Polariton chemistry: controlling molecular dynamics with optical cavities

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Toward Polaritonic Molecular Orbitals for Large Molecular Systems

A comprehensive understanding of electron-photon correlation is essential for describing the reshaping of molecular orbitals in quantum electrodynamics (QED) environments. The strong coupling QED Hartree-Fock (SC-QED-HF) theory tackles these aspects by providing consistent molecular orbitals in the strong coupling regime. The previous implementation, however, has significant convergence issues that limit the applicability. In this work, we introduce two second-order algorithms that significantly reduce the computational requirements, thereby enhancing the modeling of large molecular systems in QED environments. Furthermore, the implementation will enable the development of correlated methods based on a reliable molecular orbital framework as well as multi-level methodologies able to model the inclusion of solvent effects in this kind of complex systems.

Quantized embedding approaches for collective strong coupling-Connecting ab initio and macroscopic QED to simple models in polaritonics

Collective light-matter interactions have been used to control chemistry and energy transfer, yet accessible approaches that combine ab initio methodology with large many-body quantum optical systems are missing due to the fast increase in computational cost for explicit simulations. We introduce an accessible ab initio quantum embedding concept for many-body quantum optical systems that allows us to treat the collective coupling of molecular many-body systems effectively in the spirit of macroscopic quantum electrodynamics while keeping the rigor of ab initio quantum chemistry for the molecular structure. Our approach fully includes the quantum fluctuations of the polaritonic field and yet remains much simpler and more intuitive than complex embedding approaches such as dynamical mean-field theory. We illustrate the underlying assumptions by comparison to the Tavis-Cummings model. The intuitive application of the quantized embedding approach and its transparent limitations offer a practical framework for the field of ab initio polaritonic chemistry to describe collective effects in realistic molecular ensembles.

Nanotechnology-Enabled PCR with Tunable Energy Dynamics

This Perspective elucidates the transformative impacts of advanced nanotechnology and dynamic energy systems on the polymer chain reaction (PCR), a cornerstone technique in biomedical research and diagnostic applications. Since its invention, the optimization of PCR-specifically its efficiency, specificity, cycling rate, and detection sensitivity-has been a focal point of scientific exploration. Our analysis spans the modulation of PCR from both material and energetic perspectives, emphasizing the intricate interplay between PCR components and externally added entities such as molecules, nanoparticles (NPs), and optical microcavities. We begin with a foundational overview of PCR, detailing the basic principles of PCR modulation through molecular additives to highlight material-level interactions. Then, we delve into how NPs, with their diverse material and surface properties, influence PCR through interface interactions and hydrothermal conduction, drawing parallels to molecular behaviors. Additionally, this Perspective ventures into the energetic regulation of PCR, examining the roles of electromagnetic radiation and optical resonators. We underscore the advanced capabilities of optical technologies in PCR regulation, characterized by their ultrafast, residue-free, and noninvasive nature, alongside label-free detection methods. Notably, optical resonators present a pioneering approach to control PCR processes even in the absence of light, targeting the often-overlooked water component in PCR. By integrating discussions on photocaging and vibrational strong coupling, this review presents innovative methods for the precise regulation of PCR processes, envisioning a new era of PCR technology that enhances both research and clinical diagnostics. The synergy between nanotechnological enhancements and energy dynamics not only enriches our understanding of PCR but also opens new avenues for developing rapid, accurate, and efficient PCR systems. We hope that this Perspective will inspire further innovations in PCR technology and guide the development of next-generation clinical detection instruments.

Modulating molecular plasmons in naphthalene via intermolecular interactions and strong light-matter coupling

We conducted a theoretical investigation on the modulation of plasmon-like resonances in naphthalene - the so-called molecular plasmons - through intermolecular interactions and strong light-matter coupling. The configuration interaction with single excitations (CIS) approach and its quantum electrodynamics extension (QED-CIS-1) are used to describe the molecular plasmon states under these interactions. We detail the effects of changing intermolecular distances of the naphthalene dimer and incorporating the naphthalene molecule into optical cavities, both allowing for precise control of naphthalene's plasmonic responses. Our results show significant shifts of the plasmon peak in the absorption spectra of naphthalene, depending on the spatial configuration of the dimer and cavity parameters such as polarization, frequency, and coupling strength. Further investigation of the naphthalene dimer in a cavity reveals a synergistic effect on the plasmon peak when the two types of interactions are combined. This research provides insights into the plasmonic behavior of simple polyacenes like naphthalene and opens up possibilities for plasmon modulation in more complex systems.

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.

Exact Ansatz of Fermion-Boson Systems for a Quantum Device

We present an exact Ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schrödinger equation (CSE), our approach guides a trial wave function to the ground state of any arbitrary mixed Hamiltonian by directly measuring residuals of the mixed CSE on a quantum device. Unlike density functional and coupled cluster theories applied to electron-phonon or electron-photon systems, the accuracy of our approach is not limited by the unknown exchange-correlation functional or the uncontrolled form of the exponential Ansatz. To test the performance of the method, we study the Tavis-Cummings model, commonly used in polaritonic quantum chemistry. Our results demonstrate that the CSE is a powerful tool in the development of quantum algorithms for solving general fermion-boson many-body problems.

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.

i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations

Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.

The orientation dependence of cavity-modified chemistry

Recent theoretical studies have explored how ultra-strong light-matter coupling can be used as a handle to control chemical transformations. Ab initio cavity quantum electrodynamics calculations demonstrate that large changes to reaction energies or barrier heights can be realized by coupling electronic degrees of freedom to vacuum fluctuations associated with an optical cavity mode, provided that large enough coupling strengths can be achieved. In many cases, the cavity effects display a pronounced orientational dependence. Here, we highlight the critical role that geometry relaxation can play in such studies. As an example, we consider a recent work [Pavošević et al., Nat. Commun. 14, 2766 (2023)] that explored the influence of an optical cavity on Diels-Alder cycloaddition reactions and reported large changes to reaction enthalpies and barrier heights, as well as the observation that changes in orientation can inhibit the reaction or select for one reaction product or another. Those calculations used fixed molecular geometries optimized in the absence of the cavity and fixed relative orientations of the molecules and the cavity mode polarization axis. Here, we show that when given a chance to relax in the presence of the cavity, the molecular species reorient in a way that eliminates the orientational dependence. Moreover, in this case, we find that qualitatively different conclusions regarding the impact of the cavity on the thermodynamics of the reaction can be drawn from calculations that consider relaxed vs unrelaxed molecular structures.

Cavity Controlled Upconversion in CdSe Nanoplatelet Polaritons

Exciton-polaritons provide a versatile platform for investigating quantum electrodynamics effects in chemical systems, such as polariton-altered chemical reactivity. However, using polaritons in chemical contexts will require a better understanding of their photophysical properties under ambient conditions, where chemistry is typically performed. Here, we used cavity quality factor to control strong light-matter interactions and in particular the excited state dynamics of colloidal CdSe nanoplatelets (NPLs) coupled to a Fabry-Pérot optical cavity. With increasing cavity quality factor, we observe significant population of the upper polariton (UP) state, exemplified by the rare observation of substantial UP photoluminescence (PL). Excitation of the lower polariton (LP) states results in upconverted PL emission from the UP branch due to efficient exchange of population between the LP, UP and the reservoir of dark states present in collectively coupled polaritonic systems. In addition, we measure time scales for polariton dynamics ∼100 ps, implying great potential for NPL based polariton systems to affect photochemical reaction rates. State-of-the-art quantum dynamical simulations show outstanding quantitative agreement with experiments, and thus provide important insight into polariton photophysical dynamics of collectively coupled nanocrystal-based systems. These findings represent a significant step toward the development of practical polariton photochemistry platforms.

Do Molecular Geometries Change Under Vibrational Strong Coupling?

As pioneering experiments have shown, strong coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H2O and H2O2 resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

cclib 2.0: An updated architecture for interoperable computational chemistry

Interoperability in computational chemistry is elusive, impeded by the independent development of software packages and idiosyncratic nature of their output files. The cclib library was introduced in 2006 as an attempt to improve this situation by providing a consistent interface to the results of various quantum chemistry programs. The shared API across programs enabled by cclib has allowed users to focus on results as opposed to output and to combine data from multiple programs or develop generic downstream tools. Initial development, however, did not anticipate the rapid progress of computational capabilities, novel methods, and new programs; nor did it foresee the growing need for customizability. Here, we recount this history and present cclib 2, focused on extensibility and modularity. We also introduce recent design pivots-the formalization of cclib's intermediate data representation as a tree-based structure, a new combinator-based parser organization, and parsed chemical properties as extensible objects.

Extending the Tavis-Cummings model for molecular ensembles-Exploring the effects of dipole self-energies and static dipole moments

Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.

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.

XPS Depth-Profiling Studies of Chlorophyll Binding to Poly(cysteine methacrylate) Scaffolds in Pigment-Polymer Antenna Complexes Using a Gas Cluster Ion Source

X-ray photoelectron spectroscopy (XPS) depth-profiling with an argon gas cluster ion source (GCIS) was used to characterize the spatial distribution of chlorophyll a (Chl) within a poly(cysteine methacrylate) (PCysMA) brush grown by surface-initiated atom-transfer radical polymerization (ATRP) from a planar surface. The organization of Chl is controlled by adjusting the brush grafting density and polymerization time. For dense brushes, the C, N, S elemental composition remains constant throughout the 36 nm brush layer until the underlying gold substrate is approached. However, for either reduced density brushes (mean thickness ∼20 nm) or mushrooms grown with reduced grafting densities (mean thickness 6-9 nm), elemental intensities decrease continuously throughout the brush layer, because photoelectrons are less strongly attenuated for such systems. For all brushes, the fraction of positively charged nitrogen atoms (N+/N0) decreases with increasing depth. Chl binding causes a marked reduction in N+/N0 within the brushes and produces a new feature at 398.1 eV in the N1s core-line spectrum assigned to tetrapyrrole ring nitrogen atoms coordinated to Zn2+. For all grafting densities, the N/S atomic ratio remains approximately constant as a function of brush depth, which indicates a uniform distribution of Chl throughout the brush layer. However, a larger fraction of repeat units bound to Chl is observed at lower grafting densities, reflecting a progressive reduction in steric congestion that enables more uniform distribution of the bulky Chl units throughout the brush layer. In summary, XPS depth-profiling using a GCIS is a powerful tool for characterization of these complex materials.

Origin of Exciton-Polariton Interactions and Decoupled Dark States Dynamics in 2D Hybrid Perovskite Quantum Wells

The realization of efficient optical devices depends on the ability to harness strong nonlinearities, which are challenging to achieve with standard photonic systems. Exciton-polaritons formed in hybrid organic-inorganic perovskites offer a promising alternative, exhibiting strong interactions at room temperature (RT). Despite recent demonstrations showcasing a robust nonlinear response, further progress is hindered by an incomplete understanding of the microscopic mechanisms governing polariton interactions in perovskite-based strongly coupled systems. Here, we investigate the nonlinear properties of quasi-2D dodecylammonium lead iodide perovskite (n3-C12) crystals embedded in a planar microcavity. Polarization-resolved pump-probe measurements reveal the contribution of indirect exchange interactions assisted by dark states formation. Additionally, we identify a strong dependence of the unique spin-dependent interaction of polaritons on sample detuning. The results are pivotal for the advancement of polaritonics, and the tunability of the robust spin-dependent anisotropic interaction in n3-C12 perovskites makes this material a powerful choice for the realization of polaritonic circuits.

Room-temperature strong coupling between CdSe nanoplatelets and a metal-DBR Fabry-Pérot cavity

The generation of exciton-polaritons through strong light-matter interactions represents an emerging platform for exploring quantum phenomena. A significant challenge in colloidal nanocrystal-based polaritonic systems is the ability to operate at room temperature with high fidelity. Here, we demonstrate the generation of room-temperature exciton-polaritons through the coupling of CdSe nanoplatelets (NPLs) with a Fabry-Pérot optical cavity, leading to a Rabi splitting of 74.6 meV. Quantum-classical calculations accurately predict the complex dynamics between the many dark state excitons and the optically allowed polariton states, including the experimentally observed lower polariton photoluminescence emission, and the concentration of photoluminescence intensities at higher in-plane momenta as the cavity becomes more negatively detuned. The Rabi splitting measured at 5 K is similar to that at 300 K, validating the feasibility of the temperature-independent operation of this polaritonic system. Overall, these results show that CdSe NPLs are an excellent material to facilitate the development of room-temperature quantum technologies.

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.

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.

General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.

Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description

The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.

Assessing the Determinants of Cavity Polariton Relaxation Using Angle-Resolved Photoluminescence Excitation Spectroscopy

The strong coupling of light and matter within electromagnetic resonators leads to the formation of cavity polaritons whose hybrid nature may help certain ground and excited state chemical processes. To help enable the development of polariton chemistry, we have developed and applied a spectroscopic technique to leverage the relatively larger spatial coherence of polaritons to assess the determinants of relaxation in hybrid light-matter states. By exciting the lower polariton (LP) state in cavity samples filled with different metalloporphyrin chromophores, we measured and modeled angle-resolved photoluminescence excitation spectra. Our results suggest that the shortest lived constituent of the LP state characterized by specific Hopfield coefficients limits the light absorption of the intracavity molecules, which we equate with the effective polariton lifetime. Our results suggest that researchers need to consider the lifetimes of both photons and excitons participating in strong light-matter coupling when designing polaritonic systems and the methods they can use to assess the relaxation of polaritonic states.

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.

Cavity Catalysis of an Enantioselective Reaction under Vibrational Strong Coupling

Strong light-matter interaction is emerging as an exciting tool for controlling chemical reactions. Here, we demonstrate an L-proline-catalyzed direct asymmetric Aldol reaction under vibrational strong coupling. Both the reactants (4-nitrobenzaldehyde and acetone) carbonyl bands are coupled to an infrared photon and react in the presence of L-proline. The reaction mixture is eluted from the cavity, and the conversion yields and enantiomeric excess are quantified using NMR and chiral HPLC. The conversion yields increase by up to 90 % in ON-resonance conditions. Interestingly, a large increase in the conversion yield does not affect the enantiomeric excess. Further control experiments were carried out by varying the temperature, and we propose that the rate-limiting step may not be the deciding factor in enantioselectivity. Whereas the formation of the enamine intermediate is modified by cavity coupling experiments. For this class of enantioselective reactions, strong coupling does not change the enantiomeric excess, possibly due to the large energy difference in chiral transition states. Strong coupling can boost the formation of enamine intermediate, thereby favouring the product yield. This gives more hope to test polaritonic chemistry based on enantioselective reactions in which the branching ratios can be controlled.

Impact of Cavity on Molecular Ionization Spectra

Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.

Formulation of transition dipole gradients for non-adiabatic dynamics with polaritonic states

A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham method. The light-matter interaction is included in the Jaynes-Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light-matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined.

Linear response of molecular polaritons

In this article, we show that the collective light-matter strong coupling regime where N molecular emitters couple to the photon mode of an optical cavity can be mapped to a quantum impurity model where the photon is the impurity that is coupled to a bath of anharmonic transitions. In the thermodynamic limit where N ≫ 1, we argue that the bath can be replaced with an effective harmonic bath, leading to a dramatic simplification of the problem into one of the coupled harmonic oscillators. We derive simple analytical expressions for linear optical spectra (transmission, reflection, and absorption) where the only molecular input required is the molecular linear susceptibility. This formalism is applied to a series of illustrative examples, showing the role of temperature, disorder, vibronic coupling, and optical saturation of the molecular ensemble, explaining that it is useful even when describing an important class of nonlinear optical experiments. For completeness, we provide Appendixes A-C that include a self-contained derivation of the relevant spectroscopic observables for arbitrary anharmonic systems (for both large and small N) within the rotating-wave approximation. While some of the presented results herein have already been reported in the literature, we provide a unified presentation of the results as well as new interpretations that connect powerful concepts in open quantum systems and linear response theory with molecular polaritonics.

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.

A 2D chiral microcavity based on apparent circular dichroism

Engineering asymmetric transmission between left-handed and right-handed circularly polarized light in planar Fabry-Pérot (FP) microcavities would enable a variety of chiral light-matter phenomena, with applications in spintronics, polaritonics, and chiral lasing. Such symmetry breaking, however, generally requires Faraday rotators or nanofabricated polarization-preserving mirrors. We present a simple solution requiring no nanofabrication to induce asymmetric transmission in FP microcavities, preserving low mode volumes by embedding organic thin films exhibiting apparent circular dichroism (ACD); an optical phenomenon based on 2D chirality. Importantly, ACD interactions are opposite for counter-propagating light. Consequently, we demonstrated asymmetric transmission of cavity modes over an order of magnitude larger than that of the isolated thin film. Through circular dichroism spectroscopy, Mueller matrix ellipsometry, and simulation using theoretical scattering matrix methods, we characterize the spatial, spectral, and angular chiroptical responses of this 2D chiral microcavity.

Microscopic theory of exciton-polariton model involving multiple molecules: Macroscopic quantum electrodynamics formulation and essence of direct intermolecular interactions

Cavity quantum electrodynamics (CQED) and its extensions are widely used for the description of exciton-polariton systems. However, the exciton-polariton models based on CQED vary greatly within different contexts. One of the most significant discrepancies among these CQED models is whether one should include direct intermolecular interactions in the CQED Hamiltonian. To answer this question, in this article, we derive an effective dissipative CQED model including free-space dipole-dipole interactions (CQED-DDI) from a microscopic Hamiltonian based on macroscopic quantum electrodynamics. Dissipative CQED-DDI successfully captures the nature of vacuum fluctuations in dielectric media and separates them into free-space effects and dielectric-induced effects. The former include spontaneous emissions, dephasings, and dipole-dipole interactions in free space; the latter include exciton-polariton interactions and photonic losses due to dielectric media. We apply dissipative CQED-DDI to investigate the exciton-polariton dynamics (the population dynamics of molecules above a plasmonic surface) and compare the results with those based on the methods proposed by several previous studies. We find that direct intermolecular interactions are a crucial element when employing CQED-like models to study exciton-polariton systems involving multiple molecules.

Theoretical formulation of chemical equilibrium under vibrational strong coupling

Experiments have suggested that strong interactions between molecular ensembles and infrared microcavities can be employed to control chemical equilibria. Nevertheless, the primary mechanism and key features of the effect remain largely unexplored. In this work, we develop a theory of chemical equilibrium in optical microcavities, which allows us to relate the equilibrium composition of a mixture in different electromagnetic environments. Our theory shows that in planar microcavities under strong coupling with polyatomic molecules, hybrid modes formed between all dipole-active vibrations and cavity resonances contribute to polariton-assisted chemical equilibrium shifts. To illustrate key aspects of our formalism, we explore a model SN2 reaction within a single-mode infrared resonator. Our findings reveal that chemical equilibria can be shifted towards either direction of a chemical reaction, depending on the oscillator strength and frequencies of reactant and product normal modes. Polariton-induced zero-point energy changes provide the dominant contributions, though the effects in idealized single-mode cavities tend to diminish quickly as the temperature and number of molecules increase. Our approach is valid in generic electromagnetic environments and paves the way for understanding and controlling chemical equilibria with microcavities.

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.

Motional Narrowing through Photonic Exchange: Rational Suppression of Excitonic Disorder from Molecular Cavity Polariton Formation

Maximizing the coherence between the constituents of molecular materials remains a crucial goal toward the implementation of these systems into everyday optoelectronic technologies. Here we experimentally assess the ability of strong light-matter coupling in the collective limit to reduce energetic disorder using porphyrin-based chromophores in Fabry-Pérot (FP) microresonator structures. Following characterization of cavity polaritons formed from chemically distinct porphyrin dimers, we find that the peaks corresponding to the lower polariton (LP) state in each sample do not possess widths consistent with conventional theories. We model the behavior of the polariton peak widths effectively using the results of spectroscopic theory. We correlate differences in the suppression of excitonic energetic disorder between our samples with microscopic light-matter interactions and propose that the suppression stems from photonic exchange. Our results demonstrate that cavity polariton formation can suppress disorder and show researchers how to design coherence into hybrid molecular material systems.

On the nature of two-photon transitions for a collection of molecules in a Fabry-Perot cavity

We investigate the effect of a cavity on nonlinear two-photon transitions of a molecular system and we analyze how such an effect depends on the cavity quality factor, the field enhancement, and the possibility of dephasing. We find that the molecular response to strong light fields in a cavity with a variable quality factor can be understood as arising from a balance between (i) the ability of the cavity to enhance the field of an external probe and promote multiphoton transitions more easily and (ii) the fact that the strict selection rules on multiphoton transitions in a cavity support only one resonant frequency within the excitation range. Although our simulations use a classical level description of the radiation field (i.e., we solve Maxwell-Bloch or Maxwell-Liouville equations within the Ehrenfest approximation for the field-molecule interaction), based on experience with this level of approximation in the past studies of plasmonic and polaritonic systems, we believe that our results are valid over a wide range of external probing.

Finite temperature dynamics of the Holstein-Tavis-Cummings model

By employing the numerically accurate multiple Davydov Ansatz (mDA) formalism in combination with the thermo-field dynamics (TFD) representation of quantum mechanics, we systematically explore the influence of three parameters-temperature, photonic-mode detuning, and qubit-phonon coupling-on population dynamics and absorption spectra of the Holstein-Tavis-Cummings (HTC) model. It is found that elevated qubit-phonon couplings and/or temperatures have a similar impact on all dynamic observables: they suppress the amplitudes of Rabi oscillations in photonic populations as well as broaden the peaks and decrease their intensities in the absorption spectra. Our results unequivocally demonstrate that the HTC dynamics is very sensitive to the concerted variation of the three aforementioned parameters, and this finding can be used for fine-tuning polaritonic transport. The developed mDA-TFD methodology can be efficiently applied for modeling, predicting, optimizing, and comprehensively understanding dynamic and spectroscopic responses of actual molecular systems in microcavities.

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.

Molecularly Detailed View of Strong Coupling in Supramolecular Plexcitonic Nanohybrids

Plexcitons constitute a peculiar example of light-matter hybrids (polaritons) originating from the (strong) coupling of plasmonic modes and molecular excitations. Here we propose a fully quantum approach to model plexcitonic systems and test it against existing experiments on peculiar hybrids formed by Au nanoparticles and a well-known porphyrin derivative, involving the Q branch of the organic dye absorption spectrum. Our model extends simpler descriptions of polaritonic systems to account for the multilevel structure of the dyes, spatially varying interactions with a given plasmon mode, and the simultaneous occurrence of plasmon-molecule and intermolecular interactions. By keeping a molecularly detailed view, we were able to gain insights into the local structure and individual contributions to the resulting plexcitons. Our model can be applied to rationalize and predict energy funneling toward specific molecular sites within a plexcitonic assembly, which is highly valuable for designing and controlling chemical transformations in the new polaritonic landscapes.

Collective Strong Coupling Modifies Aggregation and Solvation

Intermolecular (Coulombic) interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around a single perturbed molecule, thus representing an impurity in an otherwise ordered system. A competition between short-range coulombic and long-range photonic correlations inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Electromagnetic enhancement spectra of one-dimensional plasmonic hotspots along silver nanowire dimer derived via surface-enhanced fluorescence

We developed a spectroscopic method for directly obtaining the spectra of electromagnetic (EM) enhancement of plasmonic hotspots (HSs). The method was applied to one-dimensional (1D) HSs generated between silver nanowire (NW) dimers. The EM enhancement spectra were derived by dividing the spectra of surface-enhanced fluorescence (SEF) from single NW dimers with SEF obtained from large nanoparticle aggregates, where aggregate-by-aggregate variations in the SEF spectra were averaged out. Some NW dimers were found to exhibit EM enhancement spectra that deviated from the plasmon resonance Rayleigh scattering spectra, indicating that their EM enhancement was not generated by superradiant plasmons. These experimental results were examined by numerical calculation based on the EM mechanism by varying the morphology of NW dimers. The calculations reproduced the spectral deviations as the NW diameter dependence of EM enhancement. Phase analysis of the enhanced EM near-fields along the 1D HSs revealed that the dipole-quadrupole coupled plasmon, which is a subradiant mode, mainly generates EM enhancement for dimers with NW diameters larger than ∼80 nm, which was consistent with scanning electron microscopic measurements.

Simulating the Excited-State Dynamics of Polaritons with Ab Initio Multiple Spawning

Over the past decade, there has been a growth of interest in polaritonic chemistry, where the formation of hybrid light-matter states (polaritons) can alter the course of photochemical reactions. These hybrid states are created by strong coupling between molecules and photons in resonant optical cavities and can even occur in the absence of light when the molecule is strongly coupled with the electromagnetic fluctuations of the vacuum field. We present a first-principles model to simulate nonadiabatic dynamics of such polaritonic states inside optical cavities by leveraging graphical processing units (GPUs). Our first implementation of this model is specialized for a single molecule coupled to a single-photon mode confined inside the optical cavity but with any number of excited states computed using complete active space configuration interaction (CASCI) and a Jaynes-Cummings-type Hamiltonian. Using this model, we have simulated the excited-state dynamics of a single salicylideneaniline (SA) molecule strongly coupled to a cavity photon with the ab initio multiple spawning (AIMS) method. We demonstrate how the branching ratios of the photodeactivation pathways for this molecule can be manipulated by coupling to the cavity. We also show how one can stop the photoreaction from happening inside of an optical cavity. Finally, we also investigate cavity-based control of the ordering of two excited states (one optically bright and the other optically dark) inside a cavity for a set of molecules, where the dark and bright states are close in energy.

Modeling the near-field effect on molecular excited states using the discrete interaction model/quantum mechanical method

Strong light-matter interactions significantly modify the optical properties of molecules in the vicinity of plasmonic metal nanoparticles. Since the dimension of the plasmonic cavity approaches that of the molecules, it is critical to explicitly describe the nanoparticle junctions. In this work, we use the discrete interaction model/quantum mechanical (DIM/QM) method to model the coupling between the plasmonic near-field and molecular excited states. DIM/QM is a combined electrodynamics/quantum mechanical model that uses an atomistic description of the nanoparticle. We extend the DIM/QM method to include the local field effects in the sum-over-state formalism of time-dependent density functional theory. As a test of the method, we study the interactions between small organic chromophores and metal nanoparticles. In particular, we examine how the inclusion of multiple electronic transitions and intermolecular interactions modify the coupling between molecules and nanoparticles. Using the sum-over-state formalism of DIM/QM, we show that two-state models break down when the plasmon excitation is detuned from the molecular excitations. To gain further insight, we compare the simple coupled-dipole model (CDM) with the DIM/QM model. We find that CDM works well for simple systems but fails when going beyond the single molecule or single nanoparticle cases. We also find that the coupling depends strongly on the site of the nanoparticle in which the chromophore couples to. Our work suggests the importance of explicitly describing the cavity to capture the atomistic level local field environment in which the molecule strongly couples to.

Theory predicts 2D chiral polaritons based on achiral Fabry-Pérot cavities using apparent circular dichroism

Realizing polariton states with high levels of chirality offers exciting prospects for quantum information, sensing, and lasing applications. Such chirality must emanate from either the involved optical resonators or the quantum emitters. Here, we theoretically demonstrate a rare opportunity for realizing polaritons with so-called 2D chirality by strong coupling of the optical modes of (high finesse) achiral Fabry-Pérot cavities with samples exhibiting "apparent circular dichroism" (ACD). ACD is a phenomenon resulting from an interference between linear birefringence and dichroic interactions. By introducing a quantum electrodynamical theory of ACD, we identify the design rules based on which 2D chiral polaritons can be produced, and their chirality can be optimized.

Quantum to Classical Cavity Chemistry Electrodynamics

Polaritonic chemistry has ushered in new avenues for controlling molecular dynamics. However, two key questions remain: (i) Can classical light sources elicit the same effects as certain quantum light sources on molecular systems? (ii) Can semiclassical treatments of light-matter interactions capture nontrivial quantum effects observed in molecular dynamics? This work presents a quantum-classical approach addressing issues of realizing cavity chemistry effects without actual cavities. It also highlights the limitations of the standard semiclassical light-matter interaction. It is demonstrated that classical light sources can mimic quantum effects up to the second order of light-matter interaction provided that the mean-field contribution, the symmetrized two-time correlation function, and the linear response function are the same in both situations. Numerical simulations show that the quantum-classical method aligns more closely with exact quantum molecular-only dynamics for quantum light states such as Fock states, superpositions of Fock states, and vacuum squeezed states than does the conventional semiclassical approach.

Coupling Molecular Systems with Plasmonic Nanocavities: A Quantum Dynamics Approach

Plasmonic nanoparticles have the capacity to confine electromagnetic fields to the subwavelength regime and provide strong coupling with few or even a single emitter at room temperature. The photophysical properties of the emitters are highly dependent on the relative distance and orientation between them and the nanocavity. Therefore, there is a need for accurate and general light-matter interaction models capable of guiding their design in application-oriented devices. In this work, we present a Hermitian formalism within the framework of quantum dynamics and based on first-principles electronic structure calculations. Our vibronic approach considers the quantum nature of the plasmonic excitations and the dynamics of nonradiative channels to model plasmonic nanocavities and their dipolar coupling to molecular electronic states. Thus, the quantized and dissipative nature of the nanocavity is fully addressed.

Strong coupling in mechanically flexible free-standing organic membranes

Strong coupling of a confined optical field to the excitonic or vibronic transitions of a molecular material results in the formation of new hybrid states called polaritons. Such effects have been extensively studied in Fabry-Pèrot microcavity structures where an organic material is placed between two highly reflective mirrors. Recently, theoretical and experimental evidence has suggested that strong coupling can be used to modify chemical reactivity as well as molecular photophysical functionalities. However, the geometry of conventional microcavity structures limits the ability of molecules "encapsulated" in a cavity to interact with their local environment. Here, we fabricate mirrorless organic membranes that utilize the refractive index contrast between the organic active material and its surrounding medium to confine an optical field with Q-factor values up to 33. Using angle-resolved white light reflectivity measurements, we confirm that our structures operate in the strong coupling regime, with Rabi-splitting energies between 60 and 80 meV in the different structures studied. The experimental results are matched by transfer matrix and coupled oscillator models that simulate the various polariton states of the free standing membranes. Our work demonstrates that mechanically flexible and easy-to-fabricate free standing membranes can support strong light-matter coupling, making such simple and versatile structures highly promising for a range of polariton applications.

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations

The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.

Cavity Click Chemistry: Cavity-Catalyzed Azide-Alkyne Cycloaddition

Click chemistry, which refers to chemical reactions that are fast and selective with high product yields, has become a powerful approach in organic synthesis and chemical biology. Due to the cytotoxicity of the transition metals employed in click chemistry reactions, a search for novel metal-free alternatives continues. Herein, we demonstrate that an optical cavity can be utilized as a metal-free alternative in the click chemistry cycloaddition reaction between cyanoacetylene and formylazide using the quantum electrodynamics coupled cluster method. We show that by changing the molecular orientation with respect to the polarization of the cavity mode(s), the reaction can be selectively catalyzed to form a major 1,4-disubstituted or 1,5-disubstituted product. This work highlights that a cavity has the same effect on the investigated cycloaddition as the transition metal catalysts traditionally employed in click chemistry reactions. We expect our findings to further stimulate research on cavity-assisted click chemistry reactions.