same line (i.e., admitting only the plasmonic component) for the second detector. Such a measurement can access the temporal sequence of both emission mechanisms and how they are linked within the internal dynamics of the system. Because each electron injected from the substrate can transfer its energy for either exciton or plasmon formation, we may speculate on finding a complex cross-antibunched correlation that can elucidate several time constants of the system at once (Figure 7b). A similar shape of the correlation function has been reported for the crosscorrelation of the biexciton−exciton emission cascade in quantum dots. 58 The application of cross-correlations may be extended to a variety of systems. Recently, it has been shown that quantum emitters like individual phthalocyanines can be optically excited locally with tip-induced plasmons. 59−61 When excitons and plasmons interact in the strong coupling regime, 62 Rabi oscillations, which are evidence of the mixed light−matter state, may be observable with HBT-STM. 63 Similarly, correlations between different excitonic channels may be employed to explore quantum systems. Because a molecular emitter can have excitons at different energies, those may interact with one another, leading to energy upconversion or mutual annihilation. Moreover, a single high-energy exciton may decay into two lower energy excitons, a process known as exciton fission, 64 which is highly sought after in solar energy conversion. Combining the techniques outlined in this Perspective may address the order of the conversion transition, the role of intermediate charge injection, time constants, and spectral relations. In general, studies of interacting molecular systems may one day enable researchers to tailor dynamic systems that produce elaborate photon emission sequences. Similarly, we envision the realization of photon-on-demand sources based on a pump−probe scheme 65 using TR-STML, where each of the two pulses would inject one of the required complementary charges. 48 Moreover, we expect that future studies will focus on in situ assembled aggregates in order to study collective effects with atomic precision. When molecular quantum emitters are brought close to each other, they start to exchange energy through incoherent 16 or coherent 66 interactions, which eventually form a single coupled system 67 and potentially emit entangled photons. 68 One molecular emitter may also be a source of single photons that interact with another molecule. 69 A different topic of interest is the atomic-scale origin of singlephoton emitters in two-dimensional materials. 70−75 Here, intrinsic or extrinsic defects will play the crucial role, similar to the excitonic emission from defects in thin C 60 films described earlier. In the next step, the interaction between defects and individual luminescent molecules 76 could be investigated as it enables various three-dimensional arrangements between the transition dipoles of the emitters. Finally, in-plane distance dependencies on the atomic scale may be addressed by defining two distinct positions on an otherwise homogeneous film, one position given by a luminescent defect and the second by the position of charge injection from the STM tip. In this way, it is possible to map variations of dynamic constants laterally to investigate the tuning of charge injection rates. 77 Such studies may be further refined to include the electric-field contributions and the tip-induced enhancement effects, both of which are strongly related to the atomic structure of the tip apex, defining the so-called picocavity. 78 In conclusion, picosecond photon correlations combined with STML are a powerful tool to study the finest details of light− matter interactions and dynamics of single entities at the atomic scale. This approach enables probing the motion of molecules as small as hydrogen, the dynamics of individual electrons, holes, and excitons, as well as the interactions between excitons and plasmons. Quantum properties of light are directly accessed with the spatial precision of STM, which provides experimentalists with exquisite control over individual single photon or photon pair emitters, all of which is necessary for future quantum information processing technologies.
Improving the time resolution can further extend the possibilities enabled by combining STM with time-resolved luminescence. Currently, photon−photon correlation measurements are limited by the output pulse time jitter of the employed SPAD detector (ca. 30 ps). However, schemes with much better temporal resolution and sufficient efficiency, such as elaborate streak cameras, have been commercialized. Moreover, by means of single-photon up-conversion with femtosecond pump pulses, single photons have been detected with 25% efficiency with a time resolution of 150 fs. 79 Recently, even higher efficiencies have been reported. 80 Note, however, that these efficiencies apply only within the time overlap of single photons with the femtosecond pump pulse. To obtain the efficiency for photons continuously generated (e.g., in the STM), the duty cycle of the up-conversion pulses has to be taken into consideration. Another approach toward faster time scales could be based on We expect that future studies will focus on in situ assembled aggregates in order to study collective effects with atomic precision. ACS Nano www.acsnano.org Perspective two-photon interference detected in the Hong−Ou−Mandel scheme, 81 which may enable researchers to measure the photon wave packet with attosecond resolution. 82 From these trends, we believe that the ground is fertile for future research to bring together the best of spatial and temporal resolution techniques.
Computation of g (2) (Δt), Monte Carlo simulations of systems described by rate equations, single photon pair emission correlation simulation, singlet−triplet emission correlation simulation, exciton−plasmon correlation simulation (PDF)