Chemistry under Vibrational Strong Coupling

Bound polariton states in the Dicke-Ising model

We present a study of hybrid light-matter excitations in cavity QED materials using the Dicke-Ising model as a theoretical framework. Leveraging linear response theory, we derive the exact excitations of the system in the thermodynamic limit. Our results demonstrate that the cavity can localize spin excitations, leading to the formation of bound polaritons, where the cavity acts as an impurity of the two-excitation band, localizing spin-wave pairs around single-spin domains. We derive the condition for the existence of these bound states and discuss its satisfiability in different regimes. Finally, we show that these effects persist in finite systems using exact-diagonalization calculations.

Mechanisms of Temperature Control of Singlet Fission in an Optical Cavity

We investigate the mechanisms of temperature control in conical-intersection-mediated singlet fission (SF) within optical cavities. Using the multiple Davydov D2 Ansatz combined with the thermo-field dynamics formalism, we model the quantum dynamics of a rubrene dimer coupled to an optical cavity at finite temperatures. The work explores the influence of temperature, cavity-matter coupling strength, photon frequency, and cavity loss on the triplet-triplet population dynamics. Results reveal that temperature enhances SF efficiency via thermal activation of coupling modes and assists in overcoming potential barriers between singlet and triplet states. It is found that strong photon-matter coupling and high photon frequencies also promote SF under conditions of resonance with excited vibronic states, while cavity losses and increased photon numbers can inhibit the process. Increased average photon numbers suppress SF as the polaritonic conical intersections shift away from the Franck-Condon region, although a photon-assisted SF effect is revealed for specific values of the average photon number at low temperatures. The study provides insights into the temperature control mechanisms of SF in optical cavities, offering potential directions for designing functional optical cavities to enhance SF efficiency, with implications for organic photovoltaics and other energy transfer technologies.

Comment on "Non-Polaritonic Effects in Cavity-Modified Photochemistry": On the Importance of Experimental Details

Recently, an article by Barnes and co-workers reported an in-depth experimental re-evaluation of the earlier work on photoisomerization reactions inside optical cavities under conditions of strong light-matter coupling. That earlier work, which constituted the first demonstration of 'polaritonic chemistry', associated cavity-induced modifications of photoisomerization rates with the emergence of strong light-matter coupling (and the formation of polaritonic states). Barnes and co-workers instead found that cavity-induced changes in light absorption can account for changes in the photochemical reaction rates. While Barnes and co-workers correctly highlight the importance of controlling irradiation conditions from sample to sample where optical cavities are involved, this comment aims to emphasize the great length the original study went to ensure exactly this. The original experimental methods are summarized to point out the significant differences between them and those conducted by Barnes and co-workers. Furthermore, the importance of monochromatic photoexcitation at an isosbestic point rather than using broadband (UV through to IR) irradiation, as well as the careful control for photon flux reaching the molecular layer in all samples, as per the original work, is discussed. Further examination of important issues facing this new and developing domain of Physical Chemistry, is anticipated.

Polariton-induced Purcell effects via a reduced semiclassical electrodynamics approach

Recent experiments have demonstrated that polariton formation provides a novel strategy for modifying local molecular processes when a large ensemble of molecules is confined within an optical cavity. Herein, a numerical strategy based on coupled Maxwell-Schrödinger equations is examined for simulating local molecular processes in a realistic cavity structure under collective strong coupling. In this approach, only a few molecules, referred to as quantum impurities, are treated quantum mechanically, while the remaining macroscopic molecular layer and the cavity structure are modeled using dielectric functions. When a single electronic two-level system embedded in a Lorentz medium is confined in a two-dimensional Bragg resonator, our numerical simulations reveal a polariton-induced Purcell effect: the radiative decay rate of the quantum impurity is significantly enhanced by the cavity when the impurity frequency matches the polariton frequency, while the rate can sometimes be greatly suppressed when the impurity is near resonance with the bulk molecules forming strong coupling. In addition, this approach demonstrates that the cavity absorption of light exhibits Rabi-splitting-dependent suppression due to the inclusion of a realistic cavity structure. Our simulations also identify a fundamental limitation of this approach-an inaccurate description of polariton dephasing rates into dark modes. This arises because the dark-mode degrees of freedom are not explicitly included when most molecules are modeled using simple dielectric functions. As the polariton-induced Purcell effect alters molecular radiative decay differently from the Purcell effect under weak coupling, this polariton-induced effect may facilitate understanding the origin of polariton-modified photochemistry under electronic strong coupling.

Unlocking delocalization: how much coupling strength is required to overcome energy disorder in molecular polaritons?

Polaritons, quasiparticles formed from the collective strong coupling of light and matter, have been shown for their capability to modify chemical reactions, energy and charge transport - amazing features that can revolutionize the way we control molecular properties. Many of these features originate from the delocalization of polaritons, i.e., polaritons possess delocalized wavefunctions, which is one of their hallmarks. Furthermore, polariton delocalization has long been assumed to be robust against disorder that is ubiquitous in chemical systems, without being fully checked. Herein, we examined the criteria to ensure delocalization in molecular polaritons, and this study reveals that transition energy disorder destroys delocalization of polaritons. In order to mitigate the impact of disorder and restore delocalization, the collective coupling strength needs to exceed four times the standard deviation of the energy disorder linewidth. This observation indicates a more stringent criterion for preserving the unique delocalization characteristics of polaritons compared to the conventionally adopted standard (Rabi splitting larger than photonic and molecular spectral linewidths). This work sheds light on previous polariton dynamic studies performed by our group and others, explaining why the onset of Rabi splitting capable of modifying dynamics is bigger than the strong coupling criteria, and it provides an important threshold to reach polariton delocalization for chemical and material research under strong coupling.

Unveiling the Dance of Molecules: Rovibrational Dynamics of Molecules under Intense Illumination at Complex Plasmonic Interfaces

Understanding the quantum dynamics of strongly coupled molecule-cavity systems remains a significant challenge in molecular polaritonics. This work develops a comprehensive self-consistent model simulating electromagnetic interactions of diatomic molecules with quantum rovibrational degrees of freedom in resonant optical cavities. The approach employs an efficient numerical methodology to solve coupled Schrödinger-Maxwell equations in real spacetime, enabling three-dimensional simulations through a novel molecular mapping technique. The study investigates the relaxation dynamics of an ensemble of molecules following intense resonant pump excitation in Fabry-Perot cavities and at three-dimensional plasmonic metasurfaces. The simulations reveal dramatically modified relaxation pathways inside cavities compared to free space, characterized by persistent molecular alignment arising from cavity-induced rotational pumping. They also indicate the presence of a previously unreported relaxation stabilization mechanism driven by dephasing of the collective molecular-cavity mode. Additionally, the study demonstrates that strong molecular coupling significantly modifies the circular dichroism spectra of chiral metasurfaces, suggesting new opportunities for controlling light-matter interactions in quantum optical systems.

Leaky Coupled Waveguide-Plasmon Modes for Enhanced Light-Matter Interaction

Plasmon waveguide resonances (PWRs) have been widely used to enhance the interaction between light and matter. PWRs have been used for chemical and biological sensing, molecular detection, and boosting other optical phenomena, such as Raman scattering and fluorescence. However, the performances of plasmon-waveguide-based structures have been investigated in the angular interrogation mode, and their potential in different spectral regions has hardly been explored. Moreover, the applications of PWRs have been limited to the weak light-matter coupling regime. In this study, we investigate leaky coupled waveguide plasmon resonances (LCWPRs) and explore their potential to enhance light-matter interaction in different spectral regions. In the weak coupling regime, we demonstrate the potential of LCWPRs for sensing in the near-IR region by detecting heavy water (D2O) and ethanol in water. The experimental results show spectral sensitivity of 15.2 nm/% and 1.41 nm/% for ethanol and D2O detection, respectively. Additionally, we show that LCWPRs can be used to achieve vibrational strong coupling (VSC) with organic molecules in the mid-IR region. We numerically show that the coupling between LCWPRs and the C=O stretching vibration of hexanal yields a Rabi splitting of 210 cm-1, putting the system in the VSC regime. We anticipate that LCWPRs will be a promising platform for enhanced spectroscopy, sensing, and strong coupling.

Chemistry Meets Plasmon Polaritons and Cavity Photons: A Perspective from Macroscopic Quantum Electrodynamics

The interaction between light and molecules under quantum electrodynamics (QED) has long been less emphasized in physical chemistry, as semiclassical theories have dominated due to their relative simplicity. Recent experimental advances in polariton chemistry highlight the need for a theoretical framework that transcends traditional cavity QED and molecular QED models. Macroscopic QED is presented as a unified framework that seamlessly incorporates infinite photonic modes and dielectric environments, enabling applications to systems involving plasmon polaritons and cavity photons. This Perspective demonstrates the applicability of macroscopic QED to chemical phenomena through breakthroughs in molecular fluorescence, resonance energy transfer, and electron transfer. The macroscopic QED framework not only resolves the limitations of classical theories in physical chemistry but also achieves parameter-free predictions of experimental results, bridging quantum optics and material science. By addressing theoretical bottlenecks and unveiling new mechanisms, macroscopic QED establishes itself as an indispensable tool for studying QED effects on chemical systems.

Ab initio study on the dynamics and spectroscopy of collective rovibrational polaritons

Accurate rovibrational molecular models are employed to gain insight in high-resolution into the collective effects and intermolecular processes arising when molecules in the gas phase interact with a resonant infrared (IR) radiation mode. An efficient theoretical approach is detailed, and numerical results are presented for the HCl, H2O, and CH4 molecules confined in an IR cavity. It is shown that by employing a rotationally resolved model for the molecules, revealing the various cavity-mediated interactions between the field-free molecular eigenstates, it is possible to obtain a detailed understanding of the physical processes governing the energy level structure, absorption spectra, and dynamic behavior of the confined systems. Collective effects, arising due to the cavity-mediated interaction between molecules, are identified in energy level shifts, in intensity borrowing effects in the absorption spectra, and in the intermolecular energy transfer occurring during Hermitian or non-Hermitian time propagation.

Molecular Assembly in Optical Cavities

Chemistry has traditionally focused on the synthesis of desired compounds, with organic synthesis being a key method for obtaining target molecules. In contrast, self-assembly -where molecules spontaneously organize into well-defined structures- has emerged as a powerful tool for fabricating intricate structures. Self-assembly was initially studied in biological systems but has been developed for synthetic methods, leading to the field of supramolecular chemistry, where non-covalent interactions/bonds guide molecular assembly. This has led to the development of complex molecular structures, such as metal-organic frameworks and hydrogen-bonded organic frameworks. Parallel to this field, cavity quantum electrodynamics (QED), developed in the mid-20th century, has recently intersected with molecular assembly. Early research in cavity strong coupling focused on inorganic solids and simple molecules, but has since extended to molecular assemblies. The strong coupling synergized with molecular assembly will generate new polaritonic phenomena and applications.

Analytical derivative approaches for vibro-polaritonic structures and properties. I. Formalism and implementation

Vibro-polaritons are hybrid light-matter states that arise from the strong coupling between the molecular vibrational transitions and the photons in an optical cavity. Developing theoretical and computational methods to describe and predict the unique properties of vibro-polaritons is of great significance for guiding the design of new materials and experiments. Here, we present the ab initio cavity Born-Oppenheimer density functional theory (CBO-DFT) and formulate the analytic energy gradient and Hessian as well as the nuclear and photonic derivatives of dipole and polarizability within the framework of CBO-DFT to efficiently calculate the harmonic vibrational frequencies, infrared absorption, and Raman scattering spectra of vibro-polaritons as well as to explore the critical points on the cavity potential energy surface. The implementation of analytic derivatives into the electronic structure package is validated by a comparison with the finite-difference method and with other reported computational results. By adopting appropriate exchange-correlation functionals, CBO-DFT can better describe the structure and properties of molecules in the cavity than CBO-Hartree-Fock method. It is expected that CBO-DFT is a useful tool for studying the polaritonic structures and properties.

Chiral polaritonics: cavity-mediated enantioselective excitation condensation

Separation of the two mirror images of a chiral molecule, the enantiomers, is a historically complicated problem of major relevance for biological systems. Since chiral molecules are optically active, it has been speculated that strong coupling to circularly polarized fields may be used as a general procedure to unlock enantiospecific reactions. In this work, we focus on how chiral cavities can be used to drive asymmetry in the photochemistry of chiral molecular systems. We first show that strong coupling to circularly polarized fields leads to enantiospecific Rabi splittings, an effect that displays a collective behavior in line with other strong coupling phenomena. Additionally, entanglement with circularly polarized light generates an asymmetry in the enantiomer population of the polaritons, leading to a condensation of the excitation on a preferred molecular configuration. These results confirm that chiral cavities represent a tantalizing opportunity to drive asymmetric photochemistry in enantiomeric mixtures.

Photon-mediated energy transfer between molecules and atoms in a cavity: A numerical study

The molecular energy transfer is crucial for many different physicochemical processes. The efficiency of traditional resonance energy transfer relies on dipole-dipole distance between molecules and becomes negligible when the distance is larger than ∼10 nm, which is difficult to overcome. Cavity polariton, formed when placing molecules inside the cavity, is a promising way to surmount the distance limit. By hybridizing a two-level atom (TLA) and a lithium fluoride (LiF) molecule with a cavity, we numerically simulate the reaction process and the energy transfer between them. Our results show that the TLA can induce a deep potential well, which can be seen as a replica of the potential energy surface of bare LiF, acting as a reservoir to absorb/release the molecular kinetic energy. In addition, the energy transfer shows a molecular nuclear kinetic energy dependent behavior, namely, more nuclear kinetic energy igniting more energy transfer. These findings show us a promising way to manipulate the energy transfer process within the cavity using an intentional TLA, which can also serve as a knob to control the reaction process.

Vibrational strong coupling of organic molecules embedded within graphene plasmon nanocavities facilitated by perfect absorbers

The strong coupling between infrared photonic resonances and vibrational transitions of organic molecules is called vibrational strong coupling (VSC), which presents attractive prospects for modifying molecular chemical characteristics and behaviors. Currently, VSC studies suffer from limited bandwidth or enormous mode volumes. In addition, in certain instances, the absorption spectrum of VSC is weaker, thus impeding the effective monitoring of the VSC effect. Here, we theoretically study the VSC effect by embedding 5-nm-thick organic molecules into a graphene plasmon nanocavity (GPNC). Pronounced anti-crossing characteristics with Rabi splitting exceeding 80 cm-1 are disclosed from the spectra of the coupled molecular system, benefiting from the ultra-small mode volume provided by the GPNC. Further assembling the GPNC into a perfect absorber configuration can significantly enhance the spectral peaks of the VSC effect, thus maximizing the reachability of the VSC phenomenon. Furthermore, the tunability of graphene enables monitoring of spectral changes by electrically adjusting graphene's Fermi level in a structure with fixed geometric parameters. In addition, we establish an analytical framework in alignment with computational simulations to elucidate the triggering criteria for the VSC mode, thereby giving a clear picture for understanding the physical processes that form the VSC mode. Given that graphene supports plasmon modes across an extensive range extending from infrared to terahertz, the suggested GPNC presents a suitable framework for investigating the VSC effect of diverse organic materials.

Revisiting cavity-coupled 2DIR: A classical approach implicates reservoir modes

Significant debate surrounds the origin of nonlinear optical responses from cavity-coupled molecular vibrations. Several groups, including our own, have previously assigned portions of the nonlinear response to polariton excited-state transitions. Here, we report a new method to approximate two-dimensional infrared spectra under vibrational strong coupling, which properly accounts for inhomogeneous broadening. We find excellent agreement between this model and experimental results for prototypical systems exhibiting both homogeneous and inhomogeneous broadening. This work implies that reservoir excitation is solely responsible for all optical response measured after the polariton modes dephase and represents an important new method for predicting and interpreting the nonlinear optical response of molecular vibrational polaritons.

Theory of molecular emission power spectra. III. Non-Hermitian interactions in multichromophoric systems coupled with polaritons

Based on our previous study [Wang et al., J. Chem. Phys. 153, 184102 (2020)], we generalize the theory of molecular emission power spectra (EPS) from one molecule to multichromophoric systems in the framework of macroscopic quantum electrodynamics. This generalized theory is applicable to ensembles of molecules, providing a comprehensive description of the molecular spontaneous emission spectrum in arbitrary inhomogeneous, dispersive, and absorbing media. In the far-field region, the analytical formula of EPS can be expressed as the product of a lineshape function (LF) and an electromagnetic environment factor (EEF). To demonstrate the polaritonic effect on multichromophoric systems, we simulate the LF and EEF for one to three molecules weakly coupled to surface plasmon polaritons above a silver surface. Our analytical expressions show that the peak broadening originates from not only the spontaneous emission rates but also the imaginary part of resonant dipole-dipole interactions (non-Hermitian interactions), which is associated with the superradiance of molecular aggregates, indicating that the superradiance rate can be controlled through an intermolecular distance and the design of dielectric environments. This study presents an alternative approach to directly analyze the hybrid-state dynamics of multichromophoric systems coupled with polaritons.

Cavity-enhanced superconductivity in MgB2 from first-principles quantum electrodynamics (QEDFT)

Strong laser pulses can control superconductivity, inducing nonequilibrium transient pairing by leveraging strong-light matter interaction. Here, we demonstrate theoretically that equilibrium ground-state phonon-mediated superconductive pairing can be affected through the vacuum fluctuating electromagnetic field in a cavity. Using the recently developed ab initio quantum electrodynamical density-functional theory approximation, we specifically investigate the phonon-mediated superconductive behavior of MgB[Formula: see text] under different cavity setups and find that in the strong light-matter coupling regime its superconducting transition temperature T[Formula: see text] can be enhanced at most by [Formula: see text]10% in an in-plane (or out-of-plane) polarized and realistic cavity via photon vacuum fluctuations. The results highlight that strong light-matter coupling in extended systems can profoundly alter material properties in a nonperturbative way by modifying their electronic structure and phononic dispersion at the same time. Our findings indicate a pathway to the experimental realization of light-controlled superconductivity in solid-state materials at equilibrium via cavity materials engineering.

Measuring Kinetics under Vibrational Strong Coupling: Testing for a Change in the Nucleophilicity of Water and Alcohols

Vibrational Strong Coupling (VSC) has been reported to change the rate of organic reactions. However, a lack of convenient and reliable methods to measure reaction kinetics under VSC makes it challenging to obtain mechanistic insight into its influence, hindering progress in the field. Here, we use recently developed fixed-width optical cavities to obtain large kinetic datasets under VSC with small errors (±1-5 %) in an operationally simple manner using UV/Vis spectroscopy. The setup is used to test whether VSC changes a fundamental kinetic property of polar reactions, nucleophilicity, for water and alcohols, species commonly used in VSC-modified chemistry. We determined the rate constants for nucleophilic capture with a library of benzhydrilium ions as reference electrophiles with and without strong coupling of the nucleophile's key vibrations. For all investigated combinations of electrophiles and nucleophiles, only minor changes in the observed rate constants of the reactions were observed independently of the coupled bands. These results indicate that VSC does not substantially alter the nucleophilicity of water and alcohols, suggesting that polar reactions are modified through other, presently unknown mechanisms. Fixed-width cavities allow for convenient and reproducible UV/Vis kinetics, facilitating mechanistic studies of VSC-modified chemistry.

Polaritonic Chemistry Enabled by Non-Local Metasurfaces

Vibrational strong coupling can modify chemical reaction pathways in unconventional ways. Thus far, Fabry-Perot cavities formed by pairs of facing mirrors have been mostly utilized to achieve vibrational strong coupling. In this study, we demonstrate the application of non-local metasurfaces that can sustain surface lattice resonances, enabling chemical reactions under vibrational strong coupling. We show that the solvolysis kinetics of para-nitrophenyl acetate can be accelerated by a factor of 2.7 by strong coupling to the carbonyl bond of the solvent and the solute with a surface lattice resonance. Our work introduces a new platform to investigate polaritonic chemical reactions. In contrast to Fabry-Perot cavities, metasurfaces define open optical cavities with single surfaces, which removes alignment hurdles, facilitating polaritonic chemistry across large areas.

General theory of cavity-mediated interactions between low-energy matter excitations

The manipulation of low-energy matter properties such as superconductivity, ferromagnetism, and ferroelectricity via cavity quantum electrodynamics engineering has been suggested as a way to enhance these many-body collective phenomena. In this work, we investigate the effective interactions between low-energy matter excitations induced by the off-resonant coupling with cavity electromagnetic modes. We extend a previous work by going beyond the dipole approximation accounting for the full polarization and magnetization densities of matter. We further include the often neglected diamagnetic interaction and, for the cavity, we consider general linear absorbing media with possibly non-local and non-reciprocal response. We demonstrate that, even in this general scenario, the effective cavity-induced interactions between the matter degrees of freedom are of electrostatic and magnetostatic nature. This confirms the necessity of a multimode description for cavity engineering of matter systems where the low-energy assumption holds. Our findings provide a theoretical framework for studying the influence of general optical environments on extended low-energy matter excitations.

Cavity induced modulation of intramolecular vibrational energy flow pathways

Recent experiments in polariton chemistry indicate that reaction rates can be significantly enhanced or suppressed inside an optical cavity. One possible explanation for the rate modulation involves the cavity mode altering the intramolecular vibrational energy redistribution (IVR) pathways by coupling to specific molecular vibrations in the vibrational strong coupling (VSC) regime. However, the mechanism for such a cavity-mediated modulation of IVR is yet to be understood. In a recent study, Ahn et al. [Science 380, 1165 (2023)] observed that the rate of alcoholysis of phenyl isocyanate (PHI) is considerably suppressed when the cavity mode is tuned to be resonant with the isocyanate (NCO) stretching mode of PHI. Here, we analyze the quantum and classical IVR dynamics of a model effective Hamiltonian for PHI involving the high-frequency NCO-stretch mode and two of the key low-frequency phenyl ring modes. We compute various indicators of the extent of IVR in the cavity-molecule system and show that tuning the cavity frequency to the NCO-stretching mode strongly perturbs the cavity-free IVR pathways. Subsequent IVR dynamics involving the cavity and the molecular anharmonic resonances lead to efficient scrambling of an initial NCO-stretching overtone state over the molecular quantum number space. We also show that the hybrid light-matter states of the effective Hamiltonian undergo a localization-delocalization transition in the VSC regime.

Spectroscopic properties under vibrational strong coupling in disordered matter from path-integral Monte Carlo simulations

Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli-Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis-Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.

Role of cavity strong coupling on single electron transfer reaction rate at electrode-electrolyte interface

The physicochemical properties of molecules can be modulated through polariton formation under strong electromagnetic confinement. Here, we discuss the possibility of exploiting this phenomenon to increase the electron transfer rate at an electrode-electrolyte interface. Electron transfer theory under strong electromagnetic confinement can be extended to the electrode-electrolyte interface, and single-electron transfer reactions can be simulated using Gerischer's theory. Although single electron transfer in free space is well described using Marcus theory, the vacuum electric field can facilitate an additional electron transfer pathway via virtual photon excitation under cavity strong coupling conditions. Therefore, this binary reaction pathway for single electron transfer can yield a quasi-two-particle electron transfer process. This quantum behavior can dominate when the mode volume is small and when there are a large number of molecules in the vacuum electric field. Exploitation of polaritons in single electron transfer reactions can lead to enhanced electrochemical energy conversion systems.

Ultrastrong coupling between molecular vibrations in water and surface lattice resonances

We investigate the vibrational ultrastrong coupling between molecular vibrations of water molecules and surface lattice resonances (SLRs) sustained by extended arrays of plasmonic microparticles. We design and fabricate an array of gold bowties, which sustain a very high field enhancement, with its SLR resonated with the OH stretching modes of water. We measure a Rabi splitting of 567 cm-1 in the strongly coupled system, whose coupling strength is 8% of the OH vibrational energy, at the onset of the ultrastrong coupling regime (10%). These results introduce metallic microparticle arrays as a platform for the investigation of ultrastrong coupling, which could be used in polaritonic chemistry to modify the dynamics of chemical reactions that require high coupling strengths.

Diagrams in Polaritonic Coupled Cluster Theory

We present a diagrammatic notation to derive the quantum-electrodynamic coupled cluster (QED-CC) equations needed for the description for polaritonic ground and excited states. Our presented notation is a generalization of the existing diagrammatic notation of standard electronic coupled-cluster theory. It is used to derive the QED-CC and QED-EOM-CC equations for the QED-CCSD-1-SD and QED-CCSD-12-SD truncation schemes. Furthermore, we present the diagrams for the CC Λ-equations and reduced density matrices which are needed for the calculation of molecular properties.

Impact of Surface Enhanced Raman Spectroscopy in Catalysis

Catalysis stands as an indispensable cornerstone of modern society, underpinning the production of over 80% of manufactured goods and driving over 90% of industrial chemical processes. As the demand for more efficient and sustainable processes grows, better catalysts are needed. Understanding the working principles of catalysts is key, and over the last 50 years, surface-enhanced Raman Spectroscopy (SERS) has become essential. Discovered in 1974, SERS has evolved into a mature and powerful analytical tool, transforming the way in which we detect molecules across disciplines. In catalysis, SERS has enabled insights into dynamic surface phenomena, facilitating the monitoring of the catalyst structure, adsorbate interactions, and reaction kinetics at very high spatial and temporal resolutions. This review explores the achievements as well as the future potential of SERS in the field of catalysis and energy conversion, thereby highlighting its role in advancing these critical areas of research.

Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling

Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate the role of complementary nonresonant electron-photon interactions in the cavity Born-Oppenheimer (CBO) approximation. In particular, we study cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [E. W. Fischer and P. Saalfrank, J. Chem. Theory Comput. 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock (HF) and coupled cluster (CC) theories. In a first step, we derive up to second-order CBO-PT cavity potential energy surfaces, which reveal non-trivial intra- and inter-molecular corrections induced by the cavity. We then introduce the concept of a cavity reaction potential (CRP), minimizing the electronic energy in the cavity subspace to discuss vibro-polaritonic reaction mechanisms. We present reformulations of CBO-HF and CBO-CC approaches for CRPs and derive second-order approximate CRPs from CBO-PT for unimolecular and bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular potential energy surfaces for selected isomerization reactions dominantly captured by the first-order dipole fluctuation correction. Excellent agreement between CBO-PT and non-perturbative wave function results indicates minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced dipole and van der Waals interactions with enhanced long-range character. An illustrative CBO-coupled cluster theory with singles and doubles-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC.

Microfluidics and Nanofluidics in Strong Light-Matter Coupling Systems

The combination of micro- or nanofluidics and strong light-matter coupling has gained much interest in the past decade, which has led to the development of advanced systems and devices with numerous potential applications in different fields, such as chemistry, biosensing, and material science. Strong light-matter coupling is achieved by placing a dipole (e.g., an atom or a molecule) into a confined electromagnetic field, with molecular transitions being in resonance with the field and the coupling strength exceeding the average dissipation rate. Despite intense research and encouraging results in this field, some challenges still need to be overcome, related to the fabrication of nano- and microscale optical cavities, stability, scaling up and production, sensitivity, signal-to-noise ratio, and real-time control and monitoring. The goal of this paper is to summarize recent developments in micro- and nanofluidic systems employing strong light-matter coupling. An overview of various methods and techniques used to achieve strong light-matter coupling in micro- or nanofluidic systems is presented, preceded by a brief outline of the fundamentals of strong light-matter coupling and optofluidics operating in the strong coupling regime. The potential applications of these integrated systems in sensing, optofluidics, and quantum technologies are explored. The challenges and prospects in this rapidly developing field are discussed.

Non-equilibrium rate theory for polariton relaxation dynamics

We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

Equilibrium Parametric Amplification in Raman-Cavity Hybrids

Parametric resonances and amplification have led to extraordinary photoinduced phenomena in pump-probe experiments. While these phenomena manifest themselves in out-of-equilibrium settings, here, we present the striking result of parametric amplification in equilibrium. We demonstrate that quantum and thermal fluctuations of a Raman-active mode amplifies light inside a cavity, at equilibrium, when the Raman mode frequency is twice the cavity mode frequency. This noise-driven amplification leads to the creation of an unusual parametric Raman polariton, intertwining the Raman mode with cavity squeezing fluctuations, with smoking gun signatures in Raman spectroscopy. In the resonant regime, we show the emergence of not only quantum light amplification but also localization and static shift of the Raman mode. Apart from the fundamental interest of equilibrium parametric amplification, our Letter suggests a resonant mechanism for controlling Raman modes and thus matter properties by cavity fluctuations. We conclude by outlining how to compute the Raman-cavity coupling, and suggest possible experimental realizations.

More than just smoke and mirrors: Gas-phase polaritons for optical control of chemistry

Gas-phase molecules are a promising platform to elucidate the mechanisms of action and scope of polaritons for optical control of chemistry. Polaritons arise from the strong coupling of a dipole-allowed molecular transition with the photonic mode of an optical cavity. There is mounting evidence of modified reactivity under polaritonic conditions; however, the complex condensed-phase environment of most experimental demonstrations impedes mechanistic understanding of this phenomenon. While the gas phase was the playground of early efforts in atomic cavity quantum electrodynamics, we have only recently demonstrated the formation of molecular polaritons under these conditions. Studying the reactivity of isolated gas-phase molecules under strong coupling would eliminate solvent interactions and enable quantum state resolution of reaction progress. In this Perspective, we contextualize recent gas-phase efforts in the field of polariton chemistry and offer a practical guide for experimental design moving forward.

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.

Wide-Dynamic-Range Control of Quantum-Electrodynamic Electron Transfer Reactions in the Weak Coupling Regime

Catalyzing reactions effectively by vacuum fluctuations of electromagnetic fields is a significant challenge within the realm of chemistry. As opposed to most studies based on vibrational strong coupling, we introduce an innovative catalytic mechanism driven by weakly coupled polaritonic fields. Through the amalgamation of macroscopic quantum electrodynamics (QED) principles with Marcus electron transfer (ET) theory, we predict that ET reaction rates can be precisely modulated across a wide dynamic range by controlling the size and structure of nanocavities. Compared to QED-driven radiative ET rates in free space, plasmonic cavities induce substantial rate enhancements spanning the range from 103- to 10-fold. By contrast, Fabry-Perot cavities engender rate suppression spanning the range from 10-2- to 10-1-fold. This work overcomes the necessity of using strong light-matter interactions in QED chemistry, opening up a new era of manipulating QED-based chemical reactions in a wide dynamic range.

Surface-Enhanced Infrared Absorption Spectroscopy by Resonant Vibrational Coupling with Plasmonic Metal Oxide Nanocrystals

Coupling between plasmonic resonances and molecular vibrations in nanocrystals (NCs) offers a promising approach for detecting molecules at low concentrations and discerning their chemical identities. Metallic NC superlattices can enhance vibrational signals under far-field detection by generating a myriad of intensified electric field hot spots between the NCs. Yet, their effectiveness is limited by the fixed electron concentration dictated by the metal composition and inefficient hot spot creation due to the large mode volume. Doped metal oxide NCs, such as tin-doped indium oxide (ITO), could overcome these limitations by enabling broad tunability of resonance frequencies in the mid-infrared range through independent variation of size and doping concentration. This study investigates the potential of close-packed ITO NC monolayers for surface-enhanced infrared absorption by quantifying trends in the coupling between their plasmon modes and various molecular vibrations. We show that maximum vibrational signal intensity occurs in monolayers composed of larger, more highly doped NCs, where the plasmon resonance peak lies at higher frequency than the molecular vibration. Using finite element and mutual polarization methods, we establish that near-field enhancement is stronger on the low-frequency side of the plasmon resonance and for more strongly coupled plasmonic NCs, thus rationalizing the design rules we experimentally uncovered. Our results can guide the development of optimal metal oxide NC-based superstructures for sensing target molecules or modifying their chemical properties through vibrational coupling.

Dark State Concentration Dependent Emission and Dynamics of CdSe Nanoplatelet Exciton-Polaritons

The recent surge of interest in polaritons has prompted fundamental questions about the role of dark states in strong light-matter coupling phenomena. Here, we systematically vary the relative number of dark states by controlling the number of stacked CdSe nanoplatelets confined in a Fabry-Pérot cavity. We find the emission spectrum to change significantly with an increasing number of nanoplatelets, with a gradual shift of the dominant emission intensity from the lower polariton branch to a manifold of dark states. Through accompanying calculations based on a kinetic model, this shift is rationalized by an entropic trapping of excitations by the dark state manifold, while a weak dark state dispersion due to local disorder explains their nonzero emission. Our results point toward the relevance of the dark state concentration to the optical and dynamical properties of cavity-embedded quantum emitters with ramifications for Bose-Einstein condensate formation, polariton lasing, polariton-based quantum transduction schemes, and polariton chemistry.

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.

Extraordinary Electrical Conductance through Amorphous Nonconducting Polymers under Vibrational Strong Coupling

Enhancing the electrical conductance through amorphous nondoped polymers is challenging. Here, we show that vibrational strong coupling (VSC) of intrinsically nonconducting and amorphous polymers such as polystyrene, deuterated polystyrene, and poly(benzyl methacrylate) to the vacuum electromagnetic field of the cavity enhances the electrical conductivity by at least 6 orders of magnitude compared to the uncoupled polymers. Remarkably, the observed extraordinary conductance is vibrational mode selective and occurs only under the VSC of the aromatic C-H(D) out-of-plane bending modes of the polymers. The conductance is thermally activated at the onset of strong coupling and becomes temperature-independent as the collective strong coupling strength increases. The electrical characterizations are performed without external light excitation, demonstrating the role of vacuum electromagnetic field-matter strong coupling in enhancing long-range transport even in amorphous nonconducting polymers.

Insights into the mechanisms of optical cavity-modified ground-state chemical reactions

In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.

Direct Observation of Polaritonic Chemistry by Nuclear Magnetic Resonance Spectroscopy

Polaritonic chemistry is emerging as a powerful approach to modifying the properties and reactivity of molecules and materials. However, probing how the electronics and dynamics of molecular systems change under strong coupling has been challenging due to the narrow range of spectroscopic techniques that can be applied in situ. Here we develop microfluidic optical cavities for vibrational strong coupling (VSC) that are compatible with nuclear magnetic resonance (NMR) spectroscopy using standard liquid NMR tubes. VSC is shown to influence the equilibrium between two conformations of a molecular balance sensitive to London dispersion forces, revealing an apparent change in the equilibrium constant under VSC. In all compounds studied, VSC does not induce detectable changes in chemical shifts, J-couplings, or spin-lattice relaxation times. This unexpected finding indicates that VSC does not substantially affect molecular electron density distributions, and in turn has profound implications for the possible mechanisms at play in polaritonic chemistry under VSC and suggests that the emergence of collective behavior is critical.

Resonance theory of vibrational polariton chemistry at the normal incidence

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.

Investigating the collective nature of cavity-modified chemical kinetics under vibrational strong coupling

In this paper, we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models, we demonstrate how reactivity in the collective VSC regime does not exhibit altered rate behavior in equilibrium but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied, which demand further scrutiny.

Hybrid architectures for terahertz molecular polaritonics

Atoms and their different arrangements into molecules are nature's building blocks. In a regime of strong coupling, matter hybridizes with light to modify physical and chemical properties, hence creating new building blocks that can be used for avant-garde technologies. However, this regime relies on the strong confinement of the optical field, which is technically challenging to achieve, especially at terahertz frequencies in the far-infrared region. Here we demonstrate several schemes of electromagnetic field confinement aimed at facilitating the collective coupling of a localized terahertz photonic mode to molecular vibrations. We observe an enhanced vacuum Rabi splitting of 200 GHz from a hybrid cavity architecture consisting of a plasmonic metasurface, coupled to glucose, and interfaced with a planar mirror. This enhanced light-matter interaction is found to emerge from the modified intracavity field of the cavity, leading to an enhanced zero-point electric field amplitude. Our study provides key insight into the design of polaritonic platforms with organic molecules to harvest the unique properties of hybrid light-matter states.

Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus, collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

Consequences of Vibrational Strong Coupling on Supramolecular Polymerization of Porphyrins

Supramolecular polymers display interesting optoelectronic properties and, thus, deploy multiple applications based on their molecular arrangement. However, controlling supramolecular interactions to achieve a desirable molecular organization is not straightforward. Over the past decade, light-matter strong coupling has emerged as a new tool for modifying chemical and material properties. This novel approach has also been shown to alter the morphology of supramolecular organization by coupling the vibrational bands of solute and solvent to the optical modes of a Fabry-Perot cavity (vibrational strong coupling, VSC). Here, we study the effect of VSC on the supramolecular polymerization of chiral zinc-porphyrins (S-Zn) via a cooperative effect. Electronic circular dichroism (ECD) measurements indicate that the elongation temperature (Te) of the supramolecular polymerization is lowered by ∼10 °C under VSC. We have also generalized this effect by exploring other supramolecular systems under strong coupling conditions. The results indicate that the solute-solvent interactions are modified under VSC, which destabilizes the nuclei of the supramolecular polymer at higher temperatures. These findings demonstrate that the VSC can indeed be used as a tool to control the energy landscape of supramolecular polymerization. Furthermore, we use this unique approach to switch between the states formed under ON- and OFF-resonance conditions, achieved by simply tuning the optical cavity in and out of resonance.

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.

Resonating with Cellular Pathways: Transcriptome Insights into Nonthermal Bioeffects of Middle Infrared Light Stimulation and Vibrational Strong Coupling on Cell Proliferation and Migration

Middle infrared stimulation (MIRS) and vibrational strong coupling (VSC) have been separately applied to physically regulate biological systems but scarcely compared with each other, especially at identical vibrational frequencies, though they both involve resonant mechanism. Taking cell proliferation and migration as typical cell-level models, herein, we comparatively studied the nonthermal bioeffects of MIRS and VSC with selecting the identical frequency (53.5 THz) of the carbonyl vibration. We found that both MIRS and VSC can notably increase the proliferation rate and migration capacity of fibroblasts. Transcriptome sequencing results reflected the differential expression of genes related to the corresponding cellular pathways. This work not only sheds light on the synergistic nonthermal bioeffects from the molecular level to the cell level but also provides new evidence and insights for modifying bioreactions, further applying MIRS and VSC to the future medicine of frequencies.

Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities

It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

Generalized Born-Huang expansion under macroscopic quantum electrodynamics framework

Born-Huang expansion is the cornerstone for studying potential energy surfaces and non-adiabatic couplings (NACs) in molecular systems. However, the traditional approach is insufficient to describe the molecular system, which strongly interacts with quantum light. Inspired by the work by Schäfer et al., we develop the generalized Born-Huang expansion theory within a macroscopic quantum electrodynamics (QED) framework. The theory we present allows us to describe electromagnetic vacuum fluctuations in dielectric media and incorporate the effects of dressed photons (or polaritons) into NACs. With the help of the generalized Born-Huang expansion, we clearly classify electronic nuclear NACs, polaritonic nuclear NACs, and polaritonic electronic NACs. Furthermore, to demonstrate the advantage of the macroscopic QED framework, we estimate polaritonic electronic NACs without any free parameter, such as the effective mode volume, and demonstrate the distance dependence of the polaritonic electronic NACs in a silver planar system. In addition, we take a hydrogen atom in free space as an example and derive spontaneous emission rates from photonic electronic NACs (polaritonic electronic NACs are reduced to photonic electronic NACs). We believe that this work not only provides an avenue for the theoretical exploration of NACs in a nucleus-electron-polariton coupled system but also offers a more comprehensive understanding for molecules coupled with quantum light.

Controlling Molecular Photoisomerization in Photonic Cavities through Polariton Funneling

Strong coupling between photonic modes and molecular electronic excitations, creating hybrid light-matter states called polaritons, is an attractive avenue for controlling chemical reactions. Nevertheless, experimental demonstrations of polariton-modified chemical reactions remain sparse. Here, we demonstrate modified photoisomerization kinetics of merocyanine and diarylethene by coupling the reactant's optical transition with photonic microcavity modes. We leverage broadband Fourier-plane optical microscopy to noninvasively and rapidly monitor photoisomerization within microcavities, enabling systematic investigation of chemical kinetics for different cavity-exciton detunings and photoexcitation conditions. We demonstrate three distinct effects of cavity coupling: first, a renormalization of the photonic density of states, akin to a Purcell effect, leads to enhanced absorption and isomerization rates at certain wavelengths, notably red-shifting the onset of photoisomerization. This effect is present under both strong and weak light-matter couplings. Second, kinetic competition between polariton localization into reactive molecular states and cavity losses leads to a suppression of the photoisomerization yield. Finally, our key result is that in reaction mixtures with multiple reactant isomers, exhibiting partially overlapping optical transitions and distinct isomerization pathways, the cavity resonance can be tuned to funnel photoexcitations into specific reactant isomers. Thus, upon decoherence, polaritons localize into a chosen isomer, selectively triggering the latter's photoisomerization despite initially being delocalized across all isomers. This result suggests that careful tuning of the cavity resonance is a promising avenue to steer chemical reactions and enhance product selectivity in reaction mixtures.