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Enhanced Molecular Spin-Photon Coupling at Superconducting Nanoconstrictions

  • Ignacio Gimeno
    Ignacio Gimeno
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
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  • , 
  • Wenzel Kersten
    Wenzel Kersten
    Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
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  • , 
  • María C. Pallarés
    María C. Pallarés
    Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain
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  • , 
  • Pablo Hermosilla
    Pablo Hermosilla
    Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain
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  • , 
  • María José Martínez-Pérez
    María José Martínez-Pérez
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain
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    Orcidhttp://orcid.org/0000-0002-8125-877X
  • , 
  • Mark D. Jenkins
    Mark D. Jenkins
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
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  • , 
  • Andreas Angerer
    Andreas Angerer
    Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
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  • , 
  • Carlos Sánchez-Azqueta
    Carlos Sánchez-Azqueta
    Departamento de Fı́sica Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain
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  • , 
  • David Zueco
    David Zueco
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain
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  • , 
  • Johannes Majer
    Johannes Majer
    Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
    National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
    Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
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  • , 
  • Anabel Lostao
    Anabel Lostao
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain
    Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain
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    Orcidhttp://orcid.org/0000-0001-7460-5916
  • , and 
  • Fernando Luis*
    Fernando Luis
    Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    *E-mail: [email protected]
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    Orcidhttp://orcid.org/0000-0001-6284-0521
Cite this: ACS Nano 2020, 14, 7, 8707–8715
Publication Date (Web):May 22, 2020
https://doi.org/10.1021/acsnano.0c03167

Copyright © 2020 American Chemical Society. This publication is licensed under these Terms of Use.

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Abstract

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We combine top-down and bottom-up nanolithography to optimize the coupling of small molecular spin ensembles to 1.4 GHz on-chip superconducting resonators. Nanoscopic constrictions, fabricated with a focused ion beam at the central transmission line, locally concentrate the microwave magnetic field. Drops of free-radical molecules have been deposited from solution onto the circuits. For the smallest ones, the molecules were delivered at the relevant circuit areas by means of an atomic force microscope. The number of spins Neff effectively coupled to each device was accurately determined combining Scanning Electron and Atomic Force Microscopies. The collective spin-photon coupling constant has been determined for samples with Neff ranging between 2 × 106 and 1012 spins, and for temperatures down to 44 mK. The results show the well-known collective enhancement of the coupling proportional to the square root of Neff. The average coupling of individual spins is enhanced by more than 4 orders of magnitude (from 4 mHz up to above 180 Hz), when the transmission line width is reduced from 400 μm down to 42 nm, and reaches maximum values near 1 kHz for molecules located on the smallest nanoconstrictions.

KEYWORDS:
The coupling of spins to superconducting circuits lies at the basis of diverse technologies. Superconducting on-chip resonators, which concentrate the microwave magnetic field in much smaller regions than conventional three-dimensional cavities, (1,2) promise to take electron spin resonance (ESR) to its utmost sensitivity level, eventually allowing the detection of single spins. (3−6) Besides, single microwave photons “trapped” in these devices provide a way to wire-up qubits (7−9) and, therefore, form a basis for hybrid quantum computation and simulation schemes based on spins. (10−16)
Different approaches have been designed and, in some cases, put into practice, to enhance the spin sensitivity and the spin-photon coupling. They often involve the use of nonlinear superconducting circuits, parametric amplifiers, to amplify the output signal, (3,4) and of low impedance resonator designs, which increase the photon magnetic field. (4,5) Experiments performed on highly coherent magnetic impurities in semiconducting hosts show spin resonance at the level of a few tens of spins and maximum spin-photon coupling strengths of order 400 Hz at frequencies of about 7 GHz. (5)
In this work, we explore experimentally a third alternative, inspired by earlier developments of micro-ESR devices. (17−19) The underlying idea is that reducing the cavity effective volume enhances the microwave magnetic field. In a superconducting resonator, this goal can be achieved by decreasing locally the width of the resonator’s transmission line (20−22) in order to bridge the very different scale lengths of superconducting circuits, with typical line widths of a few microns, and of impurity or molecular spins, which are in the range of nanometers. This approach requires moving beyond the limits of conventional optical lithography to fabricate or modify certain regions of the circuits and is fully complementary to those methods mentioned above.
The main challenge resides in the fact that the microwave field enhancement is localized in a nanoscopic region near the superconducting constriction, as can be seen in Figure 1A and 1B. Optimally profiting from such enhancement thus calls for a method able to deliver the magnetic sample at the right location and with sufficient spatial accuracy. Spins in molecules provide a good test case for addressing this challenge. Many molecules are stable in solution or can be sublimated from the crystal and can, therefore, be transferred to a solid substrate or a device. (23−28) In addition, they are one of the most promising candidates to encode spin qubits, due to the vast possibilities for design offered by chemical nanoscience. (29−34) Here, we combine top-down and bottom-up nanolithography methods to study the coupling of microwave photons to nanoensembles of the simplest molecular spins, organic free radicals with S = 1/2, deposited near constrictions of varying size.

Figure 1

Figure 1. (A) Scanning electron microscopy image of the central line of a superconducting coplanar resonator. The line was thinned down to a width of about 158 nm by focused ion beam nanolithography. (B) Color plot of the photon magnetic field in the neighborhood of this constriction, calculated with a finite-element simulation software. (35) (C) Structure of a DPPH free-radical molecule, with spin S = 1/2 and g = 2 (left) and optical microscopy image of the constriction after the deposition of DPPH by means of the tip of an Atomic Force Microscope (AFM, right). (D) AFM image of the constriction taken before and after the molecules were deposited and the solvent had evaporated.

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Results and Discussion

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This section describes the main results of this work: how devices are modified to locally enhance the spin-photon coupling, how the molecules are deposited with sufficient spatial accuracy, and how this coupling is experimentally determined as a function of the number of molecules and of temperature. The main result refers to the coupling of individual spins and its dependence on the size of the resonator dimensions and on the molecule-to-chip interface.

Circuit Fabrication and Integration of Molecular Spin Micro- and Nano-deposits

The circuits used in this work are coplanar superconducting resonators fabricated by optical lithography on 150 nm thick Nb films, which become superconducting below Tc = 8.2 K, deposited onto single crystalline sapphire wafers. Previous studies (21) show that nanoscopic constrictions, such as the one shown in Figure 1A, can be fabricated in the central transmission line by Focused Ion Beam (FIB) nanolithography, that they do not significantly alter the operation of the devices, and that they locally enhance the photon magnetic field.
As the simulation in Figure 1B shows, the enhancement is strongly localized near the superconducting nanobridge, in a region with typical dimensions w × w × L, where w is the constriction width and L is its length. The proper integration of spins plays, then, a crucial role to achieve the maximum spin sensitivity allowed by this approach. Our samples contain organic free-radical molecules of 2, 2-diphenyl-1-picrylhydrazyl, (36−38) hereafter referred to as DPPH, whose molecular structure is shown in Figure 1. Each molecule hosts an unpaired electron with a spin S = 1/2 and a close to isotropic gyromagnetic factor g ≃ 2. Under a magnetic field H, it shows a well-defined resonance line at a frequency ΩS = μ0gμBH/ℏ. In a crystalline environment, the inhomogeneous broadening arising from dipolar interactions is reduced by direct exchange interactions between nearest radicals. (39,40) The resonance line width becomes then dominated by the homogeneous broadening 1/T2, where T2 ≃ 80–120 ns is the spin coherence time. Besides, these molecules can be dissolved and remain stable in diverse organic solvents. (37)
The latter property allows delivering precise amounts of DPPH molecules onto the central transmission lines of the resonators. Large (a few mm wide, a few microns thick) molecular ensembles have been deposited either in powder form or from solution, using a micropipette, onto conventional resonators with w = 400 and 14 μm. The number of molecules was varied by controlling the concentration of the original solution, keeping the volume constant. Illustrative Scanning Electron Microscopy (SEM) images of such deposits are shown as part of the Supporting Information. They show that DPPH has a tendency to form quasi-spherical nanoaggregates.
For smaller deposits on narrower lines, we employed Dip Pen Nanolithography (DPN), (41,42) a soft lithographic technique that uses the tip of an Atomic Force Microscope (AFM) to deposit nanoscopic volumes from a solution containing the molecules of interest onto a very small area (cf. Figure 1C). This technique has the advantage of combining high spatial resolution with good control over the molecular dose transferred to the substrate without the need for chemical functionalization, thus making it well suited for placing diverse nanosamples onto solid state sensors. (25,43,44) The size of the deposits was controlled in this case by the diameter of the drops transferred by the AFM tip to the substrate, which depend on the contact time between both, and by their concentration. The deposits are then characterized by SEM and by AFM, as shown in Figure 1D and in the Supporting Information. These deposits also form nanoaggregates after the solvent has evaporated, with sizes ranging from 50 nm to above 200 nm depending on the initial concentration of the radical at the ink solution and the size of the deposited drop. This also means that the number of molecules actually transferred into the “active” region of the constriction might vary even between depositions performed under nominally identical conditions and, therefore, needs to be determined for each case.

Spin-Photon Coupling versus Spin Number

The coupling of the spins to the cavity photons, with frequency ωr/2π ≃ 1.4 GHz, reduces the microwave transmission, shifts ωr, and broadens the resonance. All these effects become maximum when ΩS ≃ ωr, i.e. when spins and photons are brought into resonance with each other by an external magnetic field H. The transmission provides information on the collective coupling GN of the spin ensemble to the resonator, where N denotes here the number of free-radical spins, as well as on the spin γ and photon κ characteristic line widths.
Illustrative results of transmission measurements performed at T = 4.2 K on resonators without and with a 158 nm wide constriction are shown in Figure 2A and 2B, respectively. In both cases, the sample was a DPPH drop with an approximate diameter of about 30 μm deposited onto the central line by DPN. This amount corresponds approximately to the sensitivity limit for the former device. By contrast, under the same conditions, the resonator with the constriction gives a clearly visible absorption signal, thus providing direct evidence for the enhancement of GN.

Figure 2

Figure 2. (Top) Color scale plots of the microwave transmission through 1.4 GHz on-chip superconducting resonators with a 14 μm wide central line (A) and with a 158 nm wide constriction (B) coupled to a DPPH deposit with N ≈ 5 × 109 molecules, corresponding to Neff ≈ 4 × 107 spins effectively coupled to the resonator at T = 4.2 K. The red dashed lines mark the position of the resonance frequency at each magnetic field. The inset in B shows transmission versus frequency data near resonance at the field values indicated by arrows, evidencing the detection of a net absorption (lower transmission and broader resonance) when the spins get into mutual resonance with the circuit. (Bottom) Magnetic field dependence of the resonance width κ for the same resonators (C without and D with constriction) coupled to ensembles of DPPH molecules of varying size. Solid lines are least-squares fits based on eq 1.

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In order to obtain quantitative estimates of this enhancement, and estimate the average coupling to individual spins, experiments on samples with decreasing N were performed. The number of molecules effectively coupling to the resonator magnetic field was estimated from the geometry and topography of the deposits, taking into account the width of the transmission line near the deposit. For conventional resonators with a 14 μm wide central line, all spins located in a 30 μm wide region around it are counted. For a nanoconstriction, the “active” area is taken as a 2 μm wide rectangular area around it.
Experiments and simulations, described below and in the Supporting Information, confirm that the coupling of spins located outside this region lies below the sensitivity limits and can, therefore, be safely neglected. Another aspect that needs to be taken into account is that these measurements were performed at a finite temperature T = 4.2 K. This lowers the population difference, or equivalently the spin polarization , between the ground and excited levels of the DPPH spins by a factor 6.7 × 10–3 with respect to zero temperature. As a result, the number of spins that contribute to the net absorption at the given temperature is also reduced from N to .
Results from these experiments are shown in Figure 2C and 2D. They confirm that introducing a nanoconstriction enables detecting much smaller deposits: the sensitivity limit is reduced from about 108 spins to 2 × 106 spins. This enhancement in sensitivity arises here from a larger spin-photon coupling, which can be determined as follows. The broadening of the cavity resonance κ can be fitted using the following expression, (45)
(1)
where κr is the broadening of the ‘empty’ cavity, as measured when it is detuned from the spins. This fit allows extracting GN and γ. γ is found to be close to 12 MHz for all but the smallest DPN deposits. This value is compatible with a pure homogeneous broadening and a T2 ≃ 80 ns, which lies within the typical values observed for DPPH. (37) A larger line width has been observed in DPPH molecules dispersed in polymeric matrices. (40) That the same phenomenon is observed in DPPH nanoaggregates deposited from solution suggests that they tend to lose crystalline order.
Figure 3 shows the dependence of GN on Neff measured in resonators with 14 μm and 158 nm transmission line widths. In both, the coupling is approximately proportional to . This result agrees with the collective enhancement of the radiation emission and absorption by spin ensembles, (46) which predicts that
(2)
where G1 is the coupling of a single spin. The ability to modify the size of the molecular ensembles over a large range allows monitoring this well-known dependence directly. The slope then directly gives the average, or typical, value of G1. These data confirm also that a strong enhancement of G1, by a factor of order 24 (from G1/2π ≃ 3.5 to 85 Hz), occurs when w is reduced by a factor 100 (from 14 μm to 158 nm).

Figure 3

Figure 3. Collective spin-photon coupling of ensembles of free-radical molecules to coplanar resonators with a 14 μm wide transmission line (top) and a 158 nm constriction (bottom). The solid lines are least-squares fits to a linear dependence on the square root of the effective number of spins that are coupled to the devices at T = 4.2 K, as predicted by eq 2. The bottom panel compares both fits to highlight the coupling enhancement generated by the constriction.

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Spin-Photon Coupling versus Temperature

In this section, we describe experiments that explore the optimal conditions in the search of a maximum spin-photon coupling: temperatures close to absolute zero, which take Neff closer to N; an average number nphotons ≃ 5 × 105 of photons in the cavity well below N, in order to avoid any saturation effects; and a central line width w ≃ 42 nm near the minimum achievable by FIB nanolithography.
Representative images of the constriction and of the DPPH nanoaggregates deposited on it by DPN are shown in Figure 4 and in the Supporting Information. The number N of DPPH molecules in the active area was, in this case, estimated to be approximately 1.6 × 108 spins, which lies below the minimum dose that was detectable in experiments performed at T = 4.2 K and for w = 158 nm (cf. Figure 3D).

Figure 4

Figure 4. AFM topographic map (A) and SEM image (B) of the region near a 42 nm wide nanoconstriction. (C and D) Color maps of the number of DPPH molecules deposited on each location and of the estimated single spin to photon couplings, respectively. The latter maps have been calculated with a discretization of space into 3 × 3 × 3 nm3 cubic cells. The number of free-radical molecules deposited in this area amounts to approximately N = 1.6 × 108, and the collective coupling estimated from the simulations is GN/2π ≃ 2.0 MHz at T = 44 mK and 2.5 MHz at T = 0.

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Results of transmission measurements performed on this device are shown in Figure 5. Thanks to the much larger spin polarization, an easily discernible absorption signal is observed at the minimum temperature T ≃ 44 mK, which corresponds to a collective coupling GN/2π ≃ 1.9 MHz. The line width γ ≃ 65 MHz is 5 times larger than what would be expected from the spin coherence times. The additional broadening probably arises from the smaller size of the DPPH nanoaggregates transferred to this device and from the fact that DPPH molecules are here dispersed in a matrix of glycerol used in the DPN deposition process (see the section Methods below and the Supporting Information (SI) for more details). As mentioned above, these effects tend to suppress direct exchange interactions between free-radical spins and, then, enhance the broadening associated with hyperfine and dipole–dipole couplings.

Figure 5

Figure 5. (A) Color plot of the microwave transmission, measured at T = 44 mK, through a superconducting resonator with a 42 nm wide constriction in its central transmission line and coupled to an ensemble of N ≃ 1.6 × 108 free-radical molecules (corresponding to Neff ≃ 108 spins effectively coupled to the resonator). (B) Color plot of the microwave transmission calculated for a collective coupling GN/2π = 2.0 MHz, as follows from the simulations described in Figure 4, and a spin line width γ = 65 MHz. (C) Magnetic field dependence of the resonance width κ for the same device measured at different temperatures. Solid lines are least-squares fits using eq 2. (D) Temperature dependence of GN extracted from these experiments. (E) Same data plotted as a function of the (temperature dependent) effective number of spins coupled to the resonator , where is the spin polarization. The solid lines are least-squares fits based on eq 2 that extrapolate to GN/2π ≃ 2.3 MHz for T → 0 (when Neff → N).

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As expected, the spin-photon coupling strength GN decreases rapidly with increasing temperature. This dependence can be accounted for by the decrease in spin polarization that determines Neff/N (cf. Figure 5D and 5E), showing again the validity of eq 2. From these data, and using the topographic and geometrical information on the sample, we estimate an average single spin coupling G1/2π ≃ 180 Hz. This represents an enhancement of nearly 2 orders of magnitude with respect to the coupling achieved for a 14 μm wide transmission line resonator.
Taking into account that the photon energy, thus also G1 ∝ ωr, it is useful to define the dimensionless coupling G1/ωr ≃ 1.3 × 10–7. This result compares favorably to the maximum single-spin coupling reported in the literature, of about 450 Hz for a 7 GHz resonator (for a ratio G1/ωr ≃ 6.4 × 10–8), (5) which was achieved with especially designed lumped-element resonators coupled to impurity spins in the Si substrate on which these devices were fabricated. Yet, it still falls short of the maximum theoretically attainable enhancement, which should scale as 1/w and therefore reach a factor of 330 in this case, thus G1/2π close to 1 kHz. (16,20)
In order better understand these results and, in particular, obtain information on how each molecular spin couples to the resonator, we have performed numerical simulations of the spin-photon interaction for this specific situation. The model uses the actual geometry (length, thickness, and width) of the nanoconstriction and a three-dimensional map of the number of spins extracted from the combined analysis of SEM and AFM images. The region surrounding the constriction is divided into a grid of cubic cells with lateral dimensions d. Further details are given in the section Methods and as part of the Supporting Information.
A 2D projection of a map calculated for the smallest d = 3 nm is shown in Figure 4C. The coupling is then evaluated as follows. First, the photon energy ℏωr is used to determine the supercurrent flowing through the constriction. This electrical current generates a magnetic field at each point in space , which was calculated using the 3D-MLSI finite-element computer simulation software (35) as in the example shown in Figure 1B. For all molecules in a given cell i, the magnetic field is assigned its value at the center of the cell. Then, the coupling of each cell is calculated with the following expression (for details, see ref (20))
(3)
where ni is the effective number of spins in the cell, calculated at the given temperature, and mS = ±1/2 denote the two eigenstates associated with opposite projections of the radical spins along the external magnetic field . The contributions of all cells can then be combined to estimate the collective coupling of the whole sample as follows (47)
(4)
For the device shown in Figure 4, eq 4 gives GN/2π ≃ 2.0 MHz at 44 mK and an average G1 ≃ 200 Hz, which agree very well with the experimental values GN = 1.9 MHz and G1 = 180 Hz and, as shown in Figure 5B, account well for the transmission experiments. The difference is in fact smaller than the unavoidable errors associated with the number of molecules and with the influence that crystalline defects have on the free radicals, which are known to turn a fraction of molecules into a diamagnetic state.
Simulations can then help in understanding how these average values ensue from the distribution of spin locations and couplings in the deposit. A projection map showing the maximum coupling obtained for cells located at different xy positions (which mainly correspond to those lying closest to the device surface along the vertical axis z) is shown in Figure 4D. It confirms that the main contribution to GN comes from those spins located in the closest proximity to the constriction. It also shows that individual couplings significantly larger than the average G1 can be achieved. Looking at those spins lying closer to the constriction, we find values as high as 0.6–0.8 kHz, depending on the exact location with respect to the surface and on the orientation of the external magnetic field.

Spin-Photon Coupling versus Transmission Line Width

Results obtained for different devices enable determining how the single spin to single photon coupling G1 depends on the dimensions of the superconducting transmission line. This dependence is shown in Figure 6, which, besides those discussed already, includes also data measured on a resonator with a 400 μm wide line (cf. Supporting Information). For w ⩾ 100 nm, these results show the expected enhancement of G1 ∝ 1/w, from G1 ⩽ 5 mHz up to nearly 100 Hz. For narrower lines, however, and as we have already pointed out above, the increase slows down.

Figure 6

Figure 6. Dependence of the average single spin to single photon coupling on the width of the central transmission line of the resonator, showing the enhancement obtained by reducing the latter down to the region of (tens of) nanometers. The lines are calculations of the coupling of a spin located over the constriction, at three different heights z, as illustrated by the figure in the inset.

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The reason for this can be understood in light of the simulations and arguments described in the previous subsection (cf. Figure 4D). A first limitation arises from the nonzero thickness of the superconducting film (nominally 150 nm but decreasing near the constriction as shown in Figure S2). This geometrical effect reduces slightly the local magnetic field generated by the supercurrents and, as a result, also the slope of the G1 vs 1/w theoretical curve of Figure 6 when w becomes smaller than the Nb thickness. It is, however, unable to account for the experimental results (see Figure S16 in the SI).
Since the coupling enhancement is concentrated close to the constriction, within a region with dimensions comparable to w, the sample integration becomes critical. The topography AFM images show that, once dry, DPPH molecules deposited by DPN tend to form nanoaggregates with characteristic dimensions of the order of 200 nm. Then, even those molecules located in grains that land next to the line can be too far when compared to w. This effect can be accounted for by numerical calculations of G1 (Figures 6 and S16). They show that G1 strongly depends on the height z of the molecular spins above the transmission line. While, for z ≃ 0, G1 ∝ 1/w, when z ≠ 0 the coupling tends to saturate as soon as w ⩽ z. Therefore, creating an optimum interface between the molecular deposits and the circuit surface, i.e. making z as close to zero as possible, becomes of utmost importance to attain the maximum spin-photon coupling.

Conclusions

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The experiments and simulations described in the previous sections validate a relatively straightforward method to enhance the coupling of molecular spins to on-chip superconducting resonators. Using conventional 1.4 GHz coplanar resonators, we have attained an average single spin coupling of about 180 Hz for central line widths of ∼40 nm, with estimated maximum couplings on the order of kHz. This approach is, in principle, applicable to any circuit design and to a large variety of samples, provided that they can be delivered from solution and with sufficient spatial accuracy. Introducing superconducting nanobridges into especially designed resonators, which minimize the circuit impedance and therefore maximize the superconducting current at the inductor, (4−6) should allow enhancing G1 by a further 2 orders of magnitude, thus reaching G1/2π values close to 0.1 MHz.
Devices based on these ideas can take electron spin spectroscopy to the single spin limit and become useful tools to investigate magnetic excitations in individual nanosystems ranging from nanosized particles to molecular nanomagnets, or even exotic topological states, such as vortices and skyrmions. (48) The molecular approach used here adds the possibility of serving as a suitable vehicle to deliver diverse samples, as well as to improve their interface with the circuit. A recent work shows that it is possible to synthesize thin molecular films onto a superconducting line, thereby achieving a close to optimum coverage with a minimum molecule to circuit distance. (28) The combination of these methods with DPN or other nanolithography tools with a high spatial resolution could then lead to major improvements.
Spins hosted in artificial molecules (29−34,49) and 2D molecular materials, such as graphene nanoribbons, (50,51) are also very promising candidates to encode qubits and qudits. In recent times, spin coherence times of these systems have been optimized by chemical design, up to values well above 10–50 μs, (52−55) and even close to ms, (56) and the strong coupling to superconducting resonators has been achieved for macroscopic molecular ensembles. (57−59) Our results show that attaining this regime for single molecules is within reach. This coherent coupling would allow the use of superconducting circuits to control, read-out, and connect spin qubits located in different molecules, an essential ingredient of a hybrid architecture for large scale quantum computation and simulation. (16)

Methods

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Device Fabrication and Characterization

Superconducting resonators are fabricated on 500 μm thick C-plane sapphire wafers. A 150 nm thick niobium layer was deposited by radio frequency sputtering and then patterned by photolithography and reactive ion etching. The circuits consist of a large 400 μm central line separated from two ground planes by two 200 μm gaps that narrow down to around 14 and 7 μm, respectively, after going through gap capacitors. The devices were tuned to show an effective impedance Z0 = 50Ω, a resonance frequency ωr/2π ≃ 1.4 GHz, and maximum quality factors Q ≃ (1–2) × 105.
Nanoscale constrictions (21) were made at the midpoint of the central line by etching it with a focused beam of Ga+ ions, using a commercial dual beam system. The ion beam also locally reduces the Nb thickness below the initial 150 nm, even down to values close to the constriction width w (see Figure S2 in the Supporting Information for an illustrative image of the smallest constriction used in this work). The ionic current was kept below 20 pA to maximize the resolution in the fabrication process and to minimize the Nb layer, on the order 10 to 15 nm thick, that is implanted with Ga. In order to avoid the buildup, and eventual discharge, of electrostatic charges during the process, the central line was connected to one of the ground planes by a few nanometer wide Pt bridge, fabricated by focused ion beam deposition. Once the nanoconstriction was fabricated, this bridge was removed using the same ion beam. Images of 158 and 42 nm wide constrictions, obtained in situ by SEM, are shown in Figure 1 and in the Supporting Information.
Prior to the deposition of the molecular samples, the microwave propagation trough all devices was characterized, as described below, as a function of magnetic field, temperature, and input power. Illustrative results are shown as part of the Supporting Information. These experiments show that the constrictions do not introduce any drastic changes to ωr and Q and that they can work under magnetic fields up to 1.4 T, provided that they are applied parallel to the plane of the chip.

Molecular Pattering onto Superconducting Resonators and Characterization of the Deposits

The molecular ink used in all depositions was prepared by dissolving 10–20 mg/mL of the free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH; Sigma-Aldrich) in N,N-Dimethylformamide (DMF; Sigma-Aldrich) with about 5–10% glycerol in volume (Panreac, ≥ 99.5%, ACS grade). DMF preserves the chemical properties of DPPH and does not turn the radical into its diamagnetic form. Glycerol is used as an additive to increase the viscosity and slow down the evaporation of the ink so that the solution does not dry before the creation of the pattern. (42) This is especially important in the deposition by DPN, when the drop has to be transferred to the device by the AFM tip.
The device was previously cleaned with isopropanol and acetone, dried by blowing nitrogen gas, and underwent plasma oxygen treatment before deposition. DPN deposition was performed using a DPN5000 based-AFM system (NanoInk, Inc., USA). For this, 1 μL of the ink solution was left in a reservoir of a microfluidic Inkwell delivery chip-based system (Acs-technologies LLC, USA). Afterward, a DPN silicon nitride DPN single A-S2 probe (Acs-technologies LLC, USA) was dipped and coated several times with the ink at the inkwell microchannel.
DPN patterning was optimized at 25 °C and 55% relative humidity. The quality and size of the free radical deposits were assayed previously on marked SiO2 substrates and small pieces of muscovite mica (see Supporting Information for illustrative images of the results). The deposition conditions were optimized to produce deposits ranging from 1 to 60 μm in diameter, such as the one shown in Figure S8. Then, different drops with diameters ranging between 5 and 60 μm and heights from 50 to 400 nm were patterned on the central line of resonators, both without constriction and with nanoconstrictions. The characterization of the deposits and the microwave transmission experiments were performed once the deposits had dried. Free radical deposits were also made far from the sensing areas and using different solvents and additives and characterized as controls.
The patterns were analyzed by optical microscopy, AFM and SEM imaging. AFM images were taken with a MultiMode 8 AFM system (Bruker) and a Cervantes SPM FullMode (Nanotec) at scan rates of 0.1–2.0 Hz. The samples were characterized using Peak Force TappingTM and TappingTM modes with 7–125 kHz triangular silicon nitride microlevers (SNL; Bruker Probes) having ultrasharp 2 nm end tip radii, and with an antimony (n) doped silicon 320 kHz ultraresonant microlever (TESP; Bruker Probes) having an 8 nm end tip radii. The images were analyzed using the WSxM (60) and Gwyddion (61) software for SPM image processing. SEM images were performed with an INSPECT-F50 (FEI).

Microwave Transmission Experiments

The microwave transmission measurements were done using a programmable network analyzer. Experiments performed at 4.2 K were aimed at measuring a large number of deposits of varying dose. In these experiments, the devices were mounted on a homemade probe and submerged in a liquid helium cryostat. The input power was attenuated by −52 dB, to avoid the possibility of exceeding the critical current at the nanoconstriction, and the output power was measured directly. The number of photons in the cavity was estimated to be on the order of 109. The external magnetic field was applied with a commercial 9T × 1T × 1T superconducting vector magnet, which allows rotating in situ, in order to align it along the central line of the device (y axis in Figures 1 and 4) with an accuracy better than 0.1°.
For experiments at lower temperatures, transmission measurements were carried out in an adiabatic demagnetization refrigerator, having a base temperature of about 45 mK. Magnetic fields up to 60 mT were applied using a homemade superconducting vector magnet. In this case, experimental constraints imposed a field orientation along the x axis, thus perpendicular to the central line within the plane of the device. As it is shown in the Supporting Information, this geometry leads to a substantial decrease in the spin-photon coupling with respect to the maximum achievable. The input signal was attenuated, down to a level of about 5 × 105 photons, and then amplified at 4.2 K and at room temperature before being detected.
The small asymmetry in the resonances measured (Figures 3 and 5) is likely caused by an interference, called Fano resonance, (62) between the resonator and a small continuous background. A possible source for that background is the off-resonant tail of the sample box mode. This small asymmetry has a very weak influence (of a few % at most) on the results for the coupling and peak width, because they are first-order independent.

Numerical Simulations

Our estimate of the spin-photon coupling relies on the calculation of the spatial distribution of , i.e., the rms magnetic field generated by the rms supercurrent nA circulating through the central line of the resonator, with Z0 ≈ 50 Ω its impedance. (20)
The spatial distribution of is computed using a finite-element based package (35) that solves the London equations for the given geometry of the superconducting wire, having London penetration depth λL = 90 nm, and assuming that the supercurrent distributes through 11 equidistant 2D sheets, parallel to the xy plane and homogeneously distributed across the thickness of the Nb layer. is then used to evaluate the rms magnetic field (with i = 1, 2, ... Ncell) at the center of Ncell cubic cells with lateral dimension d, each containing ni molecules. The grid size was varied from 0 up to 2 μm, and the cell size d, from 3 nm up to 100 nm. The constriction geometry, in particular its thickness, was found to have some influence on the coupling, but only for spins located very close to the constriction and for w ≤ 50 nm.
These simulations show also that spins located further than about 500 nm from the constriction give a close to negligible contribution. The mode volume of a 42 nm wide constriction is then ≃1 μm × 1 μm × 10 μm = 10 μm3 = 0.01 pico-l, or about 1.4 × 10–14λ3, with λ ≃ 88 mm being the resonance wavelength. It also follows that a 3 nm cell size is necessary to properly account for the coupling to spins that lie very close to the nanoconstriction, which give the maximum contribution. The maximum coupling G1 depends also on the orientation of the external magnetic field, which determines which components of the photon magnetic field couple to the spins. It is maximum for parallel to the central line (y axis). Further details can be found in the Supporting Information (Figures S12 to S16).

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.0c03167.

  • Images of the fabrication steps of resonators and of superconducting nanoconstrictions, tests results of these devices, details and additional images of the deposition of free-radical spin ensembles by DPN and their characterization by means of SEM and AFM, results of additional microwave transmission experiments, additional information, backed with plots, on how the number of molecules effectively coupled to each device has been estimated and how the spin-photon coupling has been simulated (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Ignacio Gimeno - Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    • Wenzel Kersten - Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
    • María C. Pallarés - Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain
    • Pablo Hermosilla - Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain
    • María José Martínez-Pérez - Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain;  Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain;  Orcidhttp://orcid.org/0000-0002-8125-877X
    • Mark D. Jenkins - Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
    • Andreas Angerer - Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
    • Carlos Sánchez-Azqueta - Departamento de Fı́sica Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain
    • David Zueco - Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain;  Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain
    • Johannes Majer - Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China;  National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China;  Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, 1020 Vienna, Austria
    • Anabel Lostao - Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain;  Laboratorio de Microscopı́as Avanzadas, Instituto de Nanociencia de Aragón, Universidad de Zaragoza, 50018 Zaragoza, Spain;  Fundación ARAID, Av. de Ranillas 1-D, 50018 Zaragoza, Spain;  Orcidhttp://orcid.org/0000-0001-7460-5916
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors acknowledge funding from the EU (COST Action 15128 MOLSPIN, QUANTERA SUMO and MICROSENSE projects, FET-OPEN Grant 862893 FATMOLS), the Spanish MICINN (Grants RTI2018-096075-B-C21, PCI2018-093116, MAT2017-89993-R, MAT2017-88358-C3-1-R, EUR2019-103823), the Gobierno de Aragón Ggrants E09-17R Q-MAD, E35-20R, BE and LMP55-18, FANDEPAM) and the BBVA foundation (Leonardo Grants 2018 and 2019).

References

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    Schuster, D. I.; Sears, A. P.; Ginossar, E.; Di Carlo, L.; Frunzio, L.; Morton, J. J. L.; Wu, H.; Briggs, G. A. D.; Buckley, B. B.; Awschalom, D. D.; Schoelkopf, R. J.
    Physical Review Letters (2010), 105 (14), 140501/1-140501/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Electron spins in solids are promising candidates for quantum memories for superconducting qubits because they can have long coherence times, large collective couplings, and many qubits could be encoded into spin waves of a single ensemble. The authors demonstrate the coupling of electron-spin ensembles to a superconducting transmission-line cavity at strengths greatly exceeding the cavity decay rates and comparable to the spin linewidths. The authors also perform broadband spectroscopy of ruby (Al2O3:Cr3+) at millikelvin temps. and low powers, using an on-chip feedline. The authors observe hyperfine structure in diamond P1 centers.
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  13. 13
    Kubo, Y.; Ong, F. R.; Bertet, P.; Vion, D.; Jacques, V.; Zheng, D.; Dréau, A.; Roch, J.-F.; Auffeves, A.; Jelezko, F.; Wrachtrup, J.; Barthe, M. F.; Bergonzo, P.; Esteve, D. Strong Coupling of a Spin Ensemble to a Superconducting Resonator. Phys. Rev. Lett. 2010, 105, 140502,  DOI: 10.1103/PhysRevLett.105.140502
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    13
    Strong Coupling of a Spin Ensemble to a Superconducting Resonator
    Kubo, Y.; Ong, F. R.; Bertet, P.; Vion, D.; Jacques, V.; Zheng, D.; Dreau, A.; Roch, J.-F.; Auffeves, A.; Jelezko, F.; Wrachtrup, J.; Barthe, M. F.; Bergonzo, P.; Esteve, D.
    Physical Review Letters (2010), 105 (14), 140502/1-140502/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The authors report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are N-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the N-vacancy center ESR.
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  14. 14
    Wu, H.; George, R. E.; Wesenberg, J. H.; Mølmer, K.; Schuster, D. I.; Schoelkopf, R. J.; Itoh, K. M.; Ardavan, A.; Morton, J. J. L.; Briggs, G. A. D. Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble. Phys. Rev. Lett. 2010, 105, 140503,  DOI: 10.1103/PhysRevLett.105.140503
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    14
    Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble
    Wu, Hua; George, Richard E.; Wesenberg, Janus H.; Molmer, Klaus; Schuster, David I.; Schoelkopf, Robert J.; Itoh, Kohei M.; Ardavan, Arzhang; Morton, John J. L.; Briggs, G. Andrew D.
    Physical Review Letters (2010), 105 (14), 140503/1-140503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holog. techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.
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  15. 15
    Chiorescu, I.; Groll, N.; Bertaina, S.; Mori, T.; Miyashita, S. Magnetic Strong Coupling in a Spin-Photon System and Transition to Classical Regime. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 024413,  DOI: 10.1103/PhysRevB.82.024413
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    15
    Magnetic strong coupling in a spin-photon system and transition to classical regime
    Chiorescu, I.; Groll, N.; Bertaina, S.; Mori, T.; Miyashita, S.
    Physical Review B: Condensed Matter and Materials Physics (2010), 82 (2), 024413/1-024413/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins s=1/2 coupled to a variable no. of photons. Rabi splittings are calcd. and their distribution is analyzed as a function of photon no. nmax and spin system size N. A sharp transition in the distribution of the Rabi frequency is found at nmax≈N. The width of the Rabi frequency spectrum diverges as √N at this point. For increased no. of photons nmax>N, the Rabi frequencies converge to a value proportional to √nmax. This behavior is interpreted as analogous to the classical spin-resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present exptl. data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temp. This points toward quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.
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  16. 16
    Jenkins, M. D.; Zueco, D.; Roubeau, O.; Aromí, G.; Majer, J.; Luis, F. A Scalable Architecture for Quantum Computation with Molecular Nanomagnets. Dalton Trans 2016, 45, 16682– 16693,  DOI: 10.1039/C6DT02664H
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    16
    A scalable architecture for quantum computation with molecular nanomagnets
    Jenkins, M. D.; Zueco, D.; Roubeau, O.; Aromi, G.; Majer, J.; Luis, F.
    Dalton Transactions (2016), 45 (42), 16682-16693CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
    A proposal for a magnetic quantum processor that consists of individual mol. spins coupled to superconducting coplanar resonators and transmission lines is carefully examd. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calcns., based on parameters of existing devices and mol. qubits. These results show that the proposal is feasible, provided that mols. with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the mols., and the possibility of using their internal spin degrees of freedom.
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  17. 17
    Narkowicz, R.; Suter, D.; Stonies, R. Planar Microresonators for EPR Experiments. J. Magn. Reson. 2005, 175, 275– 284,  DOI: 10.1016/j.jmr.2005.04.014
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    17
    Planar microresonators for EPR experiments
    Narkowicz, R.; Suter, D.; Stonies, R.
    Journal of Magnetic Resonance (2005), 175 (2), 275-284CODEN: JMARF3; ISSN:1090-7807. (Elsevier)
    EPR resonators on the basis of standing-wave cavities are optimized for large samples. For small samples it is possible to design different resonators that have much better power handling properties and higher sensitivity. Other parameters being equal, the sensitivity of the resonator can be increased by minimizing its size and thus increasing the filling factor. Like in NMR, it is possible to use lumped elements; coils can confine the microwave field to vols. that are much smaller than the wavelength. We discuss the design and evaluation of EPR resonators on the basis of planar microcoils. Our test resonators, which operate at a frequency of 14 GHz, have excellent microwave efficiency factors, achieving 24 ns π/2 EPR pulses with an input power of 17 mW. The sensitivity tests with DPPH samples resulted in the sensitivity value 2.3 × 109 spins · G-1Hz-1/2 at 300 K.
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  18. 18
    Narkowicz, R.; Suter, D.; Niemeyer, I. Scaling of Sensitivity and Efficiency in Planar Microresonators for Electron Spin Resonance. Rev. Sci. Instrum. 2008, 79, 084702,  DOI: 10.1063/1.2964926
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    18
    Scaling of sensitivity and efficiency in planar microresonators for electron spin resonance
    Narkowicz, R.; Suter, D.; Niemeyer, I.
    Review of Scientific Instruments (2008), 79 (8), 084702/1-084702/8CODEN: RSINAK; ISSN:0034-6748. (American Institute of Physics)
    ESR of vol.-limited samples or nanostructured materials can be made significantly more efficient by using microresonators whose size matches that of the structures under study. The authors describe planar microresonators that show large improvements over conventional ESR resonators in terms of microwave conversion efficiency (microwave field strength for a given input power) and sensitivity (min. no. of detectable spins). The authors explore the dependence of these parameters on the size of the resonator and find that both scale almost linearly with the inverse of the resonator size. Scaling down the loops of the planar microresonators from 500 down to 20 μm improves the microwave efficiency and the sensitivity of these structures by more than an order of magnitude and reduces the microwave power requirements by more than two orders of magnitude. (c) 2008 American Institute of Physics.
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  19. 19
    Banholzer, A.; Narkowicz, R.; Hassel, C.; Meckenstock, R.; Stienen, S.; Posth, O.; Suter, D.; Farle, M.; Lindner, J. Visualization of Spin Dynamics in Single Nanosized Magnetic Elements. Nanotechnology 2011, 22, 295713,  DOI: 10.1088/0957-4484/22/29/295713
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    19
    Visualization of spin dynamics in single nanosized magnetic elements
    Banholzer, A.; Narkowicz, R.; Hassel, C.; Meckenstock, R.; Stienen, S.; Posth, O.; Suter, D.; Farle, M.; Lindner, J.
    Nanotechnology (2011), 22 (29), 295713/1-295713/5CODEN: NNOTER; ISSN:1361-6528. (Institute of Physics Publishing)
    The design of future spintronic devices requires a quant. understanding of the microscopic linear and nonlinear spin relaxation processes governing the magnetization reversal in nanometer-scale ferromagnetic systems. Ferromagnetic resonance is the method of choice for a quant. anal. of relaxation rates, magnetic anisotropy and susceptibility in a single expt. The approach offers the possibility of coherent control and manipulation of nanoscaled structures by microwave irradn. Here, we analyze the different excitation modes in a single nanometer-sized ferromagnetic stripe. Measurements are performed using a microresonator set-up which offers a sensitivity to quant. analyze the dynamic and static magnetic properties of single nanomagnets with vols. of (100 nm)3. Uniform as well as non-uniform vol. modes of the spin wave excitation spectrum are identified and found to be in excellent agreement with the results of micromagnetic simulations which allow the visualization of the spatial distribution of these modes in the nanostructures.
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  20. 20
    Jenkins, M. D.; Hümmer, T.; Martínez-Pérez, M. J.; García-Ripoll, J.; Zueco, D.; Luis, F. Coupling Single-Molecule Magnets to Quantum Circuits. New J. Phys. 2013, 15, 095007,  DOI: 10.1088/1367-2630/15/9/095007
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    There is no corresponding record for this reference.
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    Jenkins, M. D.; Naether, U.; Ciria, M.; Sesé, J.; Atkinson, J.; Sánchez-Azqueta, C.; del Barco, E.; Majer, J.; Zueco, D.; Luis, F. Nanoscale Constrictions in Superconducting Coplanar Waveguide Resonators. Appl. Phys. Lett. 2014, 105, 162601,  DOI: 10.1063/1.4899141
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    21
    Nanoscale constrictions in superconducting coplanar waveguide resonators
    Jenkins, Mark David; Naether, Uta; Ciria, Miguel; Sese, Javier; Atkinson, James; Sanchez-Azqueta, Carlos; Barco, Enrique del; Majer, Johannes; Zueco, David; Luis, Fernando
    Applied Physics Letters (2014), 105 (16), 162601/1-162601/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    We report on the design, fabrication, and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concd. and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single mol. spins and have applications in circuit quantum electrodynamics, quantum computing, and ESR. (c) 2014 American Institute of Physics.
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  22. 22
    Haikka, P.; Kubo, Y.; Bienfait, A.; Bertet, P.; Mølmer, K. Proposal for Detecting a Single Electron Spin in a Microwave Resonator. Phys. Rev. A: At., Mol., Opt. Phys. 2017, 95, 022306,  DOI: 10.1103/PhysRevA.95.022306
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    There is no corresponding record for this reference.
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    Mannini, M.; Pineider, F.; Sainctavit, P.; Danieli, C.; Otero, E.; Sciancalepore, C.; Talarico, A. M.; Arrio, M.-A.; Cornia, A.; Gatteschi, D.; Sessoli, R. Magnetic Memory of a Single-Molecule Quantum Magnet Wired to a Gold Surface. Nat. Mater. 2009, 8, 194– 197,  DOI: 10.1038/nmat2374
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    23
    Magnetic memory of a single-molecule quantum magnet wired to a gold surface
    Mannini, Matteo; Pineider, Francesco; Sainctavit, Philippe; Danieli, Chiara; Otero, Edwige; Sciancalepore, Corrado; Talarico, Anna Maria; Arrio, Marie-Anne; Cornia, Andrea; Gatteschi, Dante; Sessoli, Roberta
    Nature Materials (2009), 8 (3), 194-197CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    In the field of mol. spintronics, the use of magnetic mols. for information technol. is a main target and the observation of magnetic hysteresis on individual mols. organized on surfaces is a necessary step to develop mol. memory arrays. Although simple paramagnetic mols. can show surface-induced magnetic ordering and hysteresis when deposited on ferromagnetic surfaces, information storage at the mol. level requires mols. exhibiting an intrinsic remnant magnetization, like the so-called single-mol. magnets (SMMs). These have been intensively investigated for their rich quantum behavior but no magnetic hysteresis has been so far reported for monolayers of SMMs on various nonmagnetic substrates, most probably owing to the chem. instability of clusters on surfaces. Using X-ray absorption spectroscopy and X-ray magnetic CD synchrotron-based techniques, pushed to the limits in sensitivity and operated at sub-kelvin temps., we have now found that robust, tailor-made Fe4 complexes retain magnetic hysteresis at gold surfaces. Our results demonstrate that isolated SMMs can be used for storing information. The road is now open to address individual mols. wired to a conducting surface in their blocked magnetization state, thereby enabling investigation of the elementary interactions between electron transport and magnetism degrees of freedom at the mol. scale.
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  24. 24
    Mannini, M.; Pineider, F.; Danieli, C.; Totti, F.; Sorace, L.; Sainctavit, P.; Arrio, M.-A.; Otero, E.; Joly, L.; Cezar, J. C.; Cornia, A.; Sessoli, R. Quantum Tunnelling of the Magnetization in a Monolayer of Oriented Single-Molecule Magnets. Nature 2010, 468, 417– 421,  DOI: 10.1038/nature09478
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    24
    Quantum tunnelling of the magnetization in a monolayer of oriented single-molecule magnets
    Mannini, M.; Pineider, F.; Danieli, C.; Totti, F.; Sorace, L.; Sainctavit, Ph.; Arrio, M.-A.; Otero, E.; Joly, L.; Cezar, J. C.; Cornia, A.; Sessoli, R.
    Nature (London, United Kingdom) (2010), 468 (7322), 417-421CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    A fundamental step towards at.- or mol.-scale spintronic devices has recently been made by demonstrating that the spin of an individual atom deposited on a surface, or of a small paramagnetic mol. embedded in a nanojunction, can be externally controlled. An appealing next step is the extension of such a capability to the field of information storage, by taking advantage of the magnetic bistability and rich quantum behavior of single-mol. magnets (SMMs). Recently, a proof of concept that the magnetic memory effect is retained when SMMs are chem. anchored to a metallic surface was provided. However, control of the nanoscale organization of these complex systems is required for SMMs to be integrated into mol. spintronic devices. A preferential orientation of Fe4 complexes on a gold surface can be achieved by chem. tailoring. As a result, the most striking quantum feature of SMMs, their stepped hysteresis loop, which results from resonant quantum tunneling of the magnetization, can be clearly detected using synchrotron-based spectroscopic techniques. With the aid of multiple theor. approaches, the authors relate the angular dependence of the quantum tunneling resonances to the adsorption geometry, and demonstrate that mols. predominantly lie with their easy axes close to the surface normal. The findings prove that the quantum spin dynamics can be obsd. in SMMs chem. grafted to surfaces, and offer a tool to reveal the organization of matter at the nanoscale.
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    Domingo, N.; Bellido, E.; Ruiz-Molina, D. Advances on Structuring, Integration and Magnetic Characterization of Molecular Nanomagnets on Surfaces and Devices. Chem. Soc. Rev. 2012, 41, 258– 302,  DOI: 10.1039/C1CS15096K
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    25
    Advances on structuring, integration and magnetic characterization of molecular nanomagnets on surfaces and devices
    Domingo, N.; Bellido, E.; Ruiz-Molina, D.
    Chemical Society Reviews (2012), 41 (1), 258-302CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    This crit. review represents a concise revision of the different exptl. approaches so far followed for the structuration of mol. nanomagnets on surfaces, since the first reports on the field more than ten years ago. Afterwards, a presentation of the different exptl. approaches followed for their integration in sensors is described. Such work involves mainly two families of sensors and devices, microSQUIDs sensors and three-terminal devices for single-mol. detection. Finally the last section is devoted to a detailed revision of the different exptl. techniques that can be used for the magnetic characterization of these systems on surfaces, ranging from magnetic CD to magnetic force microscopy. The use of these techniques to characterize other nanostructured magnetic materials, such as nanoparticles, is also revised. The aim is to give a broad overview of the last advances achieved with these techniques and their potential and evolution over the next years.
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    Thiele, S.; Balestro, F.; Ballou, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, W. Electrically Driven Nuclear Spin Resonance in Single-Molecule Magnets. Science 2014, 344, 1135– 1138,  DOI: 10.1126/science.1249802
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    26
    Electrically driven nuclear spin resonance in single-molecule magnets
    Thiele, Stefan; Balestro, Franck; Ballou, Rafik; Klyatskaya, Svetlana; Ruben, Mario; Wernsdorfer, Wolfgang
    Science (Washington, DC, United States) (2014), 344 (6188), 1135-1138CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    Recent advances in addressing isolated nuclear spins have opened up a path toward using nuclear-spin-based quantum bits. Local magnetic fields are normally used to coherently manipulate the state of the nuclear spin; however, elec. manipulation would allow for fast switching and spatially confined spin control. Here, the authors propose and demonstrate coherent single nuclear spin manipulation using elec. fields only. Because there is no direct coupling between the spin and the elec. field, the authors make use of the hyperfine Stark effect as a magnetic field transducer at the at. level. This quantum-mech. process is present in all nuclear spin systems, such as phosphorus or bismuth atoms in silicon, and offers a general route toward the elec. control of nuclear-spin-based devices.
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  27. 27
    Malavolti, L.; Briganti, M.; Hänze, M.; Serrano, G.; Cimatti, I.; McMurtrie, G.; Otero, E.; Ohresser, P.; Totti, F.; Mannini, M.; Sessoli, R.; Loth, S. Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules. Nano Lett. 2018, 18, 7955,  DOI: 10.1021/acs.nanolett.8b03921
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    27
    Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules
    Malavolti, Luigi; Briganti, Matteo; Haenze, Max; Serrano, Giulia; Cimatti, Irene; McMurtrie, Gregory; Otero, Edwige; Ohresser, Philippe; Totti, Federico; Mannini, Matteo; Sessoli, Roberta; Loth, Sebastian
    Nano Letters (2018), 18 (12), 7955-7961CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
    Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) mols. deposited on the Pb surface. The VOPc mol. is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied dxy-orbital and is a promising candidate for a mol. spin qubit with long coherence times. X-ray magnetic CD (XMCD) measurements show that the mol. spin remains unperturbed even for mols. directly deposited on the Pb surface. Scanning tunneling spectroscopy and d. functional theory (DFT) calcns. identify two adsorption geometries for this "asym." mol. (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Addnl., we find that in the first case a YSR state can be induced smoothly by exerting mech. force on the mols. with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated mol. spin case, through the quantum crit. point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.
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  28. 28
    Urtizberea, A.; Natividad, E.; Alonso, P. J.; Pérez-Martínez, L.; Andrés, M. A.; Gascón, I.; Gimeno, I.; Luis, F.; Roubeau, O. Vanadyl Spin Qubit 2D Arrays and their Integration on Superconducting Resonators. Mater. Horiz. 2020, 7, 885– 897,  DOI: 10.1039/C9MH01594A
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    28
    Vanadyl spin qubit 2D arrays and their integration on superconducting resonators
    Urtizberea, Ainhoa; Natividad, Eva; Alonso, Pablo J.; Perez-Martinez, Laura; Andres, Miguel A.; Gascon, Ignacio; Gimeno, Ignacio; Luis, Fernando; Roubeau, Olivier
    Materials Horizons (2020), 7 (3), 885-897CODEN: MHAOBM; ISSN:2051-6355. (Royal Society of Chemistry)
    Vanadyl systems have been shown to possess superior quantum coherence among mol. spin qubits. Meanwhile two-dimensional (2D) networks of spin qubit nodes could provide a means to achieve the control of qubit localization and orientation required for implementation of mol. spin qubits in hybrid solid-state devices. Here, the 2D metal-org. framework [{VO(TCPP)}Zn2(H2O)2]∞ is reported and its vanadyl porphyrin node is shown to exhibit superior spin dynamics and to enable coherent spin manipulations, making it a valid spin qubit candidate. Nanodomains of the MOF 2D coordination planes are efficiently formed at the air-water interface, first under Langmuir-Schaefer conditions, allowing mono- and multiple layer deposits to be transferred to a variety of substrates. Similar nanodomains are then successfully formed in situ on the surface of Nb superconducting coplanar resonators. Transmission measurements with a resonator with a 14 μm-wide constriction allow to est. that the single spin-photon coupling G1 of the vanadyl spins in the nanodomains is close to being optimal, at ca. 0.5 Hz. Altogether, these results provide the basis for developing a viable hybrid quantum computing architecture.
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    Leuenberger, M.; Loss, D. Quantum Computing in Molecular Magnets. Nature 2001, 410, 789– 793,  DOI: 10.1038/35071024
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    Quantum computing in molecular magnets
    Leuenberger, Michael N.; Loss, Daniel
    Nature (London, United Kingdom) (2001), 410 (6830), 789-793CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring nos. and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses mol. magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theor. that mol. magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast ESR pulses can be used to decode and read out stored nos. of up to 10, with access times as short as 10 s. We show that our proposal should be feasible using the mol. magnets Fe8 and Mn12.
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    Troiani, F.; Affronte, M. Molecular Spins for Quantum Information Technologies. Chem. Soc. Rev. 2011, 40, 3119– 3129,  DOI: 10.1039/c0cs00158a
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    Molecular spins for quantum information technologies
    Troiani, Filippo; Affronte, Marco
    Chemical Society Reviews (2011), 40 (6), 3119-3129CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. Technol. challenges for quantum information technologies lead us to consider aspects of mol. magnetism in a radically new perspective. The design of new derivs. and recent exptl. results on mol. nanomagnets are covered in this tutorial review through the keyhole of basic concepts of quantum information, such as the control of decoherence and entanglement at the (supra-)mol. level.
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    Aromí, G.; Aguilà, D.; Gamez, P.; Luis, F.; Roubeau, O. Design of Magnetic Coordination Complexes for Quantum Computing. Chem. Soc. Rev. 2012, 41, 537– 546,  DOI: 10.1039/C1CS15115K
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    Design of magnetic coordination complexes for quantum computing
    Aromi, Guillem; Aguila, David; Gamez, Patrick; Luis, Fernando; Roubeau, Olivier
    Chemical Society Reviews (2012), 41 (2), 537-546CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review. A very exciting prospect in coordination chem. is to manipulate spins within magnetic complexes for the realization of quantum logic operations. An introduction to the requirements for a paramagnetic mol. to act as a 2-qubit quantum gate is provided in this tutorial review. We propose synthetic methods aimed at accessing such type of functional mols., based on ligand design and inorg. synthesis. Two strategies are presented: (i) the first consists in targeting mols. contg. a pair of well-defined and weakly coupled paramagnetic metal aggregates, each acting as a carrier of one potential qubit, (ii) the second is the design of dinuclear complexes of anisotropic metal ions, exhibiting dissimilar environments and feeble magnetic coupling. The first systems obtained from this synthetic program are presented here and their properties are discussed.
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    Moreno-Pineda, E.; Godfrin, C.; Balestro, F.; Wernsdorfer, W.; Ruben, M. Molecular Spin Qudits for Quantum Algorithms. Chem. Soc. Rev. 2018, 47, 501– 513,  DOI: 10.1039/C5CS00933B
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    Molecular spin qudits for quantum algorithms
    Moreno-Pineda, Eufemio; Godfrin, Clement; Balestro, Franck; Wernsdorfer, Wolfgang; Ruben, Mario
    Chemical Society Reviews (2018), 47 (2), 501-513CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    Presently, one of the most ambitious technol. goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for purposes not achievable with even the most powerful computer resources. The large-scale implementation of quantum information would be a game changer for current technol., because it would allow unprecedented parallelised computation and secure encryption based on the principles of quantum superposition and entanglement. Currently, there are several phys. platforms racing to achieve the level of performance required for the quantum hardware to step into the realm of practical quantum information applications. Several materials have been proposed to fulfil this task, ranging from quantum dots, Bose-Einstein condensates, spin impurities, superconducting circuits, mols., amongst others. Magnetic mols. are among the list of promising building blocks, due to (i) their intrinsic monodispersity, (ii) discrete energy levels (iii) the possibility of chem. quantum state engineering, and (iv) their multilevel characteristics that lead to Qudits, where the dimension of the Hilbert space is d > 2. Herein we review how a mol. nuclear spin qudit, (d = 4), known as TbPc2, gathers all the necessary requirements to perform as a mol. hardware platform with a first generation of mol. devices enabling even quantum algorithm operations.
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    Gaita-Ariño, A.; Luis, F.; Hill, S.; Coronado, E. Molecular Spins for Quantum Computation. Nat. Chem. 2019, 11, 301– 309,  DOI: 10.1038/s41557-019-0232-y
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    Molecular spins for quantum computation
    Gaita-Arino, A.; Luis, F.; Hill, S.; Coronado, E.
    Nature Chemistry (2019), 11 (4), 301-309CODEN: NCAHBB; ISSN:1755-4330. (Nature Research)
    Spins in solids or in mols. possess discrete energy levels, and the assocd. quantum states can be tuned and coherently manipulated by means of external electromagnetic fields. Spins therefore provide one of the simplest platforms to encode a quantum bit (qubit), the elementary unit of future quantum computers. Performing any useful computation demands much more than realizing a robust qubit-one also needs a large no. of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chem.-based bottom-up approach is best-suited. Mols., being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large nos. using chem. tools.
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    Atzori, M.; Sessoli, R. The Second Quantum Revolution: Role and Challenges of Molecular Chemistry. J. Am. Chem. Soc. 2019, 141, 11339– 11352,  DOI: 10.1021/jacs.9b00984
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    The Second Quantum Revolution: Role and Challenges of Molecular Chemistry
    Atzori, Matteo; Sessoli, Roberta
    Journal of the American Chemical Society (2019), 141 (29), 11339-11352CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    A review. Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by mol. spin systems. In this Perspective, we highlight the role that mol. chem. can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of mol. components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the mol. chem. community, such as for example the design of mol. spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a crit. eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.
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    Current distribution simulation for superconducting multi-layered structures
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    Superconductor Science and Technology (2003), 16 (1), 24-27CODEN: SUSTEF; ISSN:0953-2048. (Institute of Physics Publishing)
    The software package 3D-MLSI is developed, which allows us to calc. the current distribution and to ext. inductances from multi-layered high-Tc and low-Tc superconducting circuits. Both kinetic and magnetic inductances as well as the three-dimensional distribution of the magnetic field are taken into account. We discuss the numerical approach used in 3D-MLSI and some new features such as visualization of sheet currents and anal. of circuits with holes. As an example, we present a simulation of a high-Tc double-layer transformer.
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    Weil, J. A.; Anderson, J. K. 1039. The Determination and Reaction of 2,2-Diphenyl-1-Picrylhydrazyl with Thiosalicylic Acid. J. Chem. Soc. 1965, 5567– 5570,  DOI: 10.1039/jr9650005567
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    The determination and reaction of 2,2-diphenyl-1-picrylhydrazyl with thiosalicylic acid
    Weil, John A.; Anderson, Judith K.
    Journal of the Chemical Society (1965), (Oct.), 5567-70CODEN: JCSOA9; ISSN:0368-1769.
    An accurate method for analysis of 2,2-diphenyl-1-picrylhydrazyl (DPPH) has been developed, using a simple titration procedure with thiosalicylic acid. The products of the reaction were 1,1-diphenyl-2-picrylhydrazine and 2,2'-dithiodibenzoic acid (dithiosalicylic acid). It was also observed that several forms of solvent-free DPPH exist.
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    Yordanov, N. D. Is Our Knowledge about the Chemical and Physical Properties of DPPH Enough to Consider it as a Primary Standard for Quantitative EPR Spectrometry?. Appl. Magn. Reson. 1996, 10, 339– 350,  DOI: 10.1007/BF03163117
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    Is our knowledge about the chemical and physical properties of DPPH enough to consider it as a primary standard for quantitative EPR spectrometry?
    Yordanov, Nicola D.
    Applied Magnetic Resonance (1996), 10 (1-3), 339-350CODEN: APMREI; ISSN:0937-9347. (Springer)
    A review with 41 refs. on the physico-chem. properties of the stable free radical DPPH (1,1-diphenyl-2-picrylhydrazyl) and its use as a primary std. for quant. ESR.
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    Žilić, D.; Pajić, D.; Jurić, M.; Molčanov, K.; Rakvin, B.; Planinić, P.; Zadro, K. Single Crystals of DPPH Grown from Diethyl Ether and Carbon Disulfide Solutions – Crystal Structures, IR, EPR and Magnetization Studies. J. Magn. Reson. 2010, 207, 34– 41,  DOI: 10.1016/j.jmr.2010.08.005
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    Single crystals of DPPH grown from diethyl ether and carbon disulfide solutions - Crystal structures, IR, EPR and magnetization studies
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    Journal of Magnetic Resonance (2010), 207 (1), 34-41CODEN: JMARF3; ISSN:1090-7807. (Elsevier B.V.)
    Single crystals of the free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH) obtained from di-Et ether (ether) and carbon disulfide (CS2) were characterized by the X-ray diffraction, IR, EPR and SQUID magnetization techniques. The X-ray structural anal. and IR spectra showed that the DPPH form crystd. from ether (DPPH1) is solvent free, whereas that one obtained from CS2 (DPPH2) is a solvate of the compn. 4DPPH·CS2. Principal values of the g-tensor were estd. by the X-band EPR spectroscopy at room and low (10 K) temps. Magnetization studies revealed the presence of antiferromagnetically coupled dimers in both types of crystals. However, the way of dimerization as well as the strength of exchange couplings are different in the two DPPH samples, which is in accord with their crystal structures. The obtained results improved parameters accuracy and enabled better understanding of properties of DPPH as a std. sample in the EPR spectrometry.
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    Exchange narrowing in paramagnetic resonance
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    Reviews of Modern Physics (1953), 25 (), 269-76CODEN: RMPHAT; ISSN:0034-6861.
    A math. model called the model of "random frequency modulation" is used to discuss the line shape in paramagnetic resonance when large exchange interaction is present. The assumption is made that the atom absorbs one single frequency, which varies over a distribution detd. by the dipolar local fields, but that this frequency varies in a random manner in time, at a rate detd. by the exchange interactions. Where the exchange is large, the predicted line shape is of the resonance type but fails off rapidly at the wings. Under the assumption that a good approximation to the modulation function is Gaussian noise with a Gaussian spectrum the 2nd moment (which is independent of exchange) and the 4th moment of the line shape can be calculated. The result as to line breath is given as: Δ equal or nearly equal to (Δω2)av. dipole-dipole (h/J).
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    Höcherl, G.; Wolf, H. C. Zur Konzentrationsabhängigkeit der Elektronenspin-Relaxationszeiten von Diphenyl-Picryl-Hydrazyl in fester Phase. Eur. Phys. J. A 1965, 183, 341– 351,  DOI: 10.1007/BF01380763
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    Piner, R. D.; Zhu, J.; Xu, F.; Hong, S.; Mirkin, C. A. ”Dip-Pen” Nanolithography. Science 1999, 283, 661– 663,  DOI: 10.1126/science.283.5402.661
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    "Dip-pen" nanolithography
    Piner, Richard D.; Zhu, Jin; Xu, Feng; Hong, Seunghun; Mirkin, Chad A.
    Science (Washington, D. C.) (1999), 283 (5402), 661-663CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    A direct-write "dip-pen" nanolithog. (DPN) has been developed to deliver collections of mols. in a pos. printing mode. An at. force microscope (AFM) tip is used to write alkanethiols with 30-nm linewidth resoln. on a gold thin film in a manner analogous to that of a dip pen. Mols. are delivered from the AFM tip to a solid substrate of interest via capillary transport, making DPN a potentially useful tool for creating and functionalizing nanoscale devices.
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    Bellido, E.; de Miguel, R.; Ruiz-Molina, D.; Lostao, A.; Maspoch, D. Controlling the Number of Proteins with Dip-Pen Nanolitography. Adv. Mater. 2010, 22, 352– 355,  DOI: 10.1002/adma.200902372
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    Controlling the Number of Proteins with Dip-Pen Nanolithography
    Bellido, Elena; de Miguel, Rocio; Ruiz-Molina, Daniel; Lostao, Anabel; Maspoch, Daniel
    Advanced Materials (Weinheim, Germany) (2010), 22 (3), 352-355CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
    We describe a novel strategy that utilizes the ability of dip-pen nanolithog. (DPN) to direct-write proteins on the surface of transmission electron microscopy (TEM) grids. Ferritin protein was chosen as an excellent model system because of its size and central inorg. core of hydrated iron(III) oxide, which allows its visualization by TEM, and therefore, its individual identification on the surface of the TEM grids. The data show that this is a versatile way to quantify the no. of ferritin particles written by DPN, and that this no. can be controlled by adjusting the protein concn. used to coat the at. force microscopy (AFM) tips and the dimensions of the dot-like features fabricated by DPN.
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    Martínez-Pérez, M. J.; Bellido, E.; de Miguel, R.; Sesé, J.; Lostao, A.; Gómez-Moreno, C.; Drung, D.; Schurig, T.; Ruiz-Molina, D.; Luis, F. Alternating Current Magnetic Susceptibility of a Molecular Magnet Submonolayer Directly Patterned onto a Micro Superconducting Quantum Interference Device. Appl. Phys. Lett. 2011, 99, 032504,  DOI: 10.1063/1.3609859
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    Alternating current magnetic susceptibility of a molecular magnet submonolayer directly patterned onto a micro superconducting quantum interference device
    Martinez-Perez, M. J.; Bellido, E.; de Miguel, R.; Sese, J.; Lostao, A.; Gomez-Moreno, C.; Drung, D.; Schurig, T.; Ruiz-Molina, D.; Luis, F.
    Applied Physics Letters (2011), 99 (3), 032504/1-032504/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
    We report the controlled integration, via dip pen nanolithog., of monolayer dots of ferritin-based CoO nanoparticles (12 μB) into the most sensitive areas of a microSQUID sensor. The nearly optimum flux coupling between these nanomagnets and the microSQUID improves the achievable sensitivity by a factor 102, enabling us to measure the linear susceptibility of the mol. array down to very low temps. (13 mK). This method opens the possibility of applying a.c. susceptibility expts. to characterize 2D arrays of single mol. magnets within a wide range of temps. and frequencies. (c) 2011 American Institute of Physics.
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    Bellido, E.; González-Monje, P.; Repollés, A.; Jenkins, M.; Sesé, J.; Drung, D.; Schurig, T.; Awaga, K.; Luis, F.; Ruiz-Molina, D. Mn12 Single Molecule Magnets Deposited on μ-SQUID Sensors: the Role of Interphases and Structural Modifications. Nanoscale 2013, 5, 12565– 12573,  DOI: 10.1039/c3nr02359a
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    Mn12 single molecule magnets deposited on μ-SQUID sensors: the role of interphases and structural modifications
    Bellido, Elena; Gonzalez-Monje, Pablo; Repolles, Ana; Jenkins, Mark; Sese, Javier; Drung, Dietmar; Schurig, Thomas; Awaga, Kunio; Luis, Fernando; Ruiz-Molina, Daniel
    Nanoscale (2013), 5 (24), 12565-12573CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
    Direct measurements of the linear ac susceptibility and magnetic relaxation of a few Mn12 monolayers deposited on a μ-SQUID sensor are reported. In order to integrate the mols. into the device, DPN has been the technique of choice. It enabled the structuration of the mols. on the most sensitive areas of the sensor without the need for any previous functionalization of the mol. or the substrate, while controlling the no. of mol. units deposited on each array. The measurements reveal that their characteristic SMM behavior is lost, a fact that is attributed to mol. distortions originated by the strong surface tensions arising at the mol. interphases.
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    Bushev, P.; Feofanov, A. K.; Rotzinger, H.; Protopopov, I.; Cole, J. H.; Wilson, C. M.; Fischer, G.; Lukashenko, A.; Ustinov, A. V. Ultralow-Power Spectroscopy of a Rare-Earth Spin Ensemble Using a Superconducting Resonator. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 060501,  DOI: 10.1103/PhysRevB.84.060501
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    Physical Review B: Condensed Matter and Materials Physics (2011), 84 (6), 060501/1-060501/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Interfacing superconducting quantum processors, working in the GHz frequency range, with optical quantum networks and at. qubits is a challenging task for the implementation of distributed quantum information processing as well as for quantum communication. Using spin ensembles of rare earth ions provides an excellent opportunity to bridge microwave and optical domains at the quantum level. The ultralow-power, on-chip, ESR spectroscopy of Er3+ spins doped in a Y2SiO5 crystal using a high-Q, coplanar, superconducting resonator is demonstrated.
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    Hümmer, T.; Reuther, G. M.; Hänggi, P.; Zueco, D. Nonequilibrium Phases in Hybrid Arrays with Flux Qubits and Nitrogen-Vacancy Centers. Phys. Rev. A: At., Mol., Opt. Phys. 2012, 85, 052320,  DOI: 10.1103/PhysRevA.85.052320
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    Martínez-Pérez, M. J.; Zueco, D. Strong Coupling of a Single Photon to a Magnetic Vortex. ACS Photonics 2019, 6, 360– 367,  DOI: 10.1021/acsphotonics.8b00954
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    Strong Coupling of a Single Photon to a Magnetic Vortex
    Martinez-Perez, Maria Jose; Zueco, David
    ACS Photonics (2019), 6 (2), 360-367CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
    Strong light-matter coupling means that cavity photons and other types of matter excitations are coherently exchanged. It is used to couple different qubits (matter) via a quantum bus (photons) or to communicate different types of excitations, e.g., transducing light into phonons or magnons. A, so far, unexplored interface is the coupling between light and topol. protected particle-like excitations as magnetic domain walls, skyrmions, or vortices. Theor. a single photon living in a superconducting cavity can be strongly coupled to the gyrotropic mode of a magnetic vortex in a nanodisc. Numerical and anal. calcns. were combined for a superconducting coplanar waveguide resonator and different realizations of the nanodisc (materials and sizes). For enhancing the coupling, constrictions fabricated in the resonator are crucial, allowing to reach strong coupling in CoFe disks of radius 200-400 nm having resonance frequencies of a few GHz. The strong coupling regime permits coherently exchanging a single photon and quanta of vortex gyration. The calcns. show that the device proposed here serves as a transducer between photons and gyrating vortices, opening the way to complement superconducting qubits with topol. protected spin-excitations such as vortices or skyrmions. The authors finish by discussing potential applications in quantum data processing based on the exploitation of the vortex as a short-wavelength magnon emitter.
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    Warner, M.; Din, S.; Tupitsyn, I. S.; Morley, G. W.; Stoneham, A.; Gardener, J. A.; Wu, Z.; Fisher, A. J.; Heutz, S.; Kay, C. W. M.; Aeppli, G. Ptential fot Spin-Based Information Processing in a Thin-Film Molecular Semiconductor. Nature 2013, 503, 504– 508,  DOI: 10.1038/nature12597
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    Potential for spin-based information processing in a thin-film molecular semiconductor
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    Nature (London, United Kingdom) (2013), 503 (7477), 504-508CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Org. semiconductors were studied intensively for applications in electronics and optics, and even spin-based information technol., or spintronics. Fundamental quantities in spintronics are the population relaxation time (T1) and the phase memory time (T2): T1 measures the lifetime of a classical bit, in this case embodied by a spin oriented either parallel or antiparallel to an external magnetic field, and T2 measures the corresponding lifetime of a quantum bit, encoded in the phase of the quantum state. These times are surprisingly long for a common, low-cost and chem. modifiable org. semiconductor, the blue pigment Cu phthalocyanine, in easily processed thin-film form used for device fabrication. At 5 K, a temp. reachable using inexpensive closed-cycle refrigerators, T1 and T2 are resp. 59 ms and 2.6 μs, and at 80 K, which is just above the b.p. of liq. N, they are resp. 10 μs and 1 μs, demonstrating that the performance of thin-film Cu phthalocyanine is superior to that of single-mol. magnets over the same temp. range. T2 is more than two orders of magnitude greater than the duration of the spin manipulation pulses, which suggests that Cu phthalocyanine holds promise for quantum information processing, and the long T1 indicates possibilities for medium-term storage of classical bits in all-org. devices on plastic substrates.
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    Graphene, a single-layer network of carbon atoms, has outstanding elec. and mech. properties1. Graphene ribbons with nanometer-scale widths2,3 (nanoribbons) should exhibit half-metallicity4 and quantum confinement. Magnetic edges in graphene nanoribbons5,6 have been studied extensively from a theor. standpoint because their coherent manipulation would be a milestone for spintronic7 and quantum computing devices8. However, exptl. investigations have been hampered because nanoribbon edges cannot be produced with at. precision and the graphene terminations that have been proposed are chem. unstable9. Here we address both of these problems, by using mol. graphene nanoribbons functionalized with stable spin-bearing radical groups. We observe the predicted delocalized magnetic edge states and test theor. models of the spin dynamics and spin-environment interactions. Comparison with a non-graphitized ref. material enables us to clearly identify the characteristic behavior of the radical-functionalized graphene nanoribbons. We quantify the parameters of spin-orbit coupling, define the interaction patterns and det. the spin decoherence channels. Even without any optimization, the spin coherence time is in the range of microseconds at room temp., and we perform quantum inversion operations between edge and radical spins. Our approach provides a way of testing the theory of magnetism in graphene nanoribbons exptl. The coherence times that we observe open up encouraging prospects for the use of magnetic nanoribbons in quantum spintronic devices.
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    Science (Washington, DC, United States) (2019), 366 (6469), 1107-1110CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
    A review. Robustly coherent spin centers that can be integrated into devices are a key ingredient of quantum technologies. Vacancies in semiconductors are excellent candidates, and theory predicts that defects in conjugated carbon materials should also display long coherence times. However, the quantum performance of carbon nanostructures has remained stunted by an inability to alter the sp2-carbon lattice with at. precision. Here, we demonstrate that topol. tailoring leads to superior quantum performance in mol. graphene nanostructures. We unravel the decoherence mechanisms, quantify nuclear and environmental effects, and observe spin-coherence times that outclass most nanomaterials. These results validate long-standing assumptions on the coherent behavior of topol. defects in graphene and open up the possibility of introducing controlled quantum-coherent centers in the upcoming generation of carbon-based optoelectronic, electronic, and bioactive systems.
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    Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in mol. nanomagnets for the first time. In Cr7M heterometallic wheels, with M = Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the mol. In deuterated samples T2 reaches 3 μs at low temps., which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of mol. nanomagnets in quantum information applications.
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    Nature Communications (2014), 5 (), 5304CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    The successful development of a quantum computer would change the world, and current internet encryption methods would cease to function. However, no working quantum computer that even begins to rival conventional computers has been developed yet, which is due to the lack of suitable quantum bits. A key characteristic of a quantum bit is the coherence time. Transition metal complexes are very promising quantum bits, owing to their facile surface deposition and their chem. tunability. However, reported quantum coherence times have been unimpressive. Here we report very long quantum coherence times for a transition metal complex of 68 μs at low temp. (qubit figure of merit QM=3,400) and 1 μs at room temp., much higher than previously reported values for such systems. We show that this achievement is because of the rigidity of the lattice as well as removal of nuclear spins from the vicinity of the magnetic ion.
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    Nature (London, United Kingdom) (2016), 531 (7594), 348-351CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    Quantum computing is an emerging area within the information sciences revolving around the concept of quantum bits (qubits). A major obstacle is the extreme fragility of these qubits due to interactions with their environment that destroy their quantumness. This phenomenon, known as decoherence, is of fundamental interest. There are many competing candidates for qubits, including superconducting circuits, quantum optical cavities, ultracold atoms and spin qubits, and each has its strengths and weaknesses. When dealing with spin qubits, the strongest source of decoherence is the magnetic dipolar interaction. To minimize it, spins are typically dild. in a diamagnetic matrix. For example, this diln. can be taken to the extreme of a single phosphorus atom in silicon, whereas in mol. matrixes a typical ratio is one magnetic mol. per 10,000 matrix mols. However, there is a fundamental contradiction between reducing decoherence by diln. and allowing quantum operations via the interaction between spin qubits. To resolve this contradiction, the design and engineering of quantum hardware can benefit from a 'bottom-up' approach whereby the electronic structure of magnetic mols. is chem. tailored to give the desired phys. behavior. Here we present a way of enhancing coherence in solid-state mol. spin qubits without resorting to extreme diln. It is based on the design of mol. structures with crystal field ground states possessing large tunnelling gaps that give rise to optimal operating points, or at. clock transitions, at which the quantum spin dynamics become protected against dipolar decoherence. This approach is illustrated with a holmium mol. nanomagnet in which long coherence times (up to 8.4 μs at 5 K) are obtained at unusually high concns. This finding opens new avenues for quantum computing based on mol. spin qubits.
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    Quantum information processing (QIP) could revolutionize areas ranging from chem. modeling to cryptog. One key figure of merit for the smallest unit for QIP, the qubit, is the coherence time (T2), which establishes the lifetime for the qubit. Transition metal complexes offer tremendous potential as tunable qubits, yet their development is hampered by the absence of synthetic design principles to achieve a long T2. The authors harnessed mol. design to create qubits, (Ph4P)2[V(C8S8)3] (1), (Ph4P)2[V(β-C3S5)3] (2), (Ph4P)2[V(α-C3S5)3] (3), and (Ph4P)2[V(C3S4O)3] (4), with T2s of 1-4 μs at 80 K in protiated and deuterated environments. Crucially, through chem. tuning of nuclear spin content in the V(IV) environment the authors realized a T2 of ∼1 ms for the species (d20-Ph4P)2[V(C8S8)3] (1') in CS2, a value that surpasses the coordination complex record by an order of magnitude. This value even eclipses some prominent solid-state qubits. Electrochem. and continuous wave EPR data reveal variation in the electronic influence of the ligands on the metal ion across 1-4. However, pulsed measurements indicate that the most important influence on decoherence is nuclear spins in the protiated and deuterated solvents used herein. The authors' results illuminate a path forward in synthetic design principles, which should unite CS2 soly. with nuclear spin free ligand fields to develop a new generation of mol. qubits.
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    Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temp., and we demonstrate strong coupling at base temp. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in org. crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temp.
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    Scientific reports (2017), 7 (1), 13096 ISSN:.
    Electron spins are ideal two-level systems that may couple with microwave photons so that, under specific conditions, coherent spin-photon states can be realized. This represents a fundamental step for the transfer and the manipulation of quantum information. Along with spin impurities in solids, molecular spins in concentrated phases have recently shown coherent dynamics under microwave stimuli. Here we show that it is possible to obtain high cooperativity regime between a molecular Vanadyl Phthalocyanine (VOPc) spin ensemble and a high quality factor superconducting YBa2Cu3O7 (YBCO) coplanar resonator at 0.5 K. This demonstrates that molecular spin centers can be successfully integrated in hybrid quantum devices.
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  2. Selena J. Lockyer, Alessandro Chiesa, Adam Brookfield, Grigore A. Timco, George F. S. Whitehead, Eric J. L. McInnes, Stefano Carretta, Richard E. P. Winpenny. Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States. Journal of the American Chemical Society 2022, 144 (35) , 16086-16092. https://doi.org/10.1021/jacs.2c06384
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  8. A. Chiesa, S. Roca, S. Chicco, M.C. de Ory, A. Gómez-León, A. Gomez, D. Zueco, F. Luis, S. Carretta. Blueprint for a Molecular-Spin Quantum Processor. Physical Review Applied 2023, 19 (6) https://doi.org/10.1103/PhysRevApplied.19.064060
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  11. Alessandro Lunghi. Spin-Phonon Relaxation in Magnetic Molecules: Theory, Predictions and Insights. 2023, 219-289. https://doi.org/10.1007/978-3-031-31038-6_6
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  15. Victor Rollano, Marina C. de Ory, Christian D. Buch, Marcos Rubín-Osanz, David Zueco, Carlos Sánchez-Azqueta, Alessandro Chiesa, Daniel Granados, Stefano Carretta, Alicia Gomez, Stergios Piligkos, Fernando Luis. High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture. Communications Physics 2022, 5 (1) https://doi.org/10.1038/s42005-022-01017-8
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  18. M. Chizzini, L. Crippa, A. Chiesa, F. Tacchino, F. Petiziol, I. Tavernelli, P. Santini, S. Carretta. Molecular nanomagnets with competing interactions as optimal units for qudit-based quantum computation. Physical Review Research 2022, 4 (4) https://doi.org/10.1103/PhysRevResearch.4.043135
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  • Abstract

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    Figure 1

    Figure 1. (A) Scanning electron microscopy image of the central line of a superconducting coplanar resonator. The line was thinned down to a width of about 158 nm by focused ion beam nanolithography. (B) Color plot of the photon magnetic field in the neighborhood of this constriction, calculated with a finite-element simulation software. (35) (C) Structure of a DPPH free-radical molecule, with spin S = 1/2 and g = 2 (left) and optical microscopy image of the constriction after the deposition of DPPH by means of the tip of an Atomic Force Microscope (AFM, right). (D) AFM image of the constriction taken before and after the molecules were deposited and the solvent had evaporated.

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    Figure 2

    Figure 2. (Top) Color scale plots of the microwave transmission through 1.4 GHz on-chip superconducting resonators with a 14 μm wide central line (A) and with a 158 nm wide constriction (B) coupled to a DPPH deposit with N ≈ 5 × 109 molecules, corresponding to Neff ≈ 4 × 107 spins effectively coupled to the resonator at T = 4.2 K. The red dashed lines mark the position of the resonance frequency at each magnetic field. The inset in B shows transmission versus frequency data near resonance at the field values indicated by arrows, evidencing the detection of a net absorption (lower transmission and broader resonance) when the spins get into mutual resonance with the circuit. (Bottom) Magnetic field dependence of the resonance width κ for the same resonators (C without and D with constriction) coupled to ensembles of DPPH molecules of varying size. Solid lines are least-squares fits based on eq 1.

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    Figure 3

    Figure 3. Collective spin-photon coupling of ensembles of free-radical molecules to coplanar resonators with a 14 μm wide transmission line (top) and a 158 nm constriction (bottom). The solid lines are least-squares fits to a linear dependence on the square root of the effective number of spins that are coupled to the devices at T = 4.2 K, as predicted by eq 2. The bottom panel compares both fits to highlight the coupling enhancement generated by the constriction.

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    Figure 4

    Figure 4. AFM topographic map (A) and SEM image (B) of the region near a 42 nm wide nanoconstriction. (C and D) Color maps of the number of DPPH molecules deposited on each location and of the estimated single spin to photon couplings, respectively. The latter maps have been calculated with a discretization of space into 3 × 3 × 3 nm3 cubic cells. The number of free-radical molecules deposited in this area amounts to approximately N = 1.6 × 108, and the collective coupling estimated from the simulations is GN/2π ≃ 2.0 MHz at T = 44 mK and 2.5 MHz at T = 0.

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    Figure 5

    Figure 5. (A) Color plot of the microwave transmission, measured at T = 44 mK, through a superconducting resonator with a 42 nm wide constriction in its central transmission line and coupled to an ensemble of N ≃ 1.6 × 108 free-radical molecules (corresponding to Neff ≃ 108 spins effectively coupled to the resonator). (B) Color plot of the microwave transmission calculated for a collective coupling GN/2π = 2.0 MHz, as follows from the simulations described in Figure 4, and a spin line width γ = 65 MHz. (C) Magnetic field dependence of the resonance width κ for the same device measured at different temperatures. Solid lines are least-squares fits using eq 2. (D) Temperature dependence of GN extracted from these experiments. (E) Same data plotted as a function of the (temperature dependent) effective number of spins coupled to the resonator , where is the spin polarization. The solid lines are least-squares fits based on eq 2 that extrapolate to GN/2π ≃ 2.3 MHz for T → 0 (when Neff → N).

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    Figure 6

    Figure 6. Dependence of the average single spin to single photon coupling on the width of the central transmission line of the resonator, showing the enhancement obtained by reducing the latter down to the region of (tens of) nanometers. The lines are calculations of the coupling of a spin located over the constriction, at three different heights z, as illustrated by the figure in the inset.

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  • References

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    This article references 62 other publications.

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      Strong Coupling of a Spin Ensemble to a Superconducting Resonator
      Kubo, Y.; Ong, F. R.; Bertet, P.; Vion, D.; Jacques, V.; Zheng, D.; Dreau, A.; Roch, J.-F.; Auffeves, A.; Jelezko, F.; Wrachtrup, J.; Barthe, M. F.; Bergonzo, P.; Esteve, D.
      Physical Review Letters (2010), 105 (14), 140502/1-140502/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The authors report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are N-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the N-vacancy center ESR.
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    14. 14
      Wu, H.; George, R. E.; Wesenberg, J. H.; Mølmer, K.; Schuster, D. I.; Schoelkopf, R. J.; Itoh, K. M.; Ardavan, A.; Morton, J. J. L.; Briggs, G. A. D. Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble. Phys. Rev. Lett. 2010, 105, 140503,  DOI: 10.1103/PhysRevLett.105.140503
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      14
      Storage of Multiple Coherent Microwave Excitations in an Electron Spin Ensemble
      Wu, Hua; George, Richard E.; Wesenberg, Janus H.; Molmer, Klaus; Schuster, David I.; Schoelkopf, Robert J.; Itoh, Kohei M.; Ardavan, Arzhang; Morton, John J. L.; Briggs, G. Andrew D.
      Physical Review Letters (2010), 105 (14), 140503/1-140503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Strong coupling between a microwave photon and electron spins, which could enable a long-lived quantum memory element for superconducting qubits, is possible using a large ensemble of spins. This represents an inefficient use of resources unless multiple photons, or qubits, can be orthogonally stored and retrieved. Here we employ holog. techniques to realize a coherent memory using a pulsed magnetic field gradient and demonstrate the storage and retrieval of up to 100 weak 10 GHz coherent excitations in collective states of an electron spin ensemble. We further show that such collective excitations in the electron spin can then be stored in nuclear spin states, which offer coherence times in excess of seconds.
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    15. 15
      Chiorescu, I.; Groll, N.; Bertaina, S.; Mori, T.; Miyashita, S. Magnetic Strong Coupling in a Spin-Photon System and Transition to Classical Regime. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 024413,  DOI: 10.1103/PhysRevB.82.024413
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      15
      Magnetic strong coupling in a spin-photon system and transition to classical regime
      Chiorescu, I.; Groll, N.; Bertaina, S.; Mori, T.; Miyashita, S.
      Physical Review B: Condensed Matter and Materials Physics (2010), 82 (2), 024413/1-024413/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins s=1/2 coupled to a variable no. of photons. Rabi splittings are calcd. and their distribution is analyzed as a function of photon no. nmax and spin system size N. A sharp transition in the distribution of the Rabi frequency is found at nmax≈N. The width of the Rabi frequency spectrum diverges as √N at this point. For increased no. of photons nmax>N, the Rabi frequencies converge to a value proportional to √nmax. This behavior is interpreted as analogous to the classical spin-resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present exptl. data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temp. This points toward quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.
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    16. 16
      Jenkins, M. D.; Zueco, D.; Roubeau, O.; Aromí, G.; Majer, J.; Luis, F. A Scalable Architecture for Quantum Computation with Molecular Nanomagnets. Dalton Trans 2016, 45, 16682– 16693,  DOI: 10.1039/C6DT02664H
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      16
      A scalable architecture for quantum computation with molecular nanomagnets
      Jenkins, M. D.; Zueco, D.; Roubeau, O.; Aromi, G.; Majer, J.; Luis, F.
      Dalton Transactions (2016), 45 (42), 16682-16693CODEN: DTARAF; ISSN:1477-9226. (Royal Society of Chemistry)
      A proposal for a magnetic quantum processor that consists of individual mol. spins coupled to superconducting coplanar resonators and transmission lines is carefully examd. We derive a simple magnetic quantum electrodynamics Hamiltonian to describe the underlying physics. It is shown that these hybrid devices can perform arbitrary operations on each spin qubit and induce tunable interactions between any pair of them. The combination of these two operations ensures that the processor can perform universal quantum computations. The feasibility of this proposal is critically discussed using the results of realistic calcns., based on parameters of existing devices and mol. qubits. These results show that the proposal is feasible, provided that mols. with sufficiently long coherence times can be developed and accurately integrated into specific areas of the device. This architecture has an enormous potential for scaling up quantum computation thanks to the microscopic nature of the individual constituents, the mols., and the possibility of using their internal spin degrees of freedom.
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    17. 17
      Narkowicz, R.; Suter, D.; Stonies, R. Planar Microresonators for EPR Experiments. J. Magn. Reson. 2005, 175, 275– 284,  DOI: 10.1016/j.jmr.2005.04.014
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      17
      Planar microresonators for EPR experiments
      Narkowicz, R.; Suter, D.; Stonies, R.
      Journal of Magnetic Resonance (2005), 175 (2), 275-284CODEN: JMARF3; ISSN:1090-7807. (Elsevier)
      EPR resonators on the basis of standing-wave cavities are optimized for large samples. For small samples it is possible to design different resonators that have much better power handling properties and higher sensitivity. Other parameters being equal, the sensitivity of the resonator can be increased by minimizing its size and thus increasing the filling factor. Like in NMR, it is possible to use lumped elements; coils can confine the microwave field to vols. that are much smaller than the wavelength. We discuss the design and evaluation of EPR resonators on the basis of planar microcoils. Our test resonators, which operate at a frequency of 14 GHz, have excellent microwave efficiency factors, achieving 24 ns π/2 EPR pulses with an input power of 17 mW. The sensitivity tests with DPPH samples resulted in the sensitivity value 2.3 × 109 spins · G-1Hz-1/2 at 300 K.
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    18. 18
      Narkowicz, R.; Suter, D.; Niemeyer, I. Scaling of Sensitivity and Efficiency in Planar Microresonators for Electron Spin Resonance. Rev. Sci. Instrum. 2008, 79, 084702,  DOI: 10.1063/1.2964926
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      18
      Scaling of sensitivity and efficiency in planar microresonators for electron spin resonance
      Narkowicz, R.; Suter, D.; Niemeyer, I.
      Review of Scientific Instruments (2008), 79 (8), 084702/1-084702/8CODEN: RSINAK; ISSN:0034-6748. (American Institute of Physics)
      ESR of vol.-limited samples or nanostructured materials can be made significantly more efficient by using microresonators whose size matches that of the structures under study. The authors describe planar microresonators that show large improvements over conventional ESR resonators in terms of microwave conversion efficiency (microwave field strength for a given input power) and sensitivity (min. no. of detectable spins). The authors explore the dependence of these parameters on the size of the resonator and find that both scale almost linearly with the inverse of the resonator size. Scaling down the loops of the planar microresonators from 500 down to 20 μm improves the microwave efficiency and the sensitivity of these structures by more than an order of magnitude and reduces the microwave power requirements by more than two orders of magnitude. (c) 2008 American Institute of Physics.
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    19. 19
      Banholzer, A.; Narkowicz, R.; Hassel, C.; Meckenstock, R.; Stienen, S.; Posth, O.; Suter, D.; Farle, M.; Lindner, J. Visualization of Spin Dynamics in Single Nanosized Magnetic Elements. Nanotechnology 2011, 22, 295713,  DOI: 10.1088/0957-4484/22/29/295713
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      19
      Visualization of spin dynamics in single nanosized magnetic elements
      Banholzer, A.; Narkowicz, R.; Hassel, C.; Meckenstock, R.; Stienen, S.; Posth, O.; Suter, D.; Farle, M.; Lindner, J.
      Nanotechnology (2011), 22 (29), 295713/1-295713/5CODEN: NNOTER; ISSN:1361-6528. (Institute of Physics Publishing)
      The design of future spintronic devices requires a quant. understanding of the microscopic linear and nonlinear spin relaxation processes governing the magnetization reversal in nanometer-scale ferromagnetic systems. Ferromagnetic resonance is the method of choice for a quant. anal. of relaxation rates, magnetic anisotropy and susceptibility in a single expt. The approach offers the possibility of coherent control and manipulation of nanoscaled structures by microwave irradn. Here, we analyze the different excitation modes in a single nanometer-sized ferromagnetic stripe. Measurements are performed using a microresonator set-up which offers a sensitivity to quant. analyze the dynamic and static magnetic properties of single nanomagnets with vols. of (100 nm)3. Uniform as well as non-uniform vol. modes of the spin wave excitation spectrum are identified and found to be in excellent agreement with the results of micromagnetic simulations which allow the visualization of the spatial distribution of these modes in the nanostructures.
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    20. 20
      Jenkins, M. D.; Hümmer, T.; Martínez-Pérez, M. J.; García-Ripoll, J.; Zueco, D.; Luis, F. Coupling Single-Molecule Magnets to Quantum Circuits. New J. Phys. 2013, 15, 095007,  DOI: 10.1088/1367-2630/15/9/095007
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      There is no corresponding record for this reference.
    21. 21
      Jenkins, M. D.; Naether, U.; Ciria, M.; Sesé, J.; Atkinson, J.; Sánchez-Azqueta, C.; del Barco, E.; Majer, J.; Zueco, D.; Luis, F. Nanoscale Constrictions in Superconducting Coplanar Waveguide Resonators. Appl. Phys. Lett. 2014, 105, 162601,  DOI: 10.1063/1.4899141
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      21
      Nanoscale constrictions in superconducting coplanar waveguide resonators
      Jenkins, Mark David; Naether, Uta; Ciria, Miguel; Sese, Javier; Atkinson, James; Sanchez-Azqueta, Carlos; Barco, Enrique del; Majer, Johannes; Zueco, David; Luis, Fernando
      Applied Physics Letters (2014), 105 (16), 162601/1-162601/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      We report on the design, fabrication, and characterization of superconducting coplanar waveguide resonators with nanoscopic constrictions. By reducing the size of the center line down to 50 nm, the radio frequency currents are concd. and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and internal quality factors of the same order of magnitude as the original ones. These devices could enable the achievement of higher couplings to small magnetic samples or even to single mol. spins and have applications in circuit quantum electrodynamics, quantum computing, and ESR. (c) 2014 American Institute of Physics.
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    22. 22
      Haikka, P.; Kubo, Y.; Bienfait, A.; Bertet, P.; Mølmer, K. Proposal for Detecting a Single Electron Spin in a Microwave Resonator. Phys. Rev. A: At., Mol., Opt. Phys. 2017, 95, 022306,  DOI: 10.1103/PhysRevA.95.022306
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      There is no corresponding record for this reference.
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      Mannini, M.; Pineider, F.; Sainctavit, P.; Danieli, C.; Otero, E.; Sciancalepore, C.; Talarico, A. M.; Arrio, M.-A.; Cornia, A.; Gatteschi, D.; Sessoli, R. Magnetic Memory of a Single-Molecule Quantum Magnet Wired to a Gold Surface. Nat. Mater. 2009, 8, 194– 197,  DOI: 10.1038/nmat2374
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      23
      Magnetic memory of a single-molecule quantum magnet wired to a gold surface
      Mannini, Matteo; Pineider, Francesco; Sainctavit, Philippe; Danieli, Chiara; Otero, Edwige; Sciancalepore, Corrado; Talarico, Anna Maria; Arrio, Marie-Anne; Cornia, Andrea; Gatteschi, Dante; Sessoli, Roberta
      Nature Materials (2009), 8 (3), 194-197CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      In the field of mol. spintronics, the use of magnetic mols. for information technol. is a main target and the observation of magnetic hysteresis on individual mols. organized on surfaces is a necessary step to develop mol. memory arrays. Although simple paramagnetic mols. can show surface-induced magnetic ordering and hysteresis when deposited on ferromagnetic surfaces, information storage at the mol. level requires mols. exhibiting an intrinsic remnant magnetization, like the so-called single-mol. magnets (SMMs). These have been intensively investigated for their rich quantum behavior but no magnetic hysteresis has been so far reported for monolayers of SMMs on various nonmagnetic substrates, most probably owing to the chem. instability of clusters on surfaces. Using X-ray absorption spectroscopy and X-ray magnetic CD synchrotron-based techniques, pushed to the limits in sensitivity and operated at sub-kelvin temps., we have now found that robust, tailor-made Fe4 complexes retain magnetic hysteresis at gold surfaces. Our results demonstrate that isolated SMMs can be used for storing information. The road is now open to address individual mols. wired to a conducting surface in their blocked magnetization state, thereby enabling investigation of the elementary interactions between electron transport and magnetism degrees of freedom at the mol. scale.
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    24. 24
      Mannini, M.; Pineider, F.; Danieli, C.; Totti, F.; Sorace, L.; Sainctavit, P.; Arrio, M.-A.; Otero, E.; Joly, L.; Cezar, J. C.; Cornia, A.; Sessoli, R. Quantum Tunnelling of the Magnetization in a Monolayer of Oriented Single-Molecule Magnets. Nature 2010, 468, 417– 421,  DOI: 10.1038/nature09478
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      24
      Quantum tunnelling of the magnetization in a monolayer of oriented single-molecule magnets
      Mannini, M.; Pineider, F.; Danieli, C.; Totti, F.; Sorace, L.; Sainctavit, Ph.; Arrio, M.-A.; Otero, E.; Joly, L.; Cezar, J. C.; Cornia, A.; Sessoli, R.
      Nature (London, United Kingdom) (2010), 468 (7322), 417-421CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      A fundamental step towards at.- or mol.-scale spintronic devices has recently been made by demonstrating that the spin of an individual atom deposited on a surface, or of a small paramagnetic mol. embedded in a nanojunction, can be externally controlled. An appealing next step is the extension of such a capability to the field of information storage, by taking advantage of the magnetic bistability and rich quantum behavior of single-mol. magnets (SMMs). Recently, a proof of concept that the magnetic memory effect is retained when SMMs are chem. anchored to a metallic surface was provided. However, control of the nanoscale organization of these complex systems is required for SMMs to be integrated into mol. spintronic devices. A preferential orientation of Fe4 complexes on a gold surface can be achieved by chem. tailoring. As a result, the most striking quantum feature of SMMs, their stepped hysteresis loop, which results from resonant quantum tunneling of the magnetization, can be clearly detected using synchrotron-based spectroscopic techniques. With the aid of multiple theor. approaches, the authors relate the angular dependence of the quantum tunneling resonances to the adsorption geometry, and demonstrate that mols. predominantly lie with their easy axes close to the surface normal. The findings prove that the quantum spin dynamics can be obsd. in SMMs chem. grafted to surfaces, and offer a tool to reveal the organization of matter at the nanoscale.
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    25. 25
      Domingo, N.; Bellido, E.; Ruiz-Molina, D. Advances on Structuring, Integration and Magnetic Characterization of Molecular Nanomagnets on Surfaces and Devices. Chem. Soc. Rev. 2012, 41, 258– 302,  DOI: 10.1039/C1CS15096K
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      25
      Advances on structuring, integration and magnetic characterization of molecular nanomagnets on surfaces and devices
      Domingo, N.; Bellido, E.; Ruiz-Molina, D.
      Chemical Society Reviews (2012), 41 (1), 258-302CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      This crit. review represents a concise revision of the different exptl. approaches so far followed for the structuration of mol. nanomagnets on surfaces, since the first reports on the field more than ten years ago. Afterwards, a presentation of the different exptl. approaches followed for their integration in sensors is described. Such work involves mainly two families of sensors and devices, microSQUIDs sensors and three-terminal devices for single-mol. detection. Finally the last section is devoted to a detailed revision of the different exptl. techniques that can be used for the magnetic characterization of these systems on surfaces, ranging from magnetic CD to magnetic force microscopy. The use of these techniques to characterize other nanostructured magnetic materials, such as nanoparticles, is also revised. The aim is to give a broad overview of the last advances achieved with these techniques and their potential and evolution over the next years.
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    26. 26
      Thiele, S.; Balestro, F.; Ballou, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, W. Electrically Driven Nuclear Spin Resonance in Single-Molecule Magnets. Science 2014, 344, 1135– 1138,  DOI: 10.1126/science.1249802
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      26
      Electrically driven nuclear spin resonance in single-molecule magnets
      Thiele, Stefan; Balestro, Franck; Ballou, Rafik; Klyatskaya, Svetlana; Ruben, Mario; Wernsdorfer, Wolfgang
      Science (Washington, DC, United States) (2014), 344 (6188), 1135-1138CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Recent advances in addressing isolated nuclear spins have opened up a path toward using nuclear-spin-based quantum bits. Local magnetic fields are normally used to coherently manipulate the state of the nuclear spin; however, elec. manipulation would allow for fast switching and spatially confined spin control. Here, the authors propose and demonstrate coherent single nuclear spin manipulation using elec. fields only. Because there is no direct coupling between the spin and the elec. field, the authors make use of the hyperfine Stark effect as a magnetic field transducer at the at. level. This quantum-mech. process is present in all nuclear spin systems, such as phosphorus or bismuth atoms in silicon, and offers a general route toward the elec. control of nuclear-spin-based devices.
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    27. 27
      Malavolti, L.; Briganti, M.; Hänze, M.; Serrano, G.; Cimatti, I.; McMurtrie, G.; Otero, E.; Ohresser, P.; Totti, F.; Mannini, M.; Sessoli, R.; Loth, S. Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules. Nano Lett. 2018, 18, 7955,  DOI: 10.1021/acs.nanolett.8b03921
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      27
      Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules
      Malavolti, Luigi; Briganti, Matteo; Haenze, Max; Serrano, Giulia; Cimatti, Irene; McMurtrie, Gregory; Otero, Edwige; Ohresser, Philippe; Totti, Federico; Mannini, Matteo; Sessoli, Roberta; Loth, Sebastian
      Nano Letters (2018), 18 (12), 7955-7961CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
      Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) mols. deposited on the Pb surface. The VOPc mol. is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied dxy-orbital and is a promising candidate for a mol. spin qubit with long coherence times. X-ray magnetic CD (XMCD) measurements show that the mol. spin remains unperturbed even for mols. directly deposited on the Pb surface. Scanning tunneling spectroscopy and d. functional theory (DFT) calcns. identify two adsorption geometries for this "asym." mol. (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Addnl., we find that in the first case a YSR state can be induced smoothly by exerting mech. force on the mols. with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated mol. spin case, through the quantum crit. point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.
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    28. 28
      Urtizberea, A.; Natividad, E.; Alonso, P. J.; Pérez-Martínez, L.; Andrés, M. A.; Gascón, I.; Gimeno, I.; Luis, F.; Roubeau, O. Vanadyl Spin Qubit 2D Arrays and their Integration on Superconducting Resonators. Mater. Horiz. 2020, 7, 885– 897,  DOI: 10.1039/C9MH01594A
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      Vanadyl spin qubit 2D arrays and their integration on superconducting resonators
      Urtizberea, Ainhoa; Natividad, Eva; Alonso, Pablo J.; Perez-Martinez, Laura; Andres, Miguel A.; Gascon, Ignacio; Gimeno, Ignacio; Luis, Fernando; Roubeau, Olivier
      Materials Horizons (2020), 7 (3), 885-897CODEN: MHAOBM; ISSN:2051-6355. (Royal Society of Chemistry)
      Vanadyl systems have been shown to possess superior quantum coherence among mol. spin qubits. Meanwhile two-dimensional (2D) networks of spin qubit nodes could provide a means to achieve the control of qubit localization and orientation required for implementation of mol. spin qubits in hybrid solid-state devices. Here, the 2D metal-org. framework [{VO(TCPP)}Zn2(H2O)2]∞ is reported and its vanadyl porphyrin node is shown to exhibit superior spin dynamics and to enable coherent spin manipulations, making it a valid spin qubit candidate. Nanodomains of the MOF 2D coordination planes are efficiently formed at the air-water interface, first under Langmuir-Schaefer conditions, allowing mono- and multiple layer deposits to be transferred to a variety of substrates. Similar nanodomains are then successfully formed in situ on the surface of Nb superconducting coplanar resonators. Transmission measurements with a resonator with a 14 μm-wide constriction allow to est. that the single spin-photon coupling G1 of the vanadyl spins in the nanodomains is close to being optimal, at ca. 0.5 Hz. Altogether, these results provide the basis for developing a viable hybrid quantum computing architecture.
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      Leuenberger, M.; Loss, D. Quantum Computing in Molecular Magnets. Nature 2001, 410, 789– 793,  DOI: 10.1038/35071024
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      29
      Quantum computing in molecular magnets
      Leuenberger, Michael N.; Loss, Daniel
      Nature (London, United Kingdom) (2001), 410 (6830), 789-793CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring nos. and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses mol. magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theor. that mol. magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast ESR pulses can be used to decode and read out stored nos. of up to 10, with access times as short as 10 s. We show that our proposal should be feasible using the mol. magnets Fe8 and Mn12.
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      Troiani, F.; Affronte, M. Molecular Spins for Quantum Information Technologies. Chem. Soc. Rev. 2011, 40, 3119– 3129,  DOI: 10.1039/c0cs00158a
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      Molecular spins for quantum information technologies
      Troiani, Filippo; Affronte, Marco
      Chemical Society Reviews (2011), 40 (6), 3119-3129CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. Technol. challenges for quantum information technologies lead us to consider aspects of mol. magnetism in a radically new perspective. The design of new derivs. and recent exptl. results on mol. nanomagnets are covered in this tutorial review through the keyhole of basic concepts of quantum information, such as the control of decoherence and entanglement at the (supra-)mol. level.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmsVWkurg%253D&md5=23230ed37c9c17cccac47a4e5cbb223f
    31. 31
      Aromí, G.; Aguilà, D.; Gamez, P.; Luis, F.; Roubeau, O. Design of Magnetic Coordination Complexes for Quantum Computing. Chem. Soc. Rev. 2012, 41, 537– 546,  DOI: 10.1039/C1CS15115K
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      Design of magnetic coordination complexes for quantum computing
      Aromi, Guillem; Aguila, David; Gamez, Patrick; Luis, Fernando; Roubeau, Olivier
      Chemical Society Reviews (2012), 41 (2), 537-546CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review. A very exciting prospect in coordination chem. is to manipulate spins within magnetic complexes for the realization of quantum logic operations. An introduction to the requirements for a paramagnetic mol. to act as a 2-qubit quantum gate is provided in this tutorial review. We propose synthetic methods aimed at accessing such type of functional mols., based on ligand design and inorg. synthesis. Two strategies are presented: (i) the first consists in targeting mols. contg. a pair of well-defined and weakly coupled paramagnetic metal aggregates, each acting as a carrier of one potential qubit, (ii) the second is the design of dinuclear complexes of anisotropic metal ions, exhibiting dissimilar environments and feeble magnetic coupling. The first systems obtained from this synthetic program are presented here and their properties are discussed.
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      Moreno-Pineda, E.; Godfrin, C.; Balestro, F.; Wernsdorfer, W.; Ruben, M. Molecular Spin Qudits for Quantum Algorithms. Chem. Soc. Rev. 2018, 47, 501– 513,  DOI: 10.1039/C5CS00933B
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      Molecular spin qudits for quantum algorithms
      Moreno-Pineda, Eufemio; Godfrin, Clement; Balestro, Franck; Wernsdorfer, Wolfgang; Ruben, Mario
      Chemical Society Reviews (2018), 47 (2), 501-513CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      Presently, one of the most ambitious technol. goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for purposes not achievable with even the most powerful computer resources. The large-scale implementation of quantum information would be a game changer for current technol., because it would allow unprecedented parallelised computation and secure encryption based on the principles of quantum superposition and entanglement. Currently, there are several phys. platforms racing to achieve the level of performance required for the quantum hardware to step into the realm of practical quantum information applications. Several materials have been proposed to fulfil this task, ranging from quantum dots, Bose-Einstein condensates, spin impurities, superconducting circuits, mols., amongst others. Magnetic mols. are among the list of promising building blocks, due to (i) their intrinsic monodispersity, (ii) discrete energy levels (iii) the possibility of chem. quantum state engineering, and (iv) their multilevel characteristics that lead to Qudits, where the dimension of the Hilbert space is d > 2. Herein we review how a mol. nuclear spin qudit, (d = 4), known as TbPc2, gathers all the necessary requirements to perform as a mol. hardware platform with a first generation of mol. devices enabling even quantum algorithm operations.
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      Gaita-Ariño, A.; Luis, F.; Hill, S.; Coronado, E. Molecular Spins for Quantum Computation. Nat. Chem. 2019, 11, 301– 309,  DOI: 10.1038/s41557-019-0232-y
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      Molecular spins for quantum computation
      Gaita-Arino, A.; Luis, F.; Hill, S.; Coronado, E.
      Nature Chemistry (2019), 11 (4), 301-309CODEN: NCAHBB; ISSN:1755-4330. (Nature Research)
      Spins in solids or in mols. possess discrete energy levels, and the assocd. quantum states can be tuned and coherently manipulated by means of external electromagnetic fields. Spins therefore provide one of the simplest platforms to encode a quantum bit (qubit), the elementary unit of future quantum computers. Performing any useful computation demands much more than realizing a robust qubit-one also needs a large no. of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chem.-based bottom-up approach is best-suited. Mols., being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large nos. using chem. tools.
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      Atzori, M.; Sessoli, R. The Second Quantum Revolution: Role and Challenges of Molecular Chemistry. J. Am. Chem. Soc. 2019, 141, 11339– 11352,  DOI: 10.1021/jacs.9b00984
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      The Second Quantum Revolution: Role and Challenges of Molecular Chemistry
      Atzori, Matteo; Sessoli, Roberta
      Journal of the American Chemical Society (2019), 141 (29), 11339-11352CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      A review. Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by mol. spin systems. In this Perspective, we highlight the role that mol. chem. can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of mol. components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the mol. chem. community, such as for example the design of mol. spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a crit. eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.
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      Khapaev, M. M.; Kupriyanov, M. Y.; Goldobin, E.; Siegel, M. Current Distribution Simulation for Superconducting Multi-Layered Structures. Supercond. Sci. Technol. 2003, 16, 24– 27,  DOI: 10.1088/0953-2048/16/1/305
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      Current distribution simulation for superconducting multi-layered structures
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      Superconductor Science and Technology (2003), 16 (1), 24-27CODEN: SUSTEF; ISSN:0953-2048. (Institute of Physics Publishing)
      The software package 3D-MLSI is developed, which allows us to calc. the current distribution and to ext. inductances from multi-layered high-Tc and low-Tc superconducting circuits. Both kinetic and magnetic inductances as well as the three-dimensional distribution of the magnetic field are taken into account. We discuss the numerical approach used in 3D-MLSI and some new features such as visualization of sheet currents and anal. of circuits with holes. As an example, we present a simulation of a high-Tc double-layer transformer.
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      Weil, J. A.; Anderson, J. K. 1039. The Determination and Reaction of 2,2-Diphenyl-1-Picrylhydrazyl with Thiosalicylic Acid. J. Chem. Soc. 1965, 5567– 5570,  DOI: 10.1039/jr9650005567
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      The determination and reaction of 2,2-diphenyl-1-picrylhydrazyl with thiosalicylic acid
      Weil, John A.; Anderson, Judith K.
      Journal of the Chemical Society (1965), (Oct.), 5567-70CODEN: JCSOA9; ISSN:0368-1769.
      An accurate method for analysis of 2,2-diphenyl-1-picrylhydrazyl (DPPH) has been developed, using a simple titration procedure with thiosalicylic acid. The products of the reaction were 1,1-diphenyl-2-picrylhydrazine and 2,2'-dithiodibenzoic acid (dithiosalicylic acid). It was also observed that several forms of solvent-free DPPH exist.
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      Yordanov, N. D. Is Our Knowledge about the Chemical and Physical Properties of DPPH Enough to Consider it as a Primary Standard for Quantitative EPR Spectrometry?. Appl. Magn. Reson. 1996, 10, 339– 350,  DOI: 10.1007/BF03163117
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      Is our knowledge about the chemical and physical properties of DPPH enough to consider it as a primary standard for quantitative EPR spectrometry?
      Yordanov, Nicola D.
      Applied Magnetic Resonance (1996), 10 (1-3), 339-350CODEN: APMREI; ISSN:0937-9347. (Springer)
      A review with 41 refs. on the physico-chem. properties of the stable free radical DPPH (1,1-diphenyl-2-picrylhydrazyl) and its use as a primary std. for quant. ESR.
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      Žilić, D.; Pajić, D.; Jurić, M.; Molčanov, K.; Rakvin, B.; Planinić, P.; Zadro, K. Single Crystals of DPPH Grown from Diethyl Ether and Carbon Disulfide Solutions – Crystal Structures, IR, EPR and Magnetization Studies. J. Magn. Reson. 2010, 207, 34– 41,  DOI: 10.1016/j.jmr.2010.08.005
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      Single crystals of DPPH grown from diethyl ether and carbon disulfide solutions - Crystal structures, IR, EPR and magnetization studies
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      Journal of Magnetic Resonance (2010), 207 (1), 34-41CODEN: JMARF3; ISSN:1090-7807. (Elsevier B.V.)
      Single crystals of the free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH) obtained from di-Et ether (ether) and carbon disulfide (CS2) were characterized by the X-ray diffraction, IR, EPR and SQUID magnetization techniques. The X-ray structural anal. and IR spectra showed that the DPPH form crystd. from ether (DPPH1) is solvent free, whereas that one obtained from CS2 (DPPH2) is a solvate of the compn. 4DPPH·CS2. Principal values of the g-tensor were estd. by the X-band EPR spectroscopy at room and low (10 K) temps. Magnetization studies revealed the presence of antiferromagnetically coupled dimers in both types of crystals. However, the way of dimerization as well as the strength of exchange couplings are different in the two DPPH samples, which is in accord with their crystal structures. The obtained results improved parameters accuracy and enabled better understanding of properties of DPPH as a std. sample in the EPR spectrometry.
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      Exchange narrowing in paramagnetic resonance
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      Reviews of Modern Physics (1953), 25 (), 269-76CODEN: RMPHAT; ISSN:0034-6861.
      A math. model called the model of "random frequency modulation" is used to discuss the line shape in paramagnetic resonance when large exchange interaction is present. The assumption is made that the atom absorbs one single frequency, which varies over a distribution detd. by the dipolar local fields, but that this frequency varies in a random manner in time, at a rate detd. by the exchange interactions. Where the exchange is large, the predicted line shape is of the resonance type but fails off rapidly at the wings. Under the assumption that a good approximation to the modulation function is Gaussian noise with a Gaussian spectrum the 2nd moment (which is independent of exchange) and the 4th moment of the line shape can be calculated. The result as to line breath is given as: Δ equal or nearly equal to (Δω2)av. dipole-dipole (h/J).
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      Höcherl, G.; Wolf, H. C. Zur Konzentrationsabhängigkeit der Elektronenspin-Relaxationszeiten von Diphenyl-Picryl-Hydrazyl in fester Phase. Eur. Phys. J. A 1965, 183, 341– 351,  DOI: 10.1007/BF01380763
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      Piner, R. D.; Zhu, J.; Xu, F.; Hong, S.; Mirkin, C. A. ”Dip-Pen” Nanolithography. Science 1999, 283, 661– 663,  DOI: 10.1126/science.283.5402.661
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      "Dip-pen" nanolithography
      Piner, Richard D.; Zhu, Jin; Xu, Feng; Hong, Seunghun; Mirkin, Chad A.
      Science (Washington, D. C.) (1999), 283 (5402), 661-663CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      A direct-write "dip-pen" nanolithog. (DPN) has been developed to deliver collections of mols. in a pos. printing mode. An at. force microscope (AFM) tip is used to write alkanethiols with 30-nm linewidth resoln. on a gold thin film in a manner analogous to that of a dip pen. Mols. are delivered from the AFM tip to a solid substrate of interest via capillary transport, making DPN a potentially useful tool for creating and functionalizing nanoscale devices.
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      Bellido, E.; de Miguel, R.; Ruiz-Molina, D.; Lostao, A.; Maspoch, D. Controlling the Number of Proteins with Dip-Pen Nanolitography. Adv. Mater. 2010, 22, 352– 355,  DOI: 10.1002/adma.200902372
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      Controlling the Number of Proteins with Dip-Pen Nanolithography
      Bellido, Elena; de Miguel, Rocio; Ruiz-Molina, Daniel; Lostao, Anabel; Maspoch, Daniel
      Advanced Materials (Weinheim, Germany) (2010), 22 (3), 352-355CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
      We describe a novel strategy that utilizes the ability of dip-pen nanolithog. (DPN) to direct-write proteins on the surface of transmission electron microscopy (TEM) grids. Ferritin protein was chosen as an excellent model system because of its size and central inorg. core of hydrated iron(III) oxide, which allows its visualization by TEM, and therefore, its individual identification on the surface of the TEM grids. The data show that this is a versatile way to quantify the no. of ferritin particles written by DPN, and that this no. can be controlled by adjusting the protein concn. used to coat the at. force microscopy (AFM) tips and the dimensions of the dot-like features fabricated by DPN.
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      Martínez-Pérez, M. J.; Bellido, E.; de Miguel, R.; Sesé, J.; Lostao, A.; Gómez-Moreno, C.; Drung, D.; Schurig, T.; Ruiz-Molina, D.; Luis, F. Alternating Current Magnetic Susceptibility of a Molecular Magnet Submonolayer Directly Patterned onto a Micro Superconducting Quantum Interference Device. Appl. Phys. Lett. 2011, 99, 032504,  DOI: 10.1063/1.3609859
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      Alternating current magnetic susceptibility of a molecular magnet submonolayer directly patterned onto a micro superconducting quantum interference device
      Martinez-Perez, M. J.; Bellido, E.; de Miguel, R.; Sese, J.; Lostao, A.; Gomez-Moreno, C.; Drung, D.; Schurig, T.; Ruiz-Molina, D.; Luis, F.
      Applied Physics Letters (2011), 99 (3), 032504/1-032504/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
      We report the controlled integration, via dip pen nanolithog., of monolayer dots of ferritin-based CoO nanoparticles (12 μB) into the most sensitive areas of a microSQUID sensor. The nearly optimum flux coupling between these nanomagnets and the microSQUID improves the achievable sensitivity by a factor 102, enabling us to measure the linear susceptibility of the mol. array down to very low temps. (13 mK). This method opens the possibility of applying a.c. susceptibility expts. to characterize 2D arrays of single mol. magnets within a wide range of temps. and frequencies. (c) 2011 American Institute of Physics.
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      Bellido, E.; González-Monje, P.; Repollés, A.; Jenkins, M.; Sesé, J.; Drung, D.; Schurig, T.; Awaga, K.; Luis, F.; Ruiz-Molina, D. Mn12 Single Molecule Magnets Deposited on μ-SQUID Sensors: the Role of Interphases and Structural Modifications. Nanoscale 2013, 5, 12565– 12573,  DOI: 10.1039/c3nr02359a
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      Mn12 single molecule magnets deposited on μ-SQUID sensors: the role of interphases and structural modifications
      Bellido, Elena; Gonzalez-Monje, Pablo; Repolles, Ana; Jenkins, Mark; Sese, Javier; Drung, Dietmar; Schurig, Thomas; Awaga, Kunio; Luis, Fernando; Ruiz-Molina, Daniel
      Nanoscale (2013), 5 (24), 12565-12573CODEN: NANOHL; ISSN:2040-3372. (Royal Society of Chemistry)
      Direct measurements of the linear ac susceptibility and magnetic relaxation of a few Mn12 monolayers deposited on a μ-SQUID sensor are reported. In order to integrate the mols. into the device, DPN has been the technique of choice. It enabled the structuration of the mols. on the most sensitive areas of the sensor without the need for any previous functionalization of the mol. or the substrate, while controlling the no. of mol. units deposited on each array. The measurements reveal that their characteristic SMM behavior is lost, a fact that is attributed to mol. distortions originated by the strong surface tensions arising at the mol. interphases.
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      Bushev, P.; Feofanov, A. K.; Rotzinger, H.; Protopopov, I.; Cole, J. H.; Wilson, C. M.; Fischer, G.; Lukashenko, A.; Ustinov, A. V. Ultralow-Power Spectroscopy of a Rare-Earth Spin Ensemble Using a Superconducting Resonator. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 060501,  DOI: 10.1103/PhysRevB.84.060501
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      Ultralow-power spectroscopy of a rare-earth spin ensemble using a superconducting resonator
      Bushev, P.; Feofanov, A. K.; Rotzinger, H.; Protopopov, I.; Cole, J. H.; Wilson, C. M.; Fischer, G.; Lukashenko, A.; Ustinov, A. V.
      Physical Review B: Condensed Matter and Materials Physics (2011), 84 (6), 060501/1-060501/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Interfacing superconducting quantum processors, working in the GHz frequency range, with optical quantum networks and at. qubits is a challenging task for the implementation of distributed quantum information processing as well as for quantum communication. Using spin ensembles of rare earth ions provides an excellent opportunity to bridge microwave and optical domains at the quantum level. The ultralow-power, on-chip, ESR spectroscopy of Er3+ spins doped in a Y2SiO5 crystal using a high-Q, coplanar, superconducting resonator is demonstrated.
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      Hümmer, T.; Reuther, G. M.; Hänggi, P.; Zueco, D. Nonequilibrium Phases in Hybrid Arrays with Flux Qubits and Nitrogen-Vacancy Centers. Phys. Rev. A: At., Mol., Opt. Phys. 2012, 85, 052320,  DOI: 10.1103/PhysRevA.85.052320
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      Martínez-Pérez, M. J.; Zueco, D. Strong Coupling of a Single Photon to a Magnetic Vortex. ACS Photonics 2019, 6, 360– 367,  DOI: 10.1021/acsphotonics.8b00954
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      Strong Coupling of a Single Photon to a Magnetic Vortex
      Martinez-Perez, Maria Jose; Zueco, David
      ACS Photonics (2019), 6 (2), 360-367CODEN: APCHD5; ISSN:2330-4022. (American Chemical Society)
      Strong light-matter coupling means that cavity photons and other types of matter excitations are coherently exchanged. It is used to couple different qubits (matter) via a quantum bus (photons) or to communicate different types of excitations, e.g., transducing light into phonons or magnons. A, so far, unexplored interface is the coupling between light and topol. protected particle-like excitations as magnetic domain walls, skyrmions, or vortices. Theor. a single photon living in a superconducting cavity can be strongly coupled to the gyrotropic mode of a magnetic vortex in a nanodisc. Numerical and anal. calcns. were combined for a superconducting coplanar waveguide resonator and different realizations of the nanodisc (materials and sizes). For enhancing the coupling, constrictions fabricated in the resonator are crucial, allowing to reach strong coupling in CoFe disks of radius 200-400 nm having resonance frequencies of a few GHz. The strong coupling regime permits coherently exchanging a single photon and quanta of vortex gyration. The calcns. show that the device proposed here serves as a transducer between photons and gyrating vortices, opening the way to complement superconducting qubits with topol. protected spin-excitations such as vortices or skyrmions. The authors finish by discussing potential applications in quantum data processing based on the exploitation of the vortex as a short-wavelength magnon emitter.
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      Warner, M.; Din, S.; Tupitsyn, I. S.; Morley, G. W.; Stoneham, A.; Gardener, J. A.; Wu, Z.; Fisher, A. J.; Heutz, S.; Kay, C. W. M.; Aeppli, G. Ptential fot Spin-Based Information Processing in a Thin-Film Molecular Semiconductor. Nature 2013, 503, 504– 508,  DOI: 10.1038/nature12597
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      Potential for spin-based information processing in a thin-film molecular semiconductor
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      Nature (London, United Kingdom) (2013), 503 (7477), 504-508CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Org. semiconductors were studied intensively for applications in electronics and optics, and even spin-based information technol., or spintronics. Fundamental quantities in spintronics are the population relaxation time (T1) and the phase memory time (T2): T1 measures the lifetime of a classical bit, in this case embodied by a spin oriented either parallel or antiparallel to an external magnetic field, and T2 measures the corresponding lifetime of a quantum bit, encoded in the phase of the quantum state. These times are surprisingly long for a common, low-cost and chem. modifiable org. semiconductor, the blue pigment Cu phthalocyanine, in easily processed thin-film form used for device fabrication. At 5 K, a temp. reachable using inexpensive closed-cycle refrigerators, T1 and T2 are resp. 59 ms and 2.6 μs, and at 80 K, which is just above the b.p. of liq. N, they are resp. 10 μs and 1 μs, demonstrating that the performance of thin-film Cu phthalocyanine is superior to that of single-mol. magnets over the same temp. range. T2 is more than two orders of magnitude greater than the duration of the spin manipulation pulses, which suggests that Cu phthalocyanine holds promise for quantum information processing, and the long T1 indicates possibilities for medium-term storage of classical bits in all-org. devices on plastic substrates.
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      Slota, M.; Keerthi, A.; Myers, W. K.; Tretyakov, E.; Baumgarten, M.; Ardavan, A.; Sadeghi, H.; Lambert, C. J.; Narita, A.; Müllen, K.; Bogani, L. Magnetic Edge States and Coherent Manipulation of Graphene Nanoribbons. Nature 2018, 557, 691– 695,  DOI: 10.1038/s41586-018-0154-7
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      Slota, Michael; Keerthi, Ashok; Myers, William K.; Tretyakov, Evgeny; Baumgarten, Martin; Ardavan, Arzhang; Sadeghi, Hatef; Lambert, Colin J.; Narita, Akimitsu; Mullen, Klaus; Bogani, Lapo
      Nature (London, United Kingdom) (2018), 557 (7707), 691-695CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Graphene, a single-layer network of carbon atoms, has outstanding elec. and mech. properties1. Graphene ribbons with nanometer-scale widths2,3 (nanoribbons) should exhibit half-metallicity4 and quantum confinement. Magnetic edges in graphene nanoribbons5,6 have been studied extensively from a theor. standpoint because their coherent manipulation would be a milestone for spintronic7 and quantum computing devices8. However, exptl. investigations have been hampered because nanoribbon edges cannot be produced with at. precision and the graphene terminations that have been proposed are chem. unstable9. Here we address both of these problems, by using mol. graphene nanoribbons functionalized with stable spin-bearing radical groups. We observe the predicted delocalized magnetic edge states and test theor. models of the spin dynamics and spin-environment interactions. Comparison with a non-graphitized ref. material enables us to clearly identify the characteristic behavior of the radical-functionalized graphene nanoribbons. We quantify the parameters of spin-orbit coupling, define the interaction patterns and det. the spin decoherence channels. Even without any optimization, the spin coherence time is in the range of microseconds at room temp., and we perform quantum inversion operations between edge and radical spins. Our approach provides a way of testing the theory of magnetism in graphene nanoribbons exptl. The coherence times that we observe open up encouraging prospects for the use of magnetic nanoribbons in quantum spintronic devices.
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    51. 51
      Lombardi, F.; Lodi, A.; Ma, J.; Liu, J.; Slota, M.; Narita, A.; Myers, W. K.; Müllen, K.; Feng, X.; Bogani, L. Quantum Units from the Topological Engineering of Molecular Graphenoids. Science 2019, 366, 1107– 1110,  DOI: 10.1126/science.aay7203
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      Quantum units from the topological engineering of molecular graphenoids
      Lombardi, Federico; Lodi, Alessandro; Ma, Ji; Liu, Junzhi; Slota, Michael; Narita, Akimitsu; Myers, William K.; Mullen, Klaus; Feng, Xinliang; Bogani, Lapo
      Science (Washington, DC, United States) (2019), 366 (6469), 1107-1110CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
      A review. Robustly coherent spin centers that can be integrated into devices are a key ingredient of quantum technologies. Vacancies in semiconductors are excellent candidates, and theory predicts that defects in conjugated carbon materials should also display long coherence times. However, the quantum performance of carbon nanostructures has remained stunted by an inability to alter the sp2-carbon lattice with at. precision. Here, we demonstrate that topol. tailoring leads to superior quantum performance in mol. graphene nanostructures. We unravel the decoherence mechanisms, quantify nuclear and environmental effects, and observe spin-coherence times that outclass most nanomaterials. These results validate long-standing assumptions on the coherent behavior of topol. defects in graphene and open up the possibility of introducing controlled quantum-coherent centers in the upcoming generation of carbon-based optoelectronic, electronic, and bioactive systems.
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    52. 52
      Ardavan, A.; Rival, O.; Morton, J. J. L.; Blundell, S. J.; Tyryshkin, A. M.; Timco, G. A.; Winpenny, R. E. P. Will Spin-Relaxation Times in Molecular Magnets Permit Quantum Information Processing?. Phys. Rev. Lett. 2007, 98, 057201,  DOI: 10.1103/PhysRevLett.98.057201
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      Will Spin-Relaxation Times in Molecular Magnets Permit Quantum Information Processing?
      Ardavan, Arzhang; Rival, Olivier; Morton, John J. L.; Blundell, Stephen J.; Tyryshkin, Alexei M.; Timco, Grigore A.; Winpenny, Richard E. P.
      Physical Review Letters (2007), 98 (5), 057201/1-057201/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Using X-band pulsed electron-spin resonance, we report the intrinsic spin-lattice (T1) and phase-coherence (T2) relaxation times in mol. nanomagnets for the first time. In Cr7M heterometallic wheels, with M = Ni and Mn, phase-coherence relaxation is dominated by the coupling of the electron spin to protons within the mol. In deuterated samples T2 reaches 3 μs at low temps., which is several orders of magnitude longer than the duration of spin manipulations, satisfying a prerequisite for the deployment of mol. nanomagnets in quantum information applications.
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    53. 53
      Wedge, C. J.; Timco, G. A.; Spielberg, E. T.; George, R. E.; Tuna, F.; Rigby, S.; McInnes, E. J. L.; Winpenny, R. E. P.; Blundell, S. J.; Ardavan, A. Chemical Engineering of Molecular Qubits. Phys. Rev. Lett. 2012, 108, 107204,  DOI: 10.1103/PhysRevLett.108.107204
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      Chemical engineering of molecular qubits
      Wedge, C. J.; Timco, G. A.; Spielberg, E. T.; George, R. E.; Tuna, F.; Rigby, S.; McInnes, E. J. L.; Winpenny, R. E. P.; Blundell, S. J.; Ardavan, A.
      Physical Review Letters (2012), 108 (10), 107204/1-107204/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We show that the electron spin phase memory time, the most important property of a mol. nanomagnet from the perspective of quantum information processing, can be improved dramatically by chem. engineering the mol. structure to optimize the environment of the spin. We vary systematically each structural component of the class of antiferromagnetic Cr7Ni rings to identify the sources of decoherence. The optimal structure exhibits a phase memory time exceeding 15 μs.
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    54. 54
      Bader, K.; Dengler, D.; Lenz, S.; Endeward, B.; Jiang, S.-D.; Neugebauer, P.; van Slageren, J. Room Temperature Quantum Coherence in a Potential Molecular Qubit. Nat. Commun. 2014, 5, 5304,  DOI: 10.1038/ncomms6304
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      Room temperature quantum coherence in a potential molecular qubit
      Bader, Katharina; Dengler, Dominik; Lenz, Samuel; Endeward, Burkhard; Jiang, Shang-Da; Neugebauer, Petr; van Slageren, Joris
      Nature Communications (2014), 5 (), 5304CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The successful development of a quantum computer would change the world, and current internet encryption methods would cease to function. However, no working quantum computer that even begins to rival conventional computers has been developed yet, which is due to the lack of suitable quantum bits. A key characteristic of a quantum bit is the coherence time. Transition metal complexes are very promising quantum bits, owing to their facile surface deposition and their chem. tunability. However, reported quantum coherence times have been unimpressive. Here we report very long quantum coherence times for a transition metal complex of 68 μs at low temp. (qubit figure of merit QM=3,400) and 1 μs at room temp., much higher than previously reported values for such systems. We show that this achievement is because of the rigidity of the lattice as well as removal of nuclear spins from the vicinity of the magnetic ion.
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      Shiddiq, M.; Komijani, D.; Duan, Y.; Gaita-Ariño, A.; Coronado, E.; Hill, S. Enhancing Coherence in Molecular Spin Qubits via Atomic Clock Transitions. Nature 2016, 531, 348– 351,  DOI: 10.1038/nature16984
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      Enhancing coherence in molecular spin qubits via atomic clock transitions
      Shiddiq, Muhandis; Komijani, Dorsa; Duan, Yan; Gaita-Arino, Alejandro; Coronado, Eugenio; Hill, Stephen
      Nature (London, United Kingdom) (2016), 531 (7594), 348-351CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Quantum computing is an emerging area within the information sciences revolving around the concept of quantum bits (qubits). A major obstacle is the extreme fragility of these qubits due to interactions with their environment that destroy their quantumness. This phenomenon, known as decoherence, is of fundamental interest. There are many competing candidates for qubits, including superconducting circuits, quantum optical cavities, ultracold atoms and spin qubits, and each has its strengths and weaknesses. When dealing with spin qubits, the strongest source of decoherence is the magnetic dipolar interaction. To minimize it, spins are typically dild. in a diamagnetic matrix. For example, this diln. can be taken to the extreme of a single phosphorus atom in silicon, whereas in mol. matrixes a typical ratio is one magnetic mol. per 10,000 matrix mols. However, there is a fundamental contradiction between reducing decoherence by diln. and allowing quantum operations via the interaction between spin qubits. To resolve this contradiction, the design and engineering of quantum hardware can benefit from a 'bottom-up' approach whereby the electronic structure of magnetic mols. is chem. tailored to give the desired phys. behavior. Here we present a way of enhancing coherence in solid-state mol. spin qubits without resorting to extreme diln. It is based on the design of mol. structures with crystal field ground states possessing large tunnelling gaps that give rise to optimal operating points, or at. clock transitions, at which the quantum spin dynamics become protected against dipolar decoherence. This approach is illustrated with a holmium mol. nanomagnet in which long coherence times (up to 8.4 μs at 5 K) are obtained at unusually high concns. This finding opens new avenues for quantum computing based on mol. spin qubits.
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    56. 56
      Zadrozny, J. M.; Niklas, J.; Poluektov, O. G.; Freedman, D. E. Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit. ACS Cent. Sci. 2015, 1, 488– 492,  DOI: 10.1021/acscentsci.5b00338
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      Millisecond Coherence Time in a Tunable Molecular Electronic Spin Qubit
      Zadrozny, Joseph M.; Niklas, Jens; Poluektov, Oleg G.; Freedman, Danna E.
      ACS Central Science (2015), 1 (9), 488-492CODEN: ACSCII; ISSN:2374-7951. (American Chemical Society)
      Quantum information processing (QIP) could revolutionize areas ranging from chem. modeling to cryptog. One key figure of merit for the smallest unit for QIP, the qubit, is the coherence time (T2), which establishes the lifetime for the qubit. Transition metal complexes offer tremendous potential as tunable qubits, yet their development is hampered by the absence of synthetic design principles to achieve a long T2. The authors harnessed mol. design to create qubits, (Ph4P)2[V(C8S8)3] (1), (Ph4P)2[V(β-C3S5)3] (2), (Ph4P)2[V(α-C3S5)3] (3), and (Ph4P)2[V(C3S4O)3] (4), with T2s of 1-4 μs at 80 K in protiated and deuterated environments. Crucially, through chem. tuning of nuclear spin content in the V(IV) environment the authors realized a T2 of ∼1 ms for the species (d20-Ph4P)2[V(C8S8)3] (1') in CS2, a value that surpasses the coordination complex record by an order of magnitude. This value even eclipses some prominent solid-state qubits. Electrochem. and continuous wave EPR data reveal variation in the electronic influence of the ligands on the metal ion across 1-4. However, pulsed measurements indicate that the most important influence on decoherence is nuclear spins in the protiated and deuterated solvents used herein. The authors' results illuminate a path forward in synthetic design principles, which should unite CS2 soly. with nuclear spin free ligand fields to develop a new generation of mol. qubits.
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      Ghirri, A.; Bonizzoni, C.; Troiani, F.; Buccheri, N.; Beverina, L.; Cassinese, A.; Affronte, M. Coherently Coupling Distinct Spin Ensembles through a High-Tc Superconducting Resonator. Phys. Rev. A: At., Mol., Opt. Phys. 2016, 93, 063855,  DOI: 10.1103/PhysRevA.93.063855
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      Mergenthaler, M.; Liu, J.; Le Roy, J. J.; Ares, N.; Thompson, A. L.; Bogani, L.; Luis, F.; Blundell, S. J.; Lancaster, T.; Ardavan, A.; Briggs, G. A. D.; Leek, P. J.; Laird, E. A. Strong Coupling of Microwave Photons to Antiferromagnetic Fluctuations in an Organic Magnet. Phys. Rev. Lett. 2017, 119, 147701,  DOI: 10.1103/PhysRevLett.119.147701
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      Strong coupling of microwave photons to antiferromagnetic fluctuations in an organic magnet
      Mergenthaler, Matthias; Liu, Junjie; Le Roy, Jennifer J.; Ares, Natalia; Thompson, Amber L.; Bogani, Lapo; Luis, Fernando; Blundell, Stephen J.; Lancaster, Tom; Ardavan, Arzhang; Briggs, G. Andrew D.; Leek, Peter J.; Laird, Edward A.
      Physical Review Letters (2017), 119 (14), 147701/1-147701/6CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Coupling between a crystal of di(phenyl)-(2,4,6-trinitrophenyl)iminoazanium radicals and a superconducting microwave resonator is investigated in a circuit quantum electrodynamics (circuit QED) architecture. The crystal exhibits paramagnetic behavior above 4 K, with antiferromagnetic correlations appearing below this temp., and we demonstrate strong coupling at base temp. The magnetic resonance acquires a field angle dependence as the crystal is cooled down, indicating anisotropy of the exchange interactions. These results show that multispin modes in org. crystals are suitable for circuit QED, offering a platform for their coherent manipulation. They also utilize the circuit QED architecture as a way to probe spin correlations at low temp.
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      Bonizzoni, C.; Ghirri, A.; Atzori, M.; Sorace, L.; Sessoli, R.; Affronte, M. Coherent Coupling between Vanadyl Phthalocyanine Spin Ensemble and Microwave Photons: Towards Integration of Molecular Spin Qubits into Quantum Circuits. Sci. Rep. 2017, 7, 13096,  DOI: 10.1038/s41598-017-13271-w
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      Coherent coupling between Vanadyl Phthalocyanine spin ensemble and microwave photons: towards integration of molecular spin qubits into quantum circuits
      Bonizzoni C; Affronte M; Bonizzoni C; Ghirri A; Affronte M; Atzori M; Sorace L; Sessoli R
      Scientific reports (2017), 7 (1), 13096 ISSN:.
      Electron spins are ideal two-level systems that may couple with microwave photons so that, under specific conditions, coherent spin-photon states can be realized. This represents a fundamental step for the transfer and the manipulation of quantum information. Along with spin impurities in solids, molecular spins in concentrated phases have recently shown coherent dynamics under microwave stimuli. Here we show that it is possible to obtain high cooperativity regime between a molecular Vanadyl Phthalocyanine (VOPc) spin ensemble and a high quality factor superconducting YBa2Cu3O7 (YBCO) coplanar resonator at 0.5 K. This demonstrates that molecular spin centers can be successfully integrated in hybrid quantum devices.
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      Horcas, I.; Fernández, R. WSXM: A Software for Scanning Probe Microscopy and a Tool for Nanotechnology. Rev. Sci. Instrum. 2007, 78, 013705,  DOI: 10.1063/1.2432410
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      WSXM: a software for scanning probe microscopy and a tool for nanotechnology
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      Review of Scientific Instruments (2007), 78 (1), 013705/1-013705/8CODEN: RSINAK; ISSN:0034-6748. (American Institute of Physics)
      In this work we briefly describe the most relevant features of WSXM, a freeware scanning probe microscopy software based on MS-Windows. The article is structured in three different sections: The introduction is a perspective on the importance of software on scanning probe microscopy. The second section is devoted to describe the general structure of the application; in this section the capabilities of WSXM to read third party files are stressed. Finally, a detailed discussion of some relevant procedures of the software is carried out.
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      Nečas, D.; Klapetek, P. Gwyddion: An Open-Source Software for SPM Data Analysis. Centr. Eur. J. Phys. 2012, 10, 181– 188,  DOI: 10.2478/s11534-011-0096-2
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      Fano, U. Effects of Configuration Interaction on Intensities and phase Shifts. Phys. Rev. 1961, 124, 1866– 1878,  DOI: 10.1103/PhysRev.124.1866
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      Effects of configuration interaction on intensities and phase shifts
      Fano, U.
      Physical Review (1961), 124 (), 1866-78CODEN: PHRVAO; ISSN:0031-899X.
      The interference of a discrete autoionized state with a continuum gives rise to characteristically asymmetric peaks in excitation spectra. The earlier qual. interpretation of this phenomenon is extended and revised. A theoretical formula is fitted to the shape of the 2s2p1P resonance of He observed in the inelastic scattering of electrons. The fitting dets. the parameters of the 2s2p1P resonance as follows: E2 = 60.1 e.v., γ ∼ 0.04e.v.,f ∼ 2 to 4 × 10-3. The theory is extended to the interaction of 1 discrete level with 2 or more continua, and of a set of discrete levels with one continuum. The theory can also give the position and intensity shifts produced in a Rydberg series of discrete levels by interaction with a level of another configuration. The connection with the nuclear theory of resonance scattering is indicated.
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    • Images of the fabrication steps of resonators and of superconducting nanoconstrictions, tests results of these devices, details and additional images of the deposition of free-radical spin ensembles by DPN and their characterization by means of SEM and AFM, results of additional microwave transmission experiments, additional information, backed with plots, on how the number of molecules effectively coupled to each device has been estimated and how the spin-photon coupling has been simulated (PDF)


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