Vibrational Polaritons Research Articles

A second-order kinetic model for global analysis of vibrational polariton dynamics.

The interaction between cavity photons and molecular vibrations leads to the formation of vibrational polaritons, which have demonstrated the ability to influence chemical reactivity and change material characteristics. Although ultrafast spectroscopy has been extensively applied to study vibrational polaritons, the nonlinear relationship between signal and quantum state population complicates the analysis of their kinetics. Here, we employ a second-order kinetic model and transform matrix method (TMM) to develop an effective model to capture the nonlinear relationship between the two-dimensional IR (or pump-probe) signal and excited state populations. We test this method on two types of kinetics: a sequential relaxation from the second to the first excited states of dark modes, and a Raman state relaxing into the first excited state. By globally fitting the simulated data, we demonstrate accurate extraction of relaxation rates and the ability to identify intermediate species by comparing the species spectra with theoretical ground truth, validating our method. This study demonstrates the efficacy of a second-order TMM approximation in capturing essential spectral features with up to 10% excited state population, simplifying global analysis and enabling straightforward extraction of kinetic parameters, thus empowering our methodology in understanding excited-state dynamics in polariton systems.

Quantum nature of reactivity modification in vibrational polariton chemistry.

In this work, we present a mixed quantum-classical open quantum system dynamics method for studying rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. In this approach, the cavity radiation mode is treated classically with a mean-field nuclear force averaging over the remaining degrees of freedom, both within the system and the environment, which are handled quantum mechanically within the hierarchical equations of motion framework. Using this approach, we conduct a comparative analysis by juxtaposing the mixed quantum-classical results with fully quantum-mechanical simulations. After eliminating spurious peaks that can occur when not using the rigorous definition of the rate constant, we confirm the crucial role of the quantum nature of the cavity radiation mode in reproducing the resonant peak observed in the cavity frequency-dependent rate profile. In other words, it appears necessary to explicitly consider the quantized photonic states in studying reactivity modification in vibrational polariton chemistry (at least for the model systems studied in this work), as these phenomena stem from cavity-induced reaction pathways involving resonant energy exchanges between photons and molecular vibrational transitions.

Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling.

Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-Pérot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-Pérot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as an analytic theory, i.e., incorporating many cavity modes with varying in-plane wave vectors (k∥) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single-mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with the nearest neighbor k∥. The procedure for numerically approaching the macroscopic limit is also demonstrated with CavMD by increasing the system size. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.

Spatially Resolved Near Field Spectroscopy of Vibrational Polaritons at the Small N Limit.

Vibrational polaritons, which have been primarily studied in Fabry-Pérot cavities with a large number of molecules (N ∼ 106-1010) coupled to the resonator mode, exhibit various experimentally observed effects on chemical reactions. However, the exact mechanism is elusively understood from the theoretical side, as the large number of molecules involved in an experimental strong coupling condition cannot be represented completely in simulations. This discrepancy between theory and experiment arises from computational descriptions of polariton systems typically being limited to only a few molecules, thus failing to represent the experimental conditions adequately. To address this mismatch, we used surface phonon polariton (SPhP) resonators as an alternative platform for vibrational strong coupling. SPhPs exhibit strong electromagnetic confinement on the surface and thus allow for coupling to a small number of molecules. As a result, this platform can enhance nonlinearity and slow down relaxation to the dark modes. In this study, we fabricated a pillar-shaped quartz resonator and then coated it with a thin layer of cobalt phthalocyanine (CoPc). By employing scattering-type scanning near-field optical microscopy (s-SNOM), we spatially investigated the dependency of vibrational strong coupling on the spatially varying electromagnetic field strength and demonstrated strong coupling with 38,000 molecules only-reaching to the small N limit. Through s-SNOM analysis, we found that strong coupling was observed primarily on the edge of the quartz pillar and the apex of the s-SNOM tip, where the maximum field enhancement occurs. In contrast, a weak resonance signal and lack of coupling were observed closer to the center of the pillar. This work demonstrates the importance of spatially resolved polariton systems in nanophotonic platforms and lays a foundation to explore polariton chemistry and chemical dynamics at the small N limit-one step closer to reconcile with high-level quantum calculations.

Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System.

The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.

Ultrafast Spectroscopy under Vibrational Strong Coupling in Diphenylphosphoryl Azide.

Strong coupling of cavity photons and molecular vibrations creates vibrational polaritons that have been shown to modify chemical reactivity and alter material properties. While ultrafast spectroscopy of vibrational polaritons has been performed intensively in metal complexes, ultrafast dynamics in vibrationally strongly coupled organic molecules remain unexplored. Here, we report ultrafast pump-probe measurement and two-dimensional infrared spectroscopy in diphenylphosphoryl azide under vibrational strong coupling. Early time oscillatory structures indicate coherent energy exchange between the two polariton modes, which decays in ∼2 ps. We observe a large transient absorptive feature around the lower polariton, which can be explained by the overlapped excited-state absorption and derivative-shaped structures around the lower and upper polaritons. The latter feature is explained by the Rabi splitting contraction, which is ascribed to a reduced population in the ground state. These results reassure the previously reported spectroscopic theory to describe nonlinear spectroscopy of vibrational polaritons. We have also noticed the influence of the complicated layer structure of the cavity mirrors. The penetration of the electric field distribution into the layered structure of the dielectric-mirror cavities can significantly affect the Rabi splitting and the decay time constant of polaritonic systems.

Molecular Polaritons for Chemistry, Photonics and Quantum Technologies.

Molecular polaritons are quasiparticles resulting from the hybridization between molecular and photonic modes. These composite entities, bearing characteristics inherited from both constituents, exhibit modified energy levels and wave functions, thereby capturing the attention of chemists in the past decade. The potential to modify chemical reactions has spurred many investigations, alongside efforts to enhance and manipulate optical responses for photonic and quantum applications. This Review centers on the experimental advances in this burgeoning field. Commencing with an introduction of the fundamentals, including theoretical foundations and various cavity architectures, we discuss outcomes of polariton-modified chemical reactions. Furthermore, we navigate through the ongoing debates and uncertainties surrounding the underpinning mechanism of this innovative method of controlling chemistry. Emphasis is placed on gaining a comprehensive understanding of the energy dynamics of molecular polaritons, in particular, vibrational molecular polaritons─a pivotal facet in steering chemical reactions. Additionally, we discuss the unique capability of coherent two-dimensional spectroscopy to dissect polariton and dark mode dynamics, offering insights into the critical components within the cavity that alter chemical reactions. We further expand to the potential utility of molecular polaritons in quantum applications as well as precise manipulation of molecular and photonic polarizations, notably in the context of chiral phenomena. This discussion aspires to ignite deeper curiosity and engagement in revealing the physics underpinning polariton-modified molecular properties, and a broad fascination with harnessing photonic environments to control chemistry.

Resonance theory of vibrational polariton chemistry at the normal incidence

Abstract We present a theory that explains the resonance effect of the vibrational strong coupling (VSC) modified reaction rate constant at the normal incidence of a Fabry–Pérot (FP) cavity. This analytic theory is based on a mechanistic hypothesis that cavity modes promote the transition from the ground state to the vibrational excited state of the reactant, which is the rate-limiting step of the reaction. This mechanism for a single molecule coupled to a single-mode cavity has been confirmed by numerically exact simulations in our recent work in [J. Chem. Phys. 159, 084104 (2023)]. Using Fermi’s golden rule (FGR), we formulate this rate constant for many molecules coupled to many cavity modes inside a FP microcavity. The theory provides a possible explanation for the resonance condition of the observed VSC effect and a plausible explanation of why only at the normal incident angle there is the resonance effect, whereas, for an oblique incidence, there is no apparent VSC effect for the rate constant even though both cases generate Rabi splitting and forming polariton states. On the other hand, the current theory cannot explain the collective effect when a large number of molecules are collectively coupled to the cavity, and future work is required to build a complete microscopic theory to explain all observed phenomena in VSC.

A Quantum Chemistry Approach to Linear Vibro-Polaritonic Infrared Spectra with Perturbative Electron-Photon Correlation.

In the vibrational strong coupling (VSC) regime, molecular vibrations and resonant low-frequency cavity modes form light-matter hybrid states, vibrational polaritons, with characteristic infrared (IR) spectroscopic signatures. Here, we introduce a molecular quantum chemistry-based computational scheme for linear IR spectra of vibrational polaritons in polyatomic molecules, which perturbatively accounts for nonresonant electron-photon interactions under VSC. Specifically, we formulate a cavity Born-Oppenheimer perturbation theory (CBO-PT) linear response approach, which provides an approximate but systematic description of such electron-photon correlation effects in VSC scenarios while relying on molecular ab initio quantum chemistry methods. We identify relevant electron-photon correlation effects at the second order of CBO-PT, which manifest as static polarizability-dependent Hessian corrections and an emerging polarizability-dependent cavity intensity component providing access to transmission spectra commonly measured in vibro-polaritonic chemistry. Illustratively, we address electron-photon correlation effects perturbatively in IR spectra of CO2 and Fe(CO)5 vibro-polaritonic models in sound agreement with nonperturbative CBO linear response theory.

Probing the anharmonicity of vibrational polaritons with double-quantum two-dimensional infrared spectroscopy

Abstract Strong coupling between the molecular vibrations and electromagnetic fields of light confined to an infrared cavity leads to the formation of vibro-polaritons – quasi-particles thought to provide the means to control the rates of chemical reactions inside a dark cavity. Despite the mechanisms indicating how vibrational coupling to the vacuum fields can affect the reaction rates are still not well understood, it has been recently demonstrated that the formation of the polariton states alters the ultrafast relaxation dynamics of the strongly coupled system. The relaxation dynamics in molecules, which is known to be important for the chemical reactivity, is directed by anharmonic couplings involving multiple intra- and inter-molecular vibrational degrees of freedom. However, the impact of the molecular anharmonicity on the polariton states remains elusive. Some theoretical models, employed to interpret the experimental observations, assume that vibrational polaritons are harmonic. Others assume a certain anharmonicity of vibro-polaritons; however, to date, it has not been experimentally determined. Herein, we performed double-quantum two-dimensional third-order nonlinear infrared spectroscopy of the carbonyl stretching (C=O) vibrational modes in a thin film of polymethyl methacrylate polymer (PMMA) strongly coupled to the surface lattice resonances of the periodic arrays of half-wavelength infrared disk antennas. We found that, indeed, the mechanical anharmonicity of polaritons is very small. Quantitatively, our results place an upper bound on a polariton mechanical anharmonicity of 2 cm−1, compared with that of the C=O mode in a PMMA film of 15 cm−1. Thus, our results support previous assumptions regarding the harmonic character of vibro-polaritons.

Coherent state switching using vibrational polaritons in an asymmetric double-well potential.

The quantum dynamics of vibrational polaritonic states arising from the interaction of a bistable molecule with the quantized mode of a Fabry-Perot microcavity is investigated using a generic asymmetric double-well potential as a simplified one-dimensional model of a reactive molecule. After discussing the role of the light-matter coupling strength in the emergence of avoided crossings between polaritonic states, we investigate the possibility of using these crossings to trigger a dynamical switching of these states from one potential well to the other. Two schemes are proposed to achieve this coherent state switching, either by preparing the molecule in an appropriate vibrational excited state before inserting it into the cavity, or by applying a short laser pulse inside the cavity to obtain a coherent superposition of polaritonic states. The respective influences of dipole moment amplitude and potential asymmetry on the coherent switching process are also discussed.

Piezoelectric and microfluidic tuning of an infrared cavity for vibrational polariton studies.

We developed a microfluidic system for vibrational polariton studies, which consists of two microfluidic chips: one for solution mixing and another for tuning an infrared cavity made of a pair of gold mirrors and a PDMS (polydimethylsiloxane) spacer. We show that the cavity of the system can be accurately tuned with either piezoelectric actuators or microflow-induced pressure to result in resonant coupling between a cavity mode and a variational mode of the solution molecules. Acrylonitrile solutions were chosen to prove the concept of vabriational strong coupling (VSC) of a CN stretching mode with light inside the cavity. We also show that the Rabi splitting energy is linearly proportional to the square root of molecular concentration, thereby proving the relevance and reliability of the system for VSC studies.

Ab Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems.

Recent experiments have revealed the profound effect of strong light-matter interactions in optical cavities on the electronic ground state of molecular systems. This phenomenon, known as vibrational strong coupling, can modify reaction rates and induce the formation of molecular vibrational polaritons, hybrid states involving both photon modes, and vibrational modes of molecules. We present an ab initio methodology based on the cavity Born-Oppenheimer Hartree-Fock ansatz, which is specifically powerful for ensembles of molecules, to calculate vibro-polaritonic IR spectra. This method allows for a comprehensive analysis of these hybrid states. Our semiclassical approach, validated against full quantum simulations, reproduces key features of the vibro-polaritonic spectra. The underlying analytic gradients also allow for optimization of cavity-coupled molecular systems and performing semiclassical dynamics simulations.

Resonance Enhancement of Vibrational Polariton Chemistry Obtained from the Mixed Quantum-Classical Dynamics Simulations.

We applied a variety of mixed quantum-classical (MQC) approaches to simulate the VSC-influenced reaction rate constant. All of these MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other degrees of freedom (DOFs) are treated inside the classical subsystem. We find that, as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition when the cavity frequency matches the bond vibrational frequency. This correct resonance behavior can be obtained regardless of the detailed MQC methods that one uses. The results suggest that the MQC approaches can generate semiquantitative agreement with the exact results for rate constant changes when changing the cavity frequency, the light-matter coupling strength, or the cavity lifetime. The finding of this work suggests that one can use computationally economic MQC approaches to explore the collective coupling scenario when many molecules are collectively coupled to many cavity modes in the future.

Ultrafast dynamics of CN radical reactions with chloroform solvent under vibrational strong coupling.

Polariton chemistry may provide a new means to control molecular reactivity, permitting remote, reversible modification of reaction energetics, kinetics, and product yields. A considerable body of experimental and theoretical work has already demonstrated that strong coupling between a molecular vibrational mode and the confined electromagnetic field of an optical cavity can alter chemical reactivity without external illumination. However, the mechanisms underlying cavity-altered chemistry remain unclear in large part because the experimental systems examined previously are too complex for detailed analysis of their reaction dynamics. Here, we experimentally investigate photolysis-induced reactions of cyanide radicals with strongly-coupled chloroform (CHCl3) solvent molecules and examine the intracavity rates of photofragment recombination, solvent complexation, and hydrogen abstraction. We use a microfluidic optical cavity fitted with dichroic mirrors to facilitate vibrational strong coupling (VSC) of the C-H stretching mode of CHCl3 while simultaneously permitting optical access at visible wavelengths. Ultrafast transient absorption experiments performed with cavities tuned on- and off-resonance reveal that VSC of the CHCl3 C-H stretching transition does not significantly modify any measured rate constants, including those associated with the hydrogen abstraction reaction. This work represents, to the best of our knowledge, the first experimental study of an elementary bimolecular reaction under VSC. We discuss how the conspicuous absence of cavity-altered effects in this system may provide insights into the mechanisms of modified ground state reactivity under VSC and help bridge the divide between experimental results and theoretical predictions in vibrational polariton chemistry.

Beyond Cavity Born-Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry.

The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation in effective ground state Hamiltonians. We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a vibrational strong coupling (VSC) Born-Huang expansion. We then derive nonadiabatic coupling elements arising from both "slow" nuclei and cavity modes compared to "fast" electrons via the generalized Hellmann-Feynman theorem, discuss their properties, and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. Those do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon correlation relative to the CBO ground state due to neglected cavity-induced nonadiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as a first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on nonadiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss the potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime.

Raman Probing the Local Ultrastrong Coupling of Vibrational Plasmon Polaritons on Metallic Gratings.

Strong coupling of molecular vibrations with light creates polariton states, enabling control over many optical and chemical properties. However, the near-field signatures of strong coupling are difficult to map as most cavities are closed systems. Surface-enhanced Raman microscopy of open metallic gratings under vibrational strong coupling enables the observation of spatial polariton localization in the grating near field, without the need for scanning probe microscopies. The lower polariton is localized at the grating slots, displays a strongly asymmetric line shape, and gives greater plasmon-vibration coupling strength than measured in the far field. Within these slots, the local field strength pushes the system into the ultrastrong coupling regime. Models of strong coupling which explicitly include the spatial distribution of emitters can account for these effects. Such gratings enable exploration of the rich physics of polaritons, its impact on polariton chemistry under flow conditions, and the interplay between near- and far-field properties through vibrational polariton-enhanced Raman scattering.

Spontaneous Raman scattering from vibrational polaritons is obscured by reservoir states.

Vibrational strong coupling results from the interaction between optically allowed molecular vibrational excitations and the resonant mode of an infrared cavity. Strong coupling leads to the formation of hybrid states, known as vibrational polaritons, which are readily observed in transmission measurements and a manifold of the reservoir states. In contrast, Raman spectroscopy of vibrational polaritons is elusive and has recently been the focus of both theoretical and experimental investigations. Because Raman measurements are frequently performed with high-numerical aperture excitation/collection optics, the angular dispersion of the strongly coupled system must be carefully considered. Herein, we experimentally investigated vibrational polaritons involving dispersive collective lattice resonances of infrared antenna arrays. Despite clear indications of the strong coupling to vibrational excitations in the transmission spectrum; we found that Raman spectra do not bear signatures of the polaritonic transitions. Detailed measurements indicate that the disappearance of the Raman signal is not due to the polariton dispersion in our samples. On the other hand, the Tavis-Cummings-Holstein model that we employed to interpret our results suggests that the ratio of the Raman transition strengths between the reservoir and the polariton states scales according to the number of strongly coupled molecules. Because the vibrational transitions are relatively weak, the number of molecules required to achieve strong coupling conditions is about 109 per unit cell of the array of infrared antennas. Therefore, the scaling predicted by the Tavis-Cummings-Holstein model can explain the absence of the polariton signatures in spontaneous Raman scattering experiments.

How Quantum is the Resonance Behavior in Vibrational Polariton Chemistry?

Recent experiments in polariton chemistry have demonstrated that reaction rates can be modified by vibrational strong coupling to an optical cavity mode. Importantly, this modification occurs only when the frequency of the cavity mode is tuned to closely match a molecular vibrational frequency. This sharp resonance behavior has proved to be difficult to capture theoretically. Only recently did Lindoy et al. [ Nat. Commun. 2023, 14, 2733] report the first instance of a sharp resonant effect in the cavity-modified rate simulated in a model system using exact quantum dynamics. We investigate the same model system with a different method, ring-polymer molecular dynamics (RPMD), which captures quantum statistics but treats dynamics classically. We find that RPMD does not reproduce this sharp resonant feature at the well frequency, and we discuss the implications of this finding for future studies of vibrational polariton chemistry.

Resonance theory and quantum dynamics simulations of vibrational polariton chemistry.

We present numerically exact quantum dynamics simulations using the hierarchical equation of motion approach to investigate the resonance enhancement of chemical reactions due to the vibrational strong coupling (VSC) in polariton chemistry. The results reveal that the cavity mode acts like a "rate-promoting vibrational mode" that enhances the ground state chemical reaction rate constant when the cavity mode frequency matches the vibrational transition frequency. The exact simulation predicts that the VSC-modified rate constant will change quadratically as the light-matter coupling strength increases. When changing the cavity lifetime from the lossy limit to the lossless limit, the numerically exact results predict that there will be a turnover of the rate constant. Based on the numerical observations, we present an analytic rate theory to explain the observed sharp resonance peak of the rate profile when tuning the cavity frequency to match the quantum transition frequency of the vibrational ground state to excited states. This rate theory further explains the origin of the broadening of the rate profile. The analytic rate theory agrees with the numerical results under the golden rule limit and the short cavity lifetime limit. To the best of our knowledge, this is the first analytic theory that is able to explain the sharp resonance behavior of the VSC-modified rate profile when coupling an adiabatic ground state chemical reaction to the cavity. We envision that both the numerical analysis and the analytic theory will offer invaluable theoretical insights into the fundamental mechanism of the VSC-induced rate constant modifications in polariton chemistry.