Cavity-Controlled Chemistry in Molecular Ensembles

Making molecules in cavity

Free molecules undergo processes with photons; in particular, they can undergo photoionization and photodissociation, which are relevant processes in nature and laboratory. Recently, it has been shown that in a cavity, the reverse process of photoionization, namely, electron capture becomes highly probable. The underlying mechanism is the formation of a hybrid resonance state. In this work, we demonstrate that the idea of enhanced reverse processes is more general. We discuss the case of the reverse process of photodissociation, namely, making a molecule out of separate atoms in a cavity. For bound electronic states, the interaction of atoms and molecules with quantum light as realized in cavities is known to give rise to the formation of hybrid light-matter states (usually called polaritons). In the scenarios discussed here, the hybrid light-matter states are resonance (metastable) states, which decay into the continuum of either electrons or of the fragments of a molecule. Resonances can substantially enhance the outcome of processes. In addition to the new resonant mechanism of molecule formation, the impact of the hybrid resonances on the scattering cross section of the atoms can be dramatic.

Theory and quantum dynamics simulations of exciton-polariton motional narrowing

The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light-matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1/N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.

Exciton energy transfer inside cavity-A benchmark study of polaritonic dynamics using the surface hopping method

Strong coupling between the molecular system and photon inside the cavity generates polaritons, which can alter reaction rates by orders of magnitude. In this work, we benchmark the surface hopping method to simulate non-adiabatic dynamics in a cavity. The comparison is made against a numerically exact method (the hierarchical equations of motion) for a model system investigating excitonic energy transfer for a broad range of parameters. Surface hopping captures the effects of the radiation mode well, both at resonance and off-resonance. We have further investigated parameters that can increase or decrease the rate of population transfer, and we find that surface hopping in general can capture both effects well. Finally, we show that the dipole self-energy term within our parameter regime does not significantly affect the system's dynamics.

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.

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.

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

Strong coupling of metamaterials with cavity photons: toward non-Hermitian optics

The investigation of strong coupling between light and matter is an important field of research. Its significance arises not only from the emergence of a plethora of intriguing chemical and physical phenomena, often novel and unexpected, but also from its provision of important tool sets for the design of core components for novel chemical, electronic, and photonic devices such as quantum computers, lasers, amplifiers, modulators, sensors and more. Strong coupling has been demonstrated for various material systems and spectral regimes, each exhibiting unique features and applications. In this perspective, we will focus on a sub-field of this domain of research and discuss the strong coupling between metamaterials and photonic cavities at THz frequencies. The metamaterials, themselves electromagnetic resonators, serve as "artificial atoms". We provide a concise overview of recent advances and outline possible research directions in this vital and impactful field of interdisciplinary science.

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.

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.

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.

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.

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.

Machine Learning for Polaritonic Chemistry: Accessing Chemical Kinetics

Altering chemical reactivity and material structure in confined optical environments is on the rise, and yet, a conclusive understanding of the microscopic mechanisms remains elusive. This originates mostly from the fact that accurately predicting vibrational and reactive dynamics for soluted ensembles of realistic molecules is no small endeavor, and adding (collective) strong light-matter interaction does not simplify matters. Here, we establish a framework based on a combination of machine learning (ML) models, trained using density-functional theory calculations and molecular dynamics to accelerate such simulations. We then apply this approach to evaluate strong coupling, changes in reaction rate constant, and their influence on enthalpy and entropy for the deprotection reaction of 1-phenyl-2-trimethylsilylacetylene, which has been studied previously both experimentally and using ab initio simulations. While we find qualitative agreement with critical experimental observations, especially with regard to the changes in kinetics, we also find differences in comparison with previous theoretical predictions. The features for which the ML-accelerated and ab initio simulations agree show the experimentally estimated kinetic behavior. Conflicting features indicate that a contribution of dynamic electronic polarization to the reaction process is more relevant than currently believed. Our work demonstrates the practical use of ML for polaritonic chemistry, discusses limitations of common approximations, and paves the way for a more holistic description of polaritonic chemistry.

Non-Polaritonic Effects in Cavity-Modified Photochemistry

Strong coupling of molecules to vacuum fields is widely reported to lead to modified chemical properties such as reaction rates. However, some recent attempts to reproduce infrared strong coupling results have not been successful, suggesting that factors other than strong coupling may sometimes be involved. In the first vacuum-modified chemistry experiment, changes to a molecular photoisomerization process in the ultraviolet-visible spectral range are attributed to strong coupling of the molecules to visible light. Here, this process is re-examined, finding significant variations in photoisomerization rates consistent with the original work. However, there is no evidence that these changes need to be attributed to strong coupling. Instead, it is suggested that the photoisomerization rates involved are most strongly influenced by the absorption of ultraviolet radiation in the cavity. These results indicate that care must be taken to rule out non-polaritonic effects before invoking strong coupling to explain any changes of properties arising in cavity-based experiments.

Nonadiabatic Dynamics near Metal Surfaces with Periodic Drivings: A Generalized Surface Hopping in Floquet Representation

With light-matter interaction extending into the strong regime, as well as rapid development of laser technology, systems subjecting to a time-periodic perturbation have attracted broad attention. Floquet theorem and Floquet time-independent Hamiltonian are powerful theoretical frameworks to investigate the systems subjected to time-periodic drivings. In this study, we extend the previous generalized surface hopping (SH) algorithm near a metal surface (J. Chem. Theory Comput. 2017, 13, 6, 2430-2439) to the Floquet space, and hence, we develop a generalized Floquet representation-based SH (FR-SH) algorithm. Here, we consider an open quantum system with fast drivings. We expect that the present algorithm will be useful for understanding the chemical processes of molecules under time-periodic driving near the metal surface.

Machine Learning Framework for Modeling Exciton Polaritons in Molecular Materials

A light-matter hybrid quasiparticle, called a polariton, is formed when molecules are strongly coupled to an optical cavity. Recent experiments have shown that polariton chemistry can manipulate chemical reactions. Polariton chemistry is a collective phenomenon, and its effects increase with the number of molecules in a cavity. However, simulating an ensemble of molecules in the excited state coupled to a cavity mode is theoretically and computationally challenging. Recent advances in machine learning (ML) techniques have shown promising capabilities in modeling ground-state chemical systems. This work presents a general protocol to predict excited-state properties, such as energies, transition dipoles, and nonadiabatic coupling vectors with the hierarchically interacting particle neural network. ML predictions are then applied to compute the potential energy surfaces and electronic spectra of a prototype azomethane molecule in the collective coupling scenario. These computational tools provide a much-needed framework to model and understand many molecules' emerging excited-state polariton chemistry.

Addressing the Dark State Problem in Strongly Coupled Organic Exciton-Polariton Systems

The manipulation of molecular excited state processes through strong coupling has attracted significant interest for its potential to provide precise control of photochemical phenomena. However, the key limiting factor for achieving this control has been the "dark-state problem", in which photoexcitation populates long-lived reservoir states with energies and dynamics similar to those of bare excitons. Here, we use a sensitive ultrafast transient reflection method with momentum and spectral resolution to achieve the selective excitation of organic exciton-polaritons in open photonic cavities. We show that the energy dispersions of these systems allow us to avoid the parasitic effect of the reservoir states. Under phase-matching conditions, we observe the direct population and decay of polaritons on time scales of less than 100 fs and find that momentum scattering processes occur on even faster time scales. We establish that it is possible to overcome the "dark state problem" through the careful design of strongly coupled systems.

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.

Plasmon mediated coherent population oscillations in molecular aggregates

The strong coherent coupling of quantum emitters to vacuum fluctuations of the light field offers opportunities for manipulating the optical and transport properties of nanomaterials, with potential applications ranging from ultrasensitive all-optical switching to creating polariton condensates. Often, ubiquitous decoherence processes at ambient conditions limit these couplings to such short time scales that the quantum dynamics of the interacting system remains elusive. Prominent examples are strongly coupled exciton-plasmon systems, which, so far, have mostly been investigated by linear optical spectroscopy. Here, we use ultrafast two-dimensional electronic spectroscopy to probe the quantum dynamics of J-aggregate excitons collectively coupled to the spatially structured plasmonic fields of a gold nanoslit array. We observe rich coherent Rabi oscillation dynamics reflecting a plasmon-driven coherent exciton population transfer over mesoscopic distances at room temperature. This opens up new opportunities to manipulate the coherent transport of matter excitations by coupling to vacuum fields.

Vacuum-Induced Symmetry Breaking of Chiral Enantiomer Formation in Chemical Reactions

A material with symmetry breaking inside can transmit the symmetry breaking to its vicinity by vacuum electromagnetic fluctuations. Here, we show that vacuum quantum fluctuations proximate to a parity-symmetry-broken material can induce a chirality-dependent spectral shift of chiral molecules, resulting in a chemical reaction process that favors producing one chirality over the other. We calculate concrete examples and evaluate the chirality production rate with experimentally realizable parameters, showing the promise of selecting chirality with symmetry-broken vacuum quantum fluctuations.

Cavity-Modified Chemiluminescent Reaction of Dioxetane

Chemiluminescence is a thermally activated chemical process that emits a photon of light by forming a fraction of products in the electronic excited state. A well-known example of this spectacular phenomenon is the emission of light in the firefly beetle, where the formation of a four-membered cyclic peroxide compound and subsequent dissociation produce a light-emitting product. The smallest cyclic peroxide, dioxetane, also exhibits chemiluminescence but with a low quantum yield as compared to that of firefly dioxetane. Employing the strong light-matter coupling has recently been found to be an alternative strategy to modify the chemical reactivity. In the presence of an optical cavity, the molecular degrees of freedom greatly mix with the cavity mode to form hybrid cavity-matter states called polaritons. These newly generated hybrid light-matter states manipulate the potential energy surfaces and significantly change the reaction dynamics. Here, we theoretically investigate the effects of a strong light-matter interaction on the chemiluminescent reaction of dioxetane using the extended Jaynes-Cummings model. The cavity couplings corresponding to the electronic and vibrational degrees of freedom have been included in the interaction Hamiltonian. We explore how the cavity alters the ground- and excited-state path energy barriers and reaction rates. Our results demonstrate that the formation of excited-state products in the dioxetane decomposition process can be either accelerated or suppressed, depending on the molecular orientation with respect to the cavity polarization.

Molecular van der Waals Fluids in Cavity Quantum Electrodynamics

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. In this work, we demonstrate that strong light-matter coupling can be used to control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules. For example, we find intermolecular interactions that depend on the distance between the molecules R as R-3 and R0. Moreover, we employ ab initio cavity quantum electrodynamics calculations to develop machine-learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from 12 H2 to 144 H2 molecules, we observe varying degrees of orientational order because of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order.

Polaritonic Chemistry: Hindering and Easing Ground State Polyenic Isomerization via Breakdown of σ-π Separation

The ground state conformational isomerization in polyenes is a symmetry allowed process. Its low energy barrier is governed by electron density transfer from the formal single bond that is rotated to the nearby formal double bonds. Along the reaction pathway, the transition state is therefore destabilized. The rules of polaritonic chemistry, i.e., chemistry in a nanocavity with reflecting windows, are barely beginning to be laid out. The standing electric field of the nanocavity couples strongly with the molecular wave function and modifies the potential energy curve in unexpected ways. A quantum electrodynamics approach, applied to the torsional degree of freedom of the central bond of butadiene, shows that formation of the polariton mixes the σ-π frameworks thereby stabilizing/destabilizing the planar, reactant-like conformations. The values of the fundamental mode of the cavity field used in the absence of the cavity do not trigger this mechanism.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

The Rise and Current Status of Polaritonic Photochemistry and Photophysics

The interaction between molecular electronic transitions and electromagnetic fields can be enlarged to the point where distinct hybrid light-matter states, polaritons, emerge. The photonic contribution to these states results in increased complexity as well as an opening to modify the photophysics and photochemistry beyond what normally can be seen in organic molecules. It is today evident that polaritons offer opportunities for molecular photochemistry and photophysics, which has caused an ever-rising interest in the field. Focusing on the experimental landmarks, this review takes its reader from the advent of the field of polaritonic chemistry, over the split into polariton chemistry and photochemistry, to present day status within polaritonic photochemistry and photophysics. To introduce the field, the review starts with a general description of light-matter interactions, how to enhance these, and what characterizes the coupling strength. Then the photochemistry and photophysics of strongly coupled systems using Fabry-Perot and plasmonic cavities are described. This is followed by a description of room-temperature Bose-Einstein condensation/polariton lasing in polaritonic systems. The review ends with a discussion on the benefits, limitations, and future developments of strong exciton-photon coupling using organic molecules.

Control of Photoswitching Kinetics with Strong Light-Matter Coupling in a Cavity

Most photochemistry occurs in the regime of weak light-matter coupling, in which a molecule absorbs a photon and then performs photochemistry from its excited state. In the strong coupling regime, enhanced light-matter interactions between an optical field and multiple molecules lead to collective hybrid light-matter states called polaritons. This strong coupling leads to fundamental changes in the nature of the excited states including multi-molecule delocalized excitations, modified potential energy surfaces, and dramatically altered energy levels relative to non-coupled molecules. The effect of strong light-matter coupling on covalent photochemistry has not been well explored. Photoswitches undergo reversible intramolecular photoreactions that can be readily monitored spectroscopically. In this work, we study the effect of strong light-matter coupling on the kinetics of photoswitching within optical cavities. Reproducing prior experiments, photoswitching of spiropyran/merocyanine photoswitches is decelerated in a cavity. Fulgide photoswitches, however, show the opposite effect, with strong coupling accelerating photoswitching. While modified merocyanine switching can be explained by changes in radiative decay rates or the amount of light in the cavity, modified fulgide switching kinetics suggest direct changes to excited-state reaction kinetics.

Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons

We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton-polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light-matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton-phonon coupling among polariton states due to the strong light-matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Theory for Cavity-Modified Ground-State Reactivities via Electron-Photon Interactions

We provide a simple and intuitive theory to explain how coupling a molecule to an optical cavity can modify ground-state chemical reactivity by exploiting intrinsic quantum behaviors of light-matter interactions. Using the recently developed polarized Fock states representation, we demonstrate that the change of the ground-state potential is achieved due to the scaling of diabatic electronic couplings with the overlap of the polarized Fock states. Our theory predicts that for a proton-transfer model system, the ground-state barrier height can be modified through light-matter interactions when the cavity frequency is in the electronic excitation range. Our simple theory explains several recent computational investigations that discovered the same effect. We further demonstrate that under the deep strong coupling limit of the light and matter, the polaritonic ground and first excited eigenstates become the Mulliken-Hush diabatic states, which are the eigenstates of the dipole operator. This work provides a simple but powerful theoretical framework to understand how strong coupling between the molecule and the cavity can modify ground-state reactivities.

The role of dephasing for dark state coupling in a molecular Tavis-Cummings model

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.

Controlling the electro-optic response of a semiconducting perovskite coupled to a phonon-resonant cavity

Optical cavities, resonant with vibrational or electronic transitions of material within the cavity, enable control of light-matter interaction. Previous studies have reported cavity-induced modifications of chemical reactivity, fluorescence, phase behavior, and charge transport. Here, we explore the effect of resonant cavity-phonon coupling on the transient photoconductivity in a hybrid organic-inorganic perovskite. To this end, we measure the ultrafast photoconductivity response of perovskite in a tunable Fabry-Pérot terahertz cavity, designed to be transparent for optical excitation. The terahertz-cavity field-phonon interaction causes apparent Rabi splitting between the perovskite phonon mode and the cavity mode. We explore whether the cavity-phonon interaction affects the material's electron-phonon interaction by determining the charge-carrier mobility through photoconductivity. Despite the apparent hybridization of cavity and phonon modes, we show that the perovskite properties in both ground (phonon response) and excited (photoconductive response) states remain unaffected by the tunable light-matter interaction. Yet the response of the integral perovskite-terahertz optical cavity system depends critically on the interaction strength of the cavity with the phonon: the transient terahertz response to optical excitation can be increased up to threefold by tuning the cavity-perovskite interaction strength. These results enable tunable switches and frequency-controlled induced transparency devices.

Electronic transport driven by collective light-matter coupled states in a quantum device

In the majority of optoelectronic devices, emission and absorption of light are considered as perturbative phenomena. Recently, a regime of highly non-perturbative interaction, ultra-strong light-matter coupling, has attracted considerable attention, as it has led to changes in the fundamental properties of materials such as electrical conductivity, rate of chemical reactions, topological order, and non-linear susceptibility. Here, we explore a quantum infrared detector operating in the ultra-strong light-matter coupling regime driven by collective electronic excitations, where the renormalized polariton states are strongly detuned from the bare electronic transitions. Our experiments are corroborated by microscopic quantum theory that solves the problem of calculating the fermionic transport in the presence of strong collective electronic effects. These findings open a new way of conceiving optoelectronic devices based on the coherent interaction between electrons and photons allowing, for example, the optimization of quantum cascade detectors operating in the regime of strongly non-perturbative coupling with light.

Molecular Chemistry in Cavity Strong Coupling

The coherent exchange of energy between materials and optical fields leads to strong light-matter interactions and so-called polaritonic states with intriguing properties, halfway between light and matter. Two decades ago, research on these strong light-matter interactions, using optical cavity (vacuum) fields, remained for the most part the province of the physicist, with a focus on inorganic materials requiring cryogenic temperatures and carefully fabricated, high-quality optical cavities for their study. This review explores the history and recent acceleration of interest in the application of polaritonic states to molecular properties and processes. The enormous collective oscillator strength of dense films of organic molecules, aggregates, and materials allows cavity vacuum field strong coupling to be achieved at room temperature, even in rapidly fabricated, highly lossy metallic optical cavities. This has put polaritonic states and their associated coherent phenomena at the fingertips of laboratory chemists, materials scientists, and even biochemists as a potentially new tool to control molecular chemistry. The exciting phenomena that have emerged suggest that polaritonic states are of genuine relevance within the molecular and material energy landscape.

Manipulating hydrogen bond dissociation rates and mechanisms in water dimer through vibrational strong coupling

The vibrational strong coupling (VSC) between molecular vibrations and cavity photon modes has recently emerged as a promising tool for influencing chemical reactivities. Despite numerous experimental and theoretical efforts, the underlying mechanism of VSC effects remains elusive. In this study, we combine state-of-art quantum cavity vibrational self-consistent field/configuration interaction theory (cav-VSCF/VCI), quasi-classical trajectory method, along with the quantum-chemical CCSD(T)-level machine learning potential, to simulate the hydrogen bond dissociation dynamics of water dimer under VSC. We observe that manipulating the light-matter coupling strength and cavity frequencies can either inhibit or accelerate the dissociation rate. Furthermore, we discover that the cavity surprisingly modifies the vibrational dissociation channels, with a pathway involving both water fragments in their ground vibrational states becoming the major channel, which is a minor one when the water dimer is outside the cavity. We elucidate the mechanisms behind these effects by investigating the critical role of the optical cavity in modifying the intramolecular and intermolecular coupling patterns. While our work focuses on single water dimer system, it provides direct and statistically significant evidence of VSC effects on molecular reaction dynamics.

Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities

Experiments have demonstrated that the strong light-matter coupling in polaritonic microcavities significantly enhances transport. Motivated by these experiments, we have solved the disordered multimode Tavis-Cummings model in the thermodynamic limit and used this solution to analyze its dispersion and localization properties. The solution implies that wave-vector-resolved spectroscopic quantities can be described by single-mode models, but spatially resolved quantities require the multimode solution. Nondiagonal elements of the Green's function decay exponentially with distance, which defines the coherence length. The coherent length is strongly correlated with the photon weight and exhibits inverse scaling with respect to the Rabi frequency and an unusual dependence on disorder. For energies away from the average molecular energy E_{M} and above the confinement energy E_{C}, the coherence length rapidly diverges such that it exceeds the photon resonance wavelength λ_{0}. The rapid divergence allows us to differentiate the localized and delocalized regimes and identify the transition from diffusive to ballistic transport.

Activating cavity by electrons

The interaction of atoms and molecules with quantum light as realized in cavities has become a highly topical and fast growing research field. This interaction leads to hybrid light-matter states giving rise to new phenomena and opening up pathways to control and manipulate properties of the matter. Here, we substantially extend the scope of the interaction by allowing free electrons to enter the cavity and merge and unify the two active fields of electron scattering and quantum-light-matter interaction. In the presence of matter, hybrid metastable states are formed at electron energies of choice. The properties of these states depend strongly on the frequency and on the light-matter coupling of the cavity. The incoming electrons can be captured by the matter inside the cavity solely due to the presence of the cavity. The findings are substantiated by an explicit example and general consequences are discussed.

Measurement-induced collective vibrational quantum coherence under spontaneous Raman scattering in a liquid

Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter interaction whose description necessitates quantization of the electromagnetic field. It is usually considered as an incoherent process because the scattered field lacks any predictable phase relationship with the incoming field. When probing an ensemble of molecules, the question therefore arises: What quantum state should be used to describe the molecular ensemble following spontaneous Stokes scattering? We experimentally address this question by measuring time-resolved Stokes-anti-Stokes two-photon coincidences on a molecular liquid consisting of several sub-ensembles with slightly different vibrational frequencies. When spontaneously scattered Stokes photons and subsequent anti-Stokes photons are detected into a single spatiotemporal mode, the observed dynamics is inconsistent with a statistical mixture of individually excited molecules. Instead, we show that the data are reproduced if Stokes-anti-Stokes correlations are mediated by a collective vibrational quantum, i.e. a coherent superposition of all molecules interacting with light. Our results demonstrate that the degree of coherence in the vibrational state of the liquid is not an intrinsic property of the material system, but rather depends on the optical excitation and detection geometry.

Computational study on the catalytic control of endo/exo Diels-Alder reactions by cavity quantum vacuum fluctuations

Achieving control over chemical reaction's rate and stereoselectivity realizes one of the Holy Grails in chemistry that can revolutionize chemical and pharmaceutical industries. Strong light-matter interaction in optical or nanoplasmonic cavities might provide the knob to reach such control. In this work, we demonstrate the catalytic and selectivity control of an optical cavity for two selected Diels-Alder cycloaddition reactions using the quantum electrodynamics coupled cluster (QED-CC) method. Herein, we find that by changing the molecular orientation with respect to the polarization of the cavity mode the reactions can be significantly inhibited or selectively enhanced to produce major endo or exo products on demand. This work highlights the potential of utilizing quantum vacuum fluctuations of an optical cavity to modulate the rate of Diels-Alder cycloaddition reactions and to achieve stereoselectivity in a practical and non-intrusive way. We expect that the present findings will be applicable to a larger set of relevant reactions, including the click chemical reactions.

Control and Enhancement of Single-Molecule Electroluminescence through Strong Light-Matter Coupling

The energetic positions of molecular electronic states at molecule/electrode interfaces are crucial factors for determining the transport and optoelectronic properties of molecular junctions. Strong light-matter coupling offers a potential for manipulating these factors, enabling a boost in the efficiency and versatility of these junctions. Here, we investigate electroluminescence from single-molecule junctions in which the molecule is strongly coupled with the vacuum electromagnetic field in a plasmonic nanocavity. We demonstrate an improvement in the electroluminescence efficiency by employing the strong light-matter coupling in conjunction with the characteristic feature of single-molecule junctions to selectively control the formation of the lowest-energy excited state. The mechanism of efficiency improvement is discussed based on the energetic position and composition of the formed polaritonic states. Our findings indicate the possibility to manipulate optoelectronic conversion in molecular junctions by strong light-matter coupling and contribute to providing design principles for developing efficient molecular optoelectronic devices.

Quantized Fields for Optimal Control in the Strong Coupling Regime

We tailor the quantum statistics of a bosonic field to deterministically drive a quantum system into a target state. Experimentally accessible states of the field achieve good control of multilevel or multiqubit systems, notably also at coupling strengths beyond the rotating-wave approximation. This extends optimal control theory to the realm of fully quantized, strongly coupled control and target degrees of freedom.

Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons

In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units, and have a different excited-state potential energy landscape, which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e., plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators and apply them to explore spectroscopic signatures of plexcitons. In particular, we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy and a qualitative change in the symmetry of the line shape of the nonlinear signal when crossing the exceptional point. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians.

Multidimensional Coherent Spectroscopy of Molecular Polaritons: Langevin Approach

We present a microscopic theory for nonlinear optical spectroscopy of N molecules in an optical cavity. Using the Heisenberg-Langevin equation, an analytical expression is derived for the time- and frequency-resolved signals accounting for arbitrary numbers of vibrational excitations. We identify clear signatures of the polariton-polaron interaction from multidimensional projections of the signal, e.g., pathways and timescales. Cooperative dynamics of cavity polaritons against intramolecular vibrations is revealed, along with a crosstalk between long-range coherence and vibronic coupling that may lead to localization effects. Our results further characterize the polaritonic coherence and the population transfer that is slower.

Polaritonic Huang-Rhys Factor: Basic Concepts and Quantifying Light-Matter Interactions in Media

The Huang-Rhys (HR) factor, a dimensionless factor that characterizes electron-phonon (vibronic) coupling, has been extensively employed to investigate a variety of material properties. In the same spirit, we propose a quantity called the polaritonic HR factor to quantitatively describe the effects of (i) light-matter coupling induced by permanent dipoles and (ii) dipole self-energy. The former leads to polaritonic displacements, while the latter is associated with the electronic coupling shift named reorganization dipole self-coupling. In the framework of macroscopic quantum electrodynamics, our theory can evaluate the polaritonic HR factor, reorganization dipole self-coupling, and modified light-matter coupling strength in an arbitrary dielectric environment without free parameters, whose magnitudes are in good agreement with the previous experimental results. We believe that this study provides a useful perspective on understanding and quantifying light-matter interactions in media.

Dissociation slowdown by collective optical response under strong coupling conditions

We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell-Schrödinger equations with molecular rovibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissociation slowdown at polaritonic frequencies is proposed.