Molecular vibrational polaritons, a hybridized quasiparticle formed by the strong coupling between molecular vibrational modes and photon cavity modes, have attracted tremendous attention in the chemical physics community due to their peculiar influence on chemical reactions. At the same time, the half-photon half-matter characteristics of polaritons make them suitable to possess properties from both sides and lead to new features that are useful for photonic and quantum technology applications. To eventually use polaritons for chemical and quantum applications, it is critical to understand their dynamics. Due to the intrinsic time scale of cavity modes and molecular vibrational modes in condensed phases, polaritons can experience dynamics on ultrafast time scales, e.g., relaxation from polaritons to dark modes. Thus, ultrafast vibrational spectroscopy becomes an ideal tool to investigate such dynamics. In this Perspective, we give an overview of recent ultrafast spectroscopic works by our group and others in the field. These recent works show that molecular vibrational polaritons can have distinct dynamics from its pure molecular counterparts, such as intermolecular vibrational energy transfer and hot vibrational dynamics. We then discuss some current challenges and future opportunities, such as the possible use of ultrafast vibrational dynamics, to understand cavity-modified reactions and routes to develop molecular vibrational polaritons as new room temperature quantum platforms.

Since 2014, polaritons have attracted attention in the chemistry community for their potential in modifying chemical reactions. The Ebbesen group and collaborators pioneered vibrational strong coupling (VSC)-modified reactions as being either accelerated or decelerated.1–4 A remarkable discovery is that the selectivity of two parallel reaction pathways via VSC is modified.3 In this work, a silane derivative tert-butyl-dimethyl-(4-trimethylsilylbut-3-ynoxy)silane, the reactant (R), may yield 4-trimethylsilyl-3-butyn-1-ol (P1) by breaking the Si–C bond and yield 4-(tert-butyldimethylsilyloxy)-1-butyne (P2) by breaking the Si–O bond. Without VSC, the yield of P2 is higher than that of P1. However, through VSC, for specific vibrational modes of R, the yields of the products are flipped, leading to more P1. These peculiar chemical modifications under VSC raise questions about its detailed molecular mechanisms.

Molecular vibrational polaritons (MVPs) are quasi-particles formed when cavity photon modes and molecular vibrational modes are strongly coupled.1,3,5–46 In other words, MVPs are the new eigenstates formed when the energy exchange rates between the molecular modes and cavity modes are faster than either mode's dissipation rate. Similar to chemical systems, i.e., molecular orbitals, electronic states in J- and H-aggregates, and collective vibrations in proteins, MVPs are created by strong coupling between two or more particles. Apart from the two particles being in resonance, the formation of MVPs requires the molecular vibrational polarization and the photon cavity modes to have a substantial volume overlap. To achieve this, one can fabricate pico-cavities to reach a volume match with single molecules,47–50 an active research direction, which can be described by the Jaynes–Cummings model.51 However, a more relevant approach to chemistry is to insert a high concentration of molecules into an optical micro-cavity,18,21,45 i.e., the Fabry–Pérot cavity, in which the collective macroscopic polarization volume becomes closer to the microcavity volumes. In this way, the systems consist of one cavity mode strongly coupled with N molecular modes, as described by the Tavis–Cummings (TC) model52 and the Hamiltonian in Fig. 1(a). Typically, N is on the order of 1010 molecules.40 

FIG. 1.

Basic polariton theory and properties: (a) the Hamiltonian of strongly coupled molecular vibrational modes with a cavity mode. (b) An energy diagram of vibrational polaritons coupled by strong molecular vibration and cavity modes [left—the vibrational polariton FTIR spectrum of W(CO)6]. (c) Dispersion of vibrational polaritons as a function of the tilting angle, θ. (d) Corresponding Hopfield coefficients of UP and LP states. (b) and (c) Adapted with permission from Xiang et al., Proc. Natl. Acad. Sci. U. S. A. 115, 4845 (2018). Copyright 2018 National Academy of Sciences.

FIG. 1.

Basic polariton theory and properties: (a) the Hamiltonian of strongly coupled molecular vibrational modes with a cavity mode. (b) An energy diagram of vibrational polaritons coupled by strong molecular vibration and cavity modes [left—the vibrational polariton FTIR spectrum of W(CO)6]. (c) Dispersion of vibrational polaritons as a function of the tilting angle, θ. (d) Corresponding Hopfield coefficients of UP and LP states. (b) and (c) Adapted with permission from Xiang et al., Proc. Natl. Acad. Sci. U. S. A. 115, 4845 (2018). Copyright 2018 National Academy of Sciences.

Close modal
By diagonalizing the Hamiltonian, one can find two new eigenstates with photon characters—polaritons, and the corresponding wavefunctions14,53,54 are
U P = 1 N c U P , m 1 v m 0 c + c U P , N + 1 g 1 c , L P = 1 N c L P , m 1 v m 0 c + c L P , N + 1 g 1 c ,
(1)
where cUP(LP),m and cUP(LP),N+1 are the coefficients of the excited mth molecular and cavity wavefunctions of UP (or LP), respectively, and |1v〉m indicates that the vibrational modes of the mth molecule in the cavity are at the first excited state. In contrast, the vibrational modes of all other molecules are in their ground states. |g〉 represents the vibrational modes of all molecules, which are in the ground state, and |0c〉 and |1c〉 represent no or one photon inside the cavity, respectively. Thus, the wavefunction reveals the fact that polaritons are hybridized states between molecular states and photon modes. For the case of N > 1, more than one molecular wavefunction participates in the polariton formation, in phase with each other, and therefore represents the delocalized nature of polaritons. Apart from the two polariton eigenstates, there are also N-1 eigenstates that do not have photon wavefunctions (i.e., 1 c ), referred to as dark reservoir modes. Although their wavefunction appears to be delocalized among molecular modes, local chemical environment fluctuation renders the dark reservoir modes localized on individual molecules, i.e., similar to uncoupled molecular modes.15,55,56
The eigenenergy of both polariton states and dark reservoir modes is
E L P , U P = 1 2 E c a v + E v i b 4 N β 2 + ( E c a v E v i b ) 2 ,
(2)
E d a r k = E v i b .
Thus, the energy of the polariton modes shifts away from the pure molecular states. The shift depends on the number of molecules, N, the individual molecular coupling strength, β, and the cavity detuning, Δ = EcavEvib. This shift is a critical character of polaritons. It has been used to explain polariton modified chemistry: the LP polariton energy is shifted down relative to the uncoupled systems, which creates a more significant barrier for reactions.46 In contrast, the dark reservoir mode energy remains unmodified. A representative energy diagram of the light–matter VSC phenomenon is shown in Fig. 1(b). The energy separation between LP and UP is the so-called Rabi splitting, 2 Ω N β at zero detuning. Theoretically, when Ω > 1 2 ( Γ v i b + Γ c a v ) ,57 where Γ is the half linewidth of each mode, the VSC condition is satisfied. It is obvious that when increasing the molecular concentration in the cavity, N also increases, enhancing the collective coupling strength.

By controlling the in-plane momentum of cavity modes, k|| (or the incidence angle), i.e., the detuning Δ, ELP,UP [Fig. 1(c)], and the compositions of LP and UP can be modified. For example, as indicated by the Hopfield coefficient plot [Fig. 1(d)], the UP branch would be more photon-like with increasing detuning while the LP branch shows larger molecular fractions.15,20,43

We note that regardless of whether the strong coupling is under a single-molecule (N = 1) or in the ensemble regime (N ≫ 1), the resulting polariton systems always have two optically bright polariton modes. The difference is that in the ensemble case, there are N − 1 dark reservoir modes that cannot or can only weakly interact with photons.15,55 Nevertheless, as discussed later, dark modes can change the dynamics in the VSC systems. More importantly, the N − 1 dark modes are the majority in the system compared to the two polariton modes. Thus, it is an interesting question to understand how polariton modes modify chemistry despite their relatively low population.

Thus, the exciting results of VSC modification of chemical reactions open more questions about the mechanism regarding thermodynamics and dynamics. Ultrafast spectroscopy, such as pump–probe and two-dimensional infrared (2D IR) spectroscopy,15,22,62–67 measures the molecular vibrational dynamics at its natural femtosecond time scale. Thus, it provides unique insight into the dynamics of MVPs. Owrutsky, Dunkelberger, and co-workers measured the dynamics of MVPs using femtosecond pump–probe spectroscopy.20 Our group then conducted 2D IR spectroscopic studies on MVPs extensively.5,15,26,37,44 In this Perspective, we briefly overview a few important polariton dynamic results obtained by our group and others by spectroscopic and theoretical studies. Although a detailed mechanistic picture of cavity-modified chemistry is still not available, the ultrafast spectroscopic methods have been established, revealing novel molecular dynamics. Thus, it sets the stage to unravel the novel mechanism of VSC chemistry. Furthermore, interesting nonlinear optical properties of MVPs are discovered,5,68 which could open a new route for quantum simulation and computing.

Similar to any other strongly coupled system, the dynamics of MVPs can be measured by ultrafast spectroscopy. The pump–probe technique is the most fundamental technique to observe polariton dynamics.20 An IR pump pulse excites the polaritons, and another pulse probes the excited polaritons after a certain time delay (t2). By scanning the pump–probe time delay, the polariton dynamics can be followed [Fig. 2(a)]. In our group, we also utilize the ultrafast technique of two-dimensional infrared (2D IR) spectroscopy. 2D IR15,62,63 [Fig. 2(a)] uses two pump pulses and a probe pulse to interact with samples at delayed times (t1, t2, and t3). The first IR pulse generates a vibrational coherence, which is converted into a population (or coherence) state by the second IR pulse and is characterized by scanning t1. After waiting for t2, the third IR pulse (probe) impinges on the sample and creates a macroscopic polarization that emits an IR signal. Following Fourier transform, the molecular vibrational transitions are plotted as a function of pump (ω1) and probe (ω3) frequencies in 2D IR spectra. To some level, 2D IR can be viewed as pump–probe spectroscopy with the pumping states resolved in the frequency domain, which allows the dynamics of different states to be studied separately. When implementing both pump–probe and 2D IR spectroscopy, it is critical to ensure that the incident angle (θ) of the pump and probe pulses is the same, which guarantees that polaritons with the same in-plane momentum are excited and probed [Fig. 2(b)].

FIG. 2.

2D IR and pump–probe spectroscopy: (a) 2D IR and pump–probe pulse sequences. (b) Illustration of the 2D IR experimental setup. (b) Adapted with permission from Xiang et al., Proc. Natl. Acad. Sci. U. S. A. 115, 4845 (2018). Copyright 2018 National Academy of Sciences.

FIG. 2.

2D IR and pump–probe spectroscopy: (a) 2D IR and pump–probe pulse sequences. (b) Illustration of the 2D IR experimental setup. (b) Adapted with permission from Xiang et al., Proc. Natl. Acad. Sci. U. S. A. 115, 4845 (2018). Copyright 2018 National Academy of Sciences.

Close modal

Based on the polariton lifetime, the polariton dynamics can be divided into two regimes. The polariton lifetime is limited by the shortest lifetime of the two components. Thus, the lifetimes of most MVPs are determined by the cavity lifetime, typically between 3 and 5 ps, depending on the cavity quality. When t2 is shorter than the polariton lifetime, a large population of excited polaritons and a large coherent polariton–polariton interaction contribute to the nonlinear signal;5 when t2 is larger than polariton lifetime, the polaritons lose their photon characters and relax to the dark-reservoir modes that are nearby in energy. In this regime, polariton–reservoir mode interactions are dominant.44 

Within the polariton lifetime, the pump–probe spectra show two significant transient absorptive features [Fig. 3(a)], and the 2D IR spectra show absorptive peaks in both the diagonal and cross-peaks [Fig. 3(b)]. When taking a spectral cut at either ω1 = ωLP or ωUP and scanning t2, we find that spectral peaks oscillate strongly with a period of 0.8 ps, corresponding to a frequency of 42 cm−15,20 [Fig. 3(c)]. The oscillation corresponds to the |LP〉〈UP| or |UP〉〈LP| coherence during t2, e.g., energy exchanges between cavity modes and molecular states.5,54 Using a Fourier filter, we can isolate the oscillating spectral features, which are purely absorptive.5 

FIG. 3.

Optical nonlinear signal due to polariton–polariton interactions in a short time limit. At an early time delay (compared to the cavity photon lifetime, approximately 5 ps), both (a) the pump–probe and (b) 2D IR spectra show absorptive features. (c) With broad pump spectra, the absorptive peaks show fast oscillation on top of an exponential decay. (d) Tailored pump sequences can prepare either populations, which have exponential decay dynamics (top), or coherence, which shows an oscillation signal. (e) The dip at zero time delay is visible both in the raw correlation trace and the integrated coincidence plot due to the ensemble-regime photon blockade effect (polariton blockade). (a) and (b) Adapted with permission from Xiang et al., Sci. Adv. 5, eaax5196 (2019). Copyright 2019 American Association for the Advancement of Science. (c) and (d) Adapted with permission from Yang et al., ACS Photonics 7, 919 (2020). Copyright 2020 American Chemical Society. (e) Adapted with permission from Muñoz-Matutano et al., Nat. Mater. 18, 213 (2019). Copyright 2019 Crown.

FIG. 3.

Optical nonlinear signal due to polariton–polariton interactions in a short time limit. At an early time delay (compared to the cavity photon lifetime, approximately 5 ps), both (a) the pump–probe and (b) 2D IR spectra show absorptive features. (c) With broad pump spectra, the absorptive peaks show fast oscillation on top of an exponential decay. (d) Tailored pump sequences can prepare either populations, which have exponential decay dynamics (top), or coherence, which shows an oscillation signal. (e) The dip at zero time delay is visible both in the raw correlation trace and the integrated coincidence plot due to the ensemble-regime photon blockade effect (polariton blockade). (a) and (b) Adapted with permission from Xiang et al., Sci. Adv. 5, eaax5196 (2019). Copyright 2019 American Association for the Advancement of Science. (c) and (d) Adapted with permission from Yang et al., ACS Photonics 7, 919 (2020). Copyright 2020 American Chemical Society. (e) Adapted with permission from Muñoz-Matutano et al., Nat. Mater. 18, 213 (2019). Copyright 2019 Crown.

Close modal

We further demonstrate that, by use of a pulse shaper, we can customize pulse sequences to prepare specific coherence states,37 e.g., |UP〉〈LP|, or population states, e.g., |UP〉〈UP|, and measure the corresponding 2D IR responses. When |UP〉〈LP| and |UP〉〈UP| are created, their 2D IR features appear at the same spectral location, but when scanning t2, they demonstrate completely different dynamics: |UP〉〈UP| shows exponential decays, and |UP〉〈LP| oscillates at the Rabi frequency [Fig. 3(d)]. This experiment demonstrates that we can arbitrarily prepare quantum states using the pulse shaper, paving a step for using MVPs for quantum simulations. Recently, using a pulse shaper, Grafton and co-workers69 further isolate early-time nonlinear signals from polariton population states by subtracting the overall signal from the reservoir-specific signal and isolated the polariton-specific Rabi oscillation. They also describe the origin of the polariton signal using a theoretical TC model composed of a few molecules and a cavity. Recent theoretical work by Campos-Gonzalez-Angulo and co-workers70 has also developed a generalized way to calculate the polariton energy of the generalized TC model for a large number of molecules with anharmonicities.

The transient absorptive features of polaritons indicate that the pump pulse saturates the molecular portion of polaritons, which makes the subsequent probe pulse interact less with polaritons, causing a reduction in the probe transmission. More interestingly, we find that as the cavity longitudinal length decreases, more probe photons are blocked from interacting with polaritons under the same pump fluences. This trend can be easily understood by the reduction in longitudinal length that leads to a decrease in the number of molecular absorbers in the cavity volumes, making the molecular modes easier to be saturated.5 If the cavity volume can be shrunk all the way down to a volume that supports the single molecule regime, photon blockade—light–matter interaction being switched off by a single photon—can be reached. Thereby, the ensemble-limit of 2D IR and pump–probe signals of MVPs is indeed related to photon blockade at the single-molecule-limit. It is also reported recently71,72 that, even under the ensemble-limit, a small photon blockade effect (g(2) < 1) can exist [Fig. 3(e)]. However, a complete theoretical relationship between the third-order measurements in the ensemble regime and the single-molecule photon blockade experiments remains to be developed.

When the pump–probe time delay (t2 of 2D IR) exceeds the lifetime of polaritons, they relax into the reservoir modes by losing or gaining tens of wavenumbers of energy, which matches with low-frequency modes of solvents. The excitation of reservoir modes has two effects in spectroscopy. First, it causes the so-called Rabi splitting contraction. Because Rabi splitting is proportional to the square root of molecular concentration [i.e., Eq.(2)], when polaritons relax to the excited states of reservoir modes, this relaxation also removes the ground-state population of reservoir modes that can strongly couple to the cavity modes. As a result, the UP (LP) resonance undergoes a red (blue) shift,15 resulting in derivative lineshapes in the transient spectrum [Fig. 4(a)] and 2D IR [Fig. 4(b)]. The reduction in Rabi splitting is an effective polariton–reservoir mode interactions.73 

FIG. 4.

2D IR and pump–probe spectra at long time delay. At long time delay, when polaritons relax to the dark modes, both (a) the pump–probe and (b) 2D IR show a derivative feature on the ω3 = ωUP side due to Rabi splitting contraction and a large absorptive feature on the ω3 = ωLP side due to excited state absorption of the dark modes. (c) The simulated Rabi splitting contraction feature shows that only peak intensity scales as a function of ΔN/N, where the peak positions remain unchanged. The Rabi splitting contraction features have the same lineshape as the differential transmission (δS/δω) (top). (a) and (b) Adapted with permission from Xiang et al., Sci. Adv. 5, eaax5196 (2019). Copyright 2019 American Association for the Advancement of Science.

FIG. 4.

2D IR and pump–probe spectra at long time delay. At long time delay, when polaritons relax to the dark modes, both (a) the pump–probe and (b) 2D IR show a derivative feature on the ω3 = ωUP side due to Rabi splitting contraction and a large absorptive feature on the ω3 = ωLP side due to excited state absorption of the dark modes. (c) The simulated Rabi splitting contraction feature shows that only peak intensity scales as a function of ΔN/N, where the peak positions remain unchanged. The Rabi splitting contraction features have the same lineshape as the differential transmission (δS/δω) (top). (a) and (b) Adapted with permission from Xiang et al., Sci. Adv. 5, eaax5196 (2019). Copyright 2019 American Association for the Advancement of Science.

Close modal

An alternative explanation of the derivative shape involves exciting different quanta of polaritons.74 However, we note that the polariton energy is harmonic at the ensemble regime,52 so the energy level of first and second quanta polariton excitation remains the same. Experimental evidence used to support the different quantum excitation explanations is that increasing the pump excitation power only increased the transient peak intensities instead of causing the transient peak feature to continuously shift inward, as the Rabi splitting N dependence predicts. We note that because the 2D IR experiment is still in the perturbative regime, i.e., a small fraction of reservoir modes are excited, the Rabi splitting contraction can be approximated as Δ N * d S d ω , where ΔN is the number of reservoir modes excited and d S d ω is the derivative of the linear polariton spectra. Therefore, when more reservoir modes are excited by increased pump power, it should only cause an enhancement in the transient derivative lineshape, instead of more inward peak shifts. This argument is further demonstrated by a simulation using the transform matrix method, where the excitation percentage ΔN/N is increased from 1% to 5%–10%. As shown in Fig. 4(c), only the peak intensity is increased. Thus, the classical Rabi splitting explanation is sufficient to describe the derivative feature.

The second effect of excited reservoir states is the LP absorptive feature [Figs. 4(a) and 4(b)]. This new feature is originated from the fact that the reservoir modes are anharmonic.75 The reservoir overtone transition ν12 (from first excited to second excited states) is red-shifted relative to its fundamental and near-resonant with LP transition. As a result, it borrows the transmission window of LP and can generate a large absorptive feature, which dominates the LP transient signal.15,43,74 Although this feature masks the response of LP to reservoir population, by scanning the t2, it provides a convenient way to measure polariton to reservoir mode dynamics, which is useful as described below.

Using the 2D IR technique, we recently demonstrate that under VSC conditions, molecules could transfer vibrational energy between themselves.26 Such a mechanism is rare in nature as unlike electronic dipoles, vibrational dipole–dipole interactions are weak in the liquid phase. Thus, this work has the potential to open up a new mechanism for vibrational energy transfer between molecules in the cavity, enabling cavity-modified chemistry.1 

We prepare VSC between vibrational modes from two types of molecules [asymmetric CO stretching modes of W(CO)6, donor, and W(13CO)6, acceptor] and the Fabry–Pérot (FP) cavity modes to enable the new energy transfer between molecules. The intermolecular Förster resonance energy transfer (FRET) efficiency is insignificant without cavity modes, as indicated by the lack of cross-peaks in 2D IR [Fig. 5(a)], which agrees with the insignificant FRET efficiency determined from theory.26 In the VSC regime, however, exciting UP (mainly composed of donor and cavity modes) leads to significant energy transfer to the acceptor mode, shown as the cross peak (red square) in Fig. 5(b). This cross peak indicates that when exciting UP modes, a certain amount of energy is transferred to the acceptor to populate its first excited states [Fig. 5(c), left panel]. The other cross peak identified in the black square in Fig. 5(b) corresponds to the energy relaxation from UP to donor molecules [Fig. 5(c), right panel]. Thus, we can determine how energy is deposited into the donor and acceptor from UP relatively by taking the ratio between the cross-peaks in the red and black squares. The ratio is 2.5:1. In contrast, based on Hopfield coefficients of the UP state, the composition of the donor and acceptor mode ratio in the UP state is ∼14:1. Thus, the significant experimental cross-peak ratio compared to the intrinsic population composition of UP state indicates an extraordinary energy redistribution when the two molecular modes share the same cavity mode.

FIG. 5.

VSC enabled intermolecular vibrational energy transfer. 2D IR spectra (FTIR on top) of (a) bare (uncoupled) W(CO)6/W(13CO)6 in a binary solvent (hexane-DCM) show that there are no crosspeaks due to energy transfer. (b) 2D IR of strongly coupled system shows crosspeaks, indicating intermolecular energy transfer. (c) Energy transfer pathways from UP to acceptor/donor modes. (d) Dynamic traces of UP-MP and UP-LP peak integrals where UP-MP (energy relaxation) shows a fast rise and decay dynamics, whereas the UP-LP (energy transfer) exhibits slow increasing dynamics. (e) The energy transfer (UP-LP) over energy relaxation (UP-MP) ratio vs cavity thickness shows that a longer cavity favors energy transfer at t2 = 30 ps. (a), (b), (d), and (e) Adapted with permission from Xiang et al., Sci. 368, 665 (2020). Copyright 2020 American Association for the Advancement of Science.

FIG. 5.

VSC enabled intermolecular vibrational energy transfer. 2D IR spectra (FTIR on top) of (a) bare (uncoupled) W(CO)6/W(13CO)6 in a binary solvent (hexane-DCM) show that there are no crosspeaks due to energy transfer. (b) 2D IR of strongly coupled system shows crosspeaks, indicating intermolecular energy transfer. (c) Energy transfer pathways from UP to acceptor/donor modes. (d) Dynamic traces of UP-MP and UP-LP peak integrals where UP-MP (energy relaxation) shows a fast rise and decay dynamics, whereas the UP-LP (energy transfer) exhibits slow increasing dynamics. (e) The energy transfer (UP-LP) over energy relaxation (UP-MP) ratio vs cavity thickness shows that a longer cavity favors energy transfer at t2 = 30 ps. (a), (b), (d), and (e) Adapted with permission from Xiang et al., Sci. 368, 665 (2020). Copyright 2020 American Association for the Advancement of Science.

Close modal

Time-dependent features [Fig. 5(d)] show that upon pumping UP, the donor and acceptor population follows different dynamics: the donor population increases within around 1.5 ps through UP relaxation because it is composed of most of the UP, while the acceptor population increases in about 5 ps. This result suggests that the energy transfer acceptor finishes within the lifetime of the cavity modes. Finally, the energy redistribution ratio can be controlled by modifying the cavity longitudinal length [Fig. 5(e)]. We find that a thicker length cavity gives more efficient energy transfer, i.e., by increasing the cavity from 5 to 25 μm, the energy transfer efficiency increases from 30% to 55%. This result can be explained by the fact that although the total number of round trips photons spend in the cavity (Q factor > 100) remains the same, a thicker cavity leads to a longer cavity pathlength and thereby polariton lifetime; as a result, the longer cavity ensures more time for the cavity to facilitate energy transfer between molecules.

Thus, by coupling the cavity mode with multiple molecular modes, molecular modes can benefit from the cavity’s delocalized nature. There is a particular requirement for this phenomenon: the frequency separation between two different vibrational modes should be smaller or comparable to the sum of the coupling strengths between the two vibrational modes and the cavity mode so that both modes are strongly coupled with the cavity mode. The evidence of intermolecular vibrational energy transfer could be connected to the proposed mechanism of a recent cavity catalysis work.1 In the cavity catalysis work, the cooperativity between vibrational modes of reactants and solvents is proposed to lead to changes in chemical reactivities under VSC. Indeed, VSC-enabled intermolecular energy transfer is evidence of cooperativity. Despite this critical potential, the exact mechanism that led to such fast energy transfer under VSC remains to be explored, in order to shed light on cavity catalysis and, even further, to establish design principles for cavity catalysis. A recent theoretical work suggests that the hot vibrational modes of dark states facilitate intermolecular energy transfer.76 Furthermore, VSC-enabled intermolecular energy transfer should be general and exist in other molecular and material systems, remaining to be demonstrated.

In another experiment,44 when only one type of molecule is strongly coupled to the cavity, we find that UP and LP undergo different relaxation mechanisms (Fig. 6). After a polariton loses its photon character, UP directly relaxes into the first excited state of dark modes, further relaxing to ground states over hundreds of picoseconds, as expected [Fig. 6(b)]. However, the LP first populates the second excited states of the reservoir modes.44 This finding is evident by immediately following LP decay, a noticeable ν23 transition spectral feature that appears before the ν12 transitions show up [Fig. 6(a)]. The dynamics of ν23 decay exponentially, while the ν12 transition increases at a similar rate, indicating a relaxation between the second and first excited states [Fig. 6(c)]. We note that twice of LP happens to be matched with the transition of ν02.

FIG. 6.

Hot vibrational dynamics in polariton systems: (a) the spectral cut at ωLP shows the spectral features of ν12 and ν23 transitions. (b) Relaxation dynamics when UP is pumped show an instantaneous population of the first excited state of the dark mode and a negligible signal from the second excited state. (c) Dynamics when LP is excited show a delayed relaxation of the first excited state of the dark mode and a corresponding large second excited state population. (d) LP first relaxes to second excited states through polariton–polariton scattering before relaxing to first excited dark modes. (e) An illustration of vibrational polariton dynamics to show the similarity with plasmonic dynamics. (f) The cavity molecular dynamics simulation result, where LP can undergo multiple photon excitations to populate the hot vibrational modes of the dark reservoir states. (f) Adapted from Li et al., J. Chem. Phys. 154, 094124 (2021) with the permission of AIP Publishing.

FIG. 6.

Hot vibrational dynamics in polariton systems: (a) the spectral cut at ωLP shows the spectral features of ν12 and ν23 transitions. (b) Relaxation dynamics when UP is pumped show an instantaneous population of the first excited state of the dark mode and a negligible signal from the second excited state. (c) Dynamics when LP is excited show a delayed relaxation of the first excited state of the dark mode and a corresponding large second excited state population. (d) LP first relaxes to second excited states through polariton–polariton scattering before relaxing to first excited dark modes. (e) An illustration of vibrational polariton dynamics to show the similarity with plasmonic dynamics. (f) The cavity molecular dynamics simulation result, where LP can undergo multiple photon excitations to populate the hot vibrational modes of the dark reservoir states. (f) Adapted from Li et al., J. Chem. Phys. 154, 094124 (2021) with the permission of AIP Publishing.

Close modal

Recently, in a theoretical work,31 Li, Subotnick, and Nitzan study dynamics of CO2 under VSC. Using cavity molecular dynamics simulation, they find that LP can undergo multiple photon excitations to populate the hot vibrational modes of the dark reservoir states [Fig. 6(f)]. They further find that the enhancement can be as large as two orders of magnitude with proper detuning compared to outside-the-cavity.

Thus, the mechanism of the hot vibrational dynamics could be that LP scatters with another LP and transfers energy to the second excited states of dark modes because the energy of 2LP matches with the energy gap between the second excited and ground states of the reservoir modes [summarized in Fig. 6(d)].

This hot vibrational dynamic mechanism could have two important implications: First, it suggests that polariton–polariton scattering occurs in vibrational polaritons, an essential step of condensation. Second, it suggests that with proper design, polariton–polariton scattering could populate higher excited reservoir modes. In addressing the second point, we note that there are certain similarities between polaritons and plasmonic modes in nanomaterials [Fig. 6(e)]. Plasmons are a collective oscillation of electrons in a confined space, which relaxes and generates hot electrons and holes.77 Similarly, molecular vibrational polaritons are collective vibrational motions in a confined cavity space, which can populate highly excited vibrational states throughout polariton relaxation [Fig. 6(d)]. Currently, polariton relaxation can only populate the second excited vibrational states, which is not enough to overcome the activation barrier. However, such similarity gives hope and excitement to further design cavities and experimental conditions to use polaritons to realize mode-selective chemistry.

Although strong coupling has been studied extensively as a phenomenon of physics, the combination with molecular science has only started within the last ten years. From the chemistry side, VSC has shown its revolutionary potential to alter chemical reactivity and selectivity; from the quantum technology side, the hybridization between molecular nonlinearity with photon modes also provides a potential new quantum simulation platform. However, opportunities and challenges remain in this emerging field.

First and foremost, it is essential to have a clear mechanistic picture of chemical reactions under VSC. Currently, both accelerated and decelerated reaction rates under VSC have been reported.1–3 Although thermodynamic analysis provides insights into the alteration of enthalpy and entropy of reactions under VSC, it remains challenging to understand why VSC can accelerate certain reactions but decelerate others. In addition, it is recognized that the dark reservoir modes occupy the majority population under VSC, which essentially has uncoupled molecular properties. Thus, it remains unclear how the small polariton population can influence chemical reactions. Besides this, it is observed that the VSC influence on reactions strongly depends on the detuning at k|| = 0, which leaves a mystery about the role of other polaritons at higher k||. Some theoretical investigations propose mechanisms where VSC can change the chemical reaction rate.9 Other studies also predict that VSC should have a negligible effect on any reaction under equilibrium transition state theory16,23 and non-equilibrium effects with classical or quantum origins are necessary to initiate the influence of VSC on reactions. Because the vibrational energy dissipation and transfer happen on the ultrafast time scale, ultrafast spectroscopy can provide unique insights into how VSC changes molecular dynamics. Furthermore, theory and simulations make connections between ultrafast dynamics and reaction kinetics. Thus, a joint force between theorists, ultrafast spectroscopists, and VSC reaction experts working together to solve the puzzle and reach a consensus in VSC reaction mechanisms is necessary.

Second, most of the VSC cavities are microcavities formed by assembling two partial reflectors into the Fabry–Pérot cavity. While easy to prepare, the microcavity volume is limited to the order of λ 2 , substantially restricting the coupling strength, which is inversely proportional to cavity volume. Tip-enhanced approaches using STM or AFM have been demonstrated.48,78 However, it requires special treatment of the tips and perhaps will remain as specialized techniques. Thus, there is a need to reduce cavity volume further to advance VSC in general. Fortunately, advances in photonics and nanotechnology have provided several plausible directions. The epsilon-near-zero (ENZ) mode has demonstrated ultra-strong coupling to phonon modes of SiO2.79 Photolithography techniques have also provided means to apply lateral confinement to the microcavity.68 The IR plasmon mode has also been shown to strongly couple to water modes.80 In addition, topological polaritons and nano-light canalization provide an ideal means to confine light to further interact with matters.81,82 Thus, it is expected that VSC will be further advanced by combining with these novel cavity modes to achieve even stronger coupling or miniaturized volume for fewer-molecule strong coupling.

Finally, VSC already shows its potential in quantum technology despite its infancy stage, including the potential for single-photon IR sources and quantum bits. The benefit of using MVPs for quantum technology is that there are many molecular vibrational modes across the entire mid-IR regime, thereby enhancing the complexity of the quantum simulation, such as multi-color quantum bits. Furthermore, it will also overcome the shortage of single-photon IR sources. There are obvious obstacles to overcome in order to proceed. For example, to use MVPs as quantum bits, their coherence lifetime needs to be significantly lengthened. Such a task may be achieved by combining isolated vibrational chromophores in hosted materials and high-quality cavity, as mentioned in the previous paragraph. In addition, to make single-photon IR sources, VSC needs to be achieved with fewer molecules, which could be achieved with miniaturized photonic cavities.

Overall, vibrational strong coupling represents an emerging field with a great deal of excitement and unsolved puzzles that benefit from existing and new physical-chemical tools. Understanding and advancing this new field could impact other fields such as synthetic chemistry, photonics, and quantum technology.

We thank Professor Joel Yuen-Zhou and Professor Raphael F. Ribeiro for useful discussions. We thank Garret Wiesehan for language polishing. The works in our group were financially supported by the National Science Foundation (Grant No. DMR-1848215), the Air Force Office of Scientific Research (Grant No. FA9550-17-1-0094), and the Defense Advanced Research Projects Agency Young Faculty Award Program (No. D15AP00107).

1.
J.
Lather
,
P.
Bhatt
,
A.
Thomas
,
T. W.
Ebbesen
, and
J.
George
,
Angew. Chem., Int. Ed.
58
,
10635
(
2019
).
2.
R. M. A.
Vergauwe
,
A.
Thomas
,
K.
Nagarajan
,
A.
Shalabney
,
J.
George
,
T.
Chervy
,
M.
Seidel
,
E.
Devaux
,
V.
Torbeev
, and
T. W.
Ebbesen
,
Angew. Chem., Int. Ed.
58
,
15324
(
2019
).
3.
A.
Thomas
,
L.
Lethuillier-Karl
,
K.
Nagarajan
,
R. M. A.
Vergauwe
,
J.
George
,
T.
Chervy
,
A.
Shalabney
,
E.
Devaux
,
C.
Genet
,
J.
Moran
, and
T. W.
Ebbesen
,
Science
363
,
615
(
2019
).
4.
A.
Thomas
,
J.
George
,
A.
Shalabney
,
M.
Dryzhakov
,
S. J.
Varma
,
J.
Moran
,
T.
Chervy
,
X.
Zhong
,
E.
Devaux
,
C.
Genet
,
J. A.
Hutchison
, and
T. W.
Ebbesen
,
Angew. Chem., Int. Ed.
55
,
11462
(
2016
).
5.
B.
Xiang
,
R. F.
Ribeiro
,
Y.
Li
,
A. D.
Dunkelberger
,
B. B.
Simpkins
,
J.
Yuen-Zhou
, and
W.
Xiong
,
Sci. Adv.
5
,
eaax5196
(
2019
).
6.
T.
Schwartz
,
J. A.
Hutchison
,
J.
Léonard
,
C.
Genet
,
S.
Haacke
, and
T. W.
Ebbesen
,
ChemPhysChem
14
,
125
(
2013
).
8.
X.
Zhong
,
T.
Chervy
,
L.
Zhang
,
A.
Thomas
,
J.
George
,
C.
Genet
,
J. A.
Hutchison
, and
T. W.
Ebbesen
,
Angew. Chem., Int. Ed.
56
,
9034
(
2017
).
9.
J. A.
Campos-Gonzalez-Angulo
,
R. F.
Ribeiro
, and
J.
Yuen-Zhou
,
Nat. Commun.
10
,
4685
(
2019
).
10.
J.
Yuen-Zhou
and
V. M.
Menon
,
Proc. Natl. Acad. Sci. U. S. A.
116
,
5214
(
2019
).
11.
J.
Yuen-Zhou
,
S. K.
Saikin
, and
V. M.
Menon
,
J. Phys. Chem. Lett.
9
,
6511
(
2018
).
12.
M.
Du
,
R. F.
Ribeiro
, and
J.
Yuen-Zhou
,
Chem
5
,
1167
(
2019
).
13.
R. F.
Ribeiro
,
L. A.
Martínez-Martínez
,
M.
Du
,
J.
Campos-Gonzalez-Angulo
, and
J.
Yuen-Zhou
,
Chem. Sci.
9
,
6325
(
2018
).
14.
M.
Du
,
L. A.
Martínez-Martínez
,
R. F.
Ribeiro
,
Z.
Hu
,
V. M.
Menon
, and
J.
Yuen-Zhou
,
Chem. Sci.
9
,
6659
(
2018
).
15.
B.
Xiang
,
R. F.
Ribeiro
,
A. D.
Dunkelberger
,
J.
Wang
,
Y.
Li
,
B. S.
Simpkins
,
J. C.
Owrutsky
,
J.
Yuen-Zhou
, and
W.
Xiong
,
Proc. Natl. Acad. Sci. U. S. A.
115
,
4845
(
2018
).
16.
I.
Vurgaftman
,
B. S.
Simpkins
,
A. D.
Dunkelberger
, and
J. C.
Owrutsky
,
J. Phys. Chem. Lett.
11
,
3557
(
2020
).
17.
A. D.
Dunkelberger
,
R. B.
Davidson
,
W.
Ahn
,
B. S.
Simpkins
, and
J. C.
Owrutsky
,
J. Phys. Chem. A
122
,
965
(
2018
).
18.
B. S.
Simpkins
,
K. P.
Fears
,
W. J.
Dressick
,
B. T.
Spann
,
A. D.
Dunkelberger
, and
J. C.
Owrutsky
,
ACS Photonics
2
,
1460
(
2015
).
19.
A. D.
Dunkelberger
,
A. B.
Grafton
,
I.
Vurgaftman
,
Ö. O.
Soykal
,
T. L.
Reinecke
,
R. B.
Davidson
,
B. S.
Simpkins
, and
J. C.
Owrutsky
,
ACS Photonics
6
,
2719
(
2019
).
20.
A. D.
Dunkelberger
,
B. T.
Spann
,
K. P.
Fears
,
B. S.
Simpkins
, and
J. C.
Owrutsky
,
Nat. Commun.
7
,
13504
(
2016
).
21.
J. P.
Long
and
B. S.
Simpkins
,
ACS Photonics
2
,
130
(
2015
).
22.
P.
Saurabh
and
S.
Mukamel
,
J. Chem. Phys.
144
,
124115
(
2016
).
23.
T. E.
Li
,
A.
Nitzan
, and
J. E.
Subotnik
,
J. Chem. Phys.
152
,
234107
(
2020
).
24.
M.
Reitz
and
C.
Genes
,
J. Chem. Phys.
153
,
234305
(
2020
).
25.
M.
Du
,
J. A.
Campos-Gonzalez-Angulo
, and
J.
Yuen-Zhou
,
J. Chem. Phys.
154
,
084108
(
2021
).
26.
B.
Xiang
,
R. F.
Ribeiro
,
M.
Du
,
L.
Chen
,
Z.
Yang
,
J.
Wang
,
J.
Yuen-Zhou
, and
W.
Xiong
,
Science
368
,
665
(
2020
).
27.
S. N.
Chowdhury
,
A.
Mandal
, and
P.
Huo
,
J. Chem. Phys.
154
,
044109
(
2021
).
28.
Z.
Zhang
,
P.
Saurabh
,
K. E.
Dorfman
,
A.
Debnath
, and
S.
Mukamel
,
J. Chem. Phys.
148
,
074302
(
2018
).
29.
J. B.
Pérez-Sánchez
and
J.
Yuen-Zhou
,
J. Phys. Chem. Lett.
11
,
152
(
2020
).
30.
J. A.
Campos-Gonzalez-Angulo
and
J.
Yuen-Zhou
,
J. Chem. Phys.
152
,
161101
(
2020
).
31.
T. E.
Li
,
A.
Nitzan
, and
J. E.
Subotnik
,
J. Chem. Phys.
154
,
094124
(
2021
).
32.
F.
Herrera
and
J.
Owrutsky
,
J. Chem. Phys.
152
,
100902
(
2020
).
33.
T. E.
Li
,
J. E.
Subotnik
, and
A.
Nitzan
,
Proc. Natl. Acad. Sci. U. S. A.
117
,
18324
(
2020
).
34.
E. W.
Fischer
and
P.
Saalfrank
,
J. Chem. Phys.
154
,
104311
(
2021
).
35.
T.
Szidarovszky
,
P.
Badankó
,
G. J.
Halász
, and
Á.
Vibók
,
J. Chem. Phys.
154
,
064305
(
2021
).
36.
X.
Li
,
A.
Mandal
, and
P.
Huo
,
Nat. Commun.
12
,
1315
(
2021
).
37.
Z.
Yang
,
B.
Xiang
, and
W.
Xiong
,
ACS Photonics
7
,
919
(
2020
).
38.
W. M.
Takele
,
F.
Wackenhut
,
L.
Piatkowski
,
A. J.
Meixner
, and
J.
Waluk
,
J. Phys. Chem. B
124
,
5709
(
2020
).
39.
F. J.
Hernández
and
F.
Herrera
,
J. Chem. Phys.
151
,
144116
(
2019
).
40.
J. D.
Erwin
,
M.
Smotzer
, and
J. V.
Coe
,
J. Phys. Chem. B
123
,
1302
(
2019
).
41.
I.
Imran
,
G. E.
Nicolai
,
N. D.
Stavinski
, and
J. R.
Sparks
,
ACS Photonics
6
,
2405
(
2019
).
42.
S.
Kéna-Cohen
and
J.
Yuen-Zhou
,
ACS Cent. Sci.
5
,
386
(
2019
).
43.
R. F.
Ribeiro
,
A. D.
Dunkelberger
,
B.
Xiang
,
W.
Xiong
,
B. S.
Simpkins
,
J. C.
Owrutsky
, and
J.
Yuen-Zhou
,
J. Phys. Chem. Lett.
9
,
3766
(
2018
).
44.
B.
Xiang
,
R. F.
Ribeiro
,
L.
Chen
,
J.
Wang
,
M.
Du
,
J.
Yuen-Zhou
, and
W.
Xiong
,
J. Phys. Chem. A
123
,
5918
(
2019
).
45.
A.
Shalabney
,
J.
George
,
J.
Hutchison
,
G.
Pupillo
,
C.
Genet
, and
T. W.
Ebbesen
,
Nat. Commun.
6
,
5981
(
2015
).
46.
J. A.
Hutchison
,
T.
Schwartz
,
C.
Genet
,
E.
Devaux
, and
T. W.
Ebbesen
,
Angew. Chem., Int. Ed. Engl.
51
,
1592
(
2012
).
47.
B.
Metzger
,
E.
Muller
,
J.
Nishida
,
B.
Pollard
,
M.
Hentschel
, and
M. B.
Raschke
,
Phys. Rev. Lett.
123
,
153001
(
2019
).
48.
K.-D.
Park
,
M. A.
May
,
H.
Leng
,
J.
Wang
,
J. A.
Kropp
,
T.
Gougousi
,
M.
Pelton
, and
M. B.
Raschke
,
Sci. Adv.
5
,
eaav5931
(
2019
).
49.
O. S.
Ojambati
,
R.
Chikkaraddy
,
W. D.
Deacon
,
M.
Horton
,
D.
Kos
,
V. A.
Turek
,
U. F.
Keyser
, and
J. J.
Baumberg
,
Nat. Commun.
10
,
1049
(
2019
).
50.
R.
Chikkaraddy
,
B.
de Nijs
,
F.
Benz
,
S. J.
Barrow
,
O. A.
Scherman
,
E.
Rosta
,
A.
Demetriadou
,
P.
Fox
,
O.
Hess
, and
J. J.
Baumberg
,
Nature
535
,
127
(
2016
).
51.
E. T.
Jaynes
and
F. W.
Cummings
,
Proc. IEEE
51
,
89
(
1963
).
52.
M.
Tavis
and
F. W.
Cummings
,
Phys. Rev.
170
,
379
(
1968
).
53.
H.
Deng
,
H.
Haug
, and
Y.
Yamamoto
,
Rev. Mod. Phys.
82
,
1489
(
2010
).
54.
G.
Khitrova
,
H. M.
Gibbs
,
F.
Jahnke
,
M.
Kira
, and
S. W.
Koch
,
Rev. Mod. Phys.
71
,
1591
(
1999
).
55.
R.
Houdré
,
R. P.
Stanley
, and
M.
Ilegems
,
Phys. Rev. A
53
,
2711
(
1996
).
56.
T.
Botzung
,
D.
Hagenmüller
,
S.
Schütz
,
J.
Dubail
,
G.
Pupillo
, and
J.
Schachenmayer
,
Phys. Rev. B
102
,
144202
(
2020
).
57.
L.
Zhang
,
R.
Gogna
,
W.
Burg
,
E.
Tutuc
, and
H.
Deng
,
Nat. Commun.
9
,
713
(
2018
).
58.
J. M.
Anna
,
C. R.
Baiz
,
M. R.
Ross
,
R.
McCanne
, and
K. J.
Kubarych
,
Int. Rev. Phys. Chem.
31
,
367
(
2012
).
59.
I.
Noda
,
A. E.
Dowrey
, and
C.
Marcott
,
Appl. Spectrosc.
47
,
1317
(
1993
).
60.
W.
Xiong
,
J. E.
Laaser
,
P.
Paoprasert
,
R. A.
Franking
,
R. J.
Hamers
,
P.
Gopalan
, and
M. T.
Zanni
,
J. Am. Chem. Soc.
131
,
18040
(
2009
).
61.
T. M.
Porter
,
J.
Wang
,
Y.
Li
,
B.
Xiang
,
C.
Salsman
,
J. S.
Miller
,
W.
Xiong
, and
C. P.
Kubiak
,
Chem. Sci.
10
,
113
(
2019
).
62.
L. E.
Buchanan
and
W.
Xiong
,
Encycl. Mod. Opt.
2018
,
164
183
.
63.
P.
Hamm
and
M.
Zanni
,
Concepts and Methods of 2D Infrared Spectroscopy
(
Cambridge University Press
,
2011
).
64.
65.
S. K.
Karthick Kumar
,
A.
Tamimi
, and
M. D.
Fayer
,
J. Chem. Phys.
137
,
184201
(
2012
).
66.
D. J.
Hoffman
,
S. M.
Fica-Contreras
, and
M. D.
Fayer
,
J. Chem. Phys.
150
,
124507
(
2019
).
67.
S.-H.
Shim
and
M. T.
Zanni
,
Phys. Chem. Chem. Phys.
11
,
748
(
2009
).
68.
B.
Xiang
,
J.
Wang
,
Z.
Yang
, and
W.
Xiong
,
Sci. Adv.
7
,
eabf6397
(
2021
).
69.
A. B.
Grafton
,
A. D.
Dunkelberger
,
B. S.
Simpkins
,
J. F.
Triana
,
F. J.
Hernández
,
F.
Herrera
, and
J. C.
Owrutsky
,
Nat. Commun.
12
,
214
(
2021
).
70.
J. A.
Campos-Gonzalez-Angulo
,
R. F.
Ribeiro
, and
J.
Yuen Zhou
, “
Generalization of the Tavis-Cummings model for multi-level anharmonic systems
,”
New J. Phys.
(to be published) (
2021
).
71.
G.
Muñoz-Matutano
,
A.
Wood
,
M.
Johnsson
,
X.
Vidal
,
B. Q.
Baragiola
,
A.
Reinhard
,
A.
Lemaître
,
J.
Bloch
,
A.
Amo
,
G.
Nogues
,
B.
Besga
,
M.
Richard
, and
T.
Volz
,
Nat. Mater.
18
,
213
(
2019
).
72.
A.
Delteil
,
T.
Fink
,
A.
Schade
,
S.
Höfling
,
C.
Schneider
, and
A.
İmamoğlu
,
Nat. Mater.
18
,
219
(
2019
).
73.
T.
Yagafarov
,
D.
Sannikov
,
A.
Zasedatelev
,
K.
Georgiou
,
A.
Baranikov
,
O.
Kyriienko
,
I.
Shelykh
,
L.
Gai
,
Z.
Shen
,
D.
Lidzey
, and
P.
Lagoudakis
,
Commun. Phys.
3
,
18
(
2020
).
74.
C. A.
DelPo
,
B.
Kudisch
,
K. H.
Park
,
S.-U.-Z.
Khan
,
F.
Fassioli
,
D.
Fausti
,
B. P.
Rand
, and
G. D.
Scholes
,
J. Phys. Chem. Lett.
11
,
2667
(
2020
).
75.
S. M.
Arrivo
,
T. P.
Dougherty
,
W. T.
Grubbs
, and
E. J.
Heilweil
,
Chem. Phys. Lett.
235
,
247
(
1995
).
76.
T. E.
Li
,
A.
Nitzan
, and
J. E.
Subotnik
, “
Collective vibrational strong coupling effects on molecular vibrational relaxation and energy transfer: Numerical insights via cavity molecular dynamics simulations
,”
Angew. Chemie Int. Ed.
(published online) (
2021
).
77.
M. L.
Brongersma
,
N. J.
Halas
, and
P.
Nordlander
,
Nat. Nanotechnol.
10
,
25
(
2015
).
78.
A.
Sanders
,
R. W.
Bowman
,
L.
Zhang
,
V.
Turek
,
D. O.
Sigle
,
A.
Lombardi
,
L.
Weller
, and
J. J.
Baumberg
,
Appl. Phys. Lett.
109
,
153110
(
2016
).
79.
D.
Yoo
,
F.
de León-Pérez
,
M.
Pelton
,
I.-H.
Lee
,
D. A.
Mohr
,
M. B.
Raschke
,
J. D.
Caldwell
,
L.
Martín-Moreno
, and
S.-H.
Oh
,
Nat. Photonics
15
,
125
(
2021
).
80.
Z. T.
Brawley
,
S. D.
Storm
,
D. A.
Contreras Mora
,
M.
Pelton
, and
M.
Sheldon
,
J. Chem. Phys.
154
,
104305
(
2021
).
81.
G.
Hu
,
Q.
Ou
,
G.
Si
,
Y.
Wu
,
J.
Wu
,
Z.
Dai
,
A.
Krasnok
,
Y.
Mazor
,
Q.
Zhang
,
Q.
Bao
,
C.-W.
Qiu
, and
A.
Alù
,
Nature
582
,
209
(
2020
).
82.
P.
Li
,
G.
Hu
,
I.
Dolado
,
M.
Tymchenko
,
C.-W.
Qiu
,
F. J.
Alfaro-Mozaz
,
F.
Casanova
,
L. E.
Hueso
,
S.
Liu
,
J. H.
Edgar
,
S.
Vélez
,
A.
Alu
, and
R.
Hillenbrand
,
Nat. Commun.
11
,
3663
(
2020
).