Electron transfer in confined electromagnetic fields

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.

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.

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.

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.

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.

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.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

Recent experiments suggest that ground state chemical reactivity can be modified when placing molecular systems inside infrared cavities where molecular vibrations are strongly coupled to electromagnetic radiation. This phenomenon lacks a firm theoretical explanation. Here, we employ an exact quantum dynamics approach to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multilayered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multilayered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

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.

Polariton enhanced free charge carrier generation in donor-acceptor cavity systems by a second-hybridization mechanism

Cavity quantum electrodynamics has been studied as a potential approach to modify free charge carrier generation in donor-acceptor heterojunctions because of the delocalization and controllable energy level properties of hybridized light-matter states known as polaritons. However, in many experimental systems, cavity coupling decreases charge separation. Here, we theoretically study the quantum dynamics of a coherent and dissipative donor-acceptor cavity system, to investigate the dynamical mechanism and further discover the conditions under which polaritons may enhance free charge carrier generation. We use open quantum system methods based on single-pulse pumping to find that polaritons have the potential to connect excitonic states and charge separated states, further enhancing free charge generation on an ultrafast timescale of several hundred femtoseconds. The mechanism involves polaritons with optimal energy levels that allow the exciton to overcome the high Coulomb barrier induced by electron-hole attraction. Moreover, we propose that a second-hybridization between a polariton state and dark states with similar energy enables the formation of the hybrid charge separated states that are optically active. These two mechanisms lead to a maximum of 50% enhancement of free charge carrier generation on a short timescale. However, our simulation reveals that on the longer timescale of picoseconds, internal conversion and cavity loss dominate and suppress free charge carrier generation, reproducing the experimental results. Thus, our work shows that polaritons can affect the charge separation mechanism and promote free charge carrier generation efficiency, but predominantly on a short timescale after photoexcitation.

Interference between Molecular and Photon Field-Mediated Electron Transfer Coupling Pathways in Cavities

Cavity polaritonics creates novel opportunities to direct chemical reactions. Electron transfer (ET) reactions are among the simplest reactions, and they underpin energy conversion. New strategies to manipulate and direct electron flow at the nanoscale are of particular interest in biochemistry, energy science, bioinspired materials science, and chemistry. We show that optical cavities can modulate electron transfer pathway interferences and ET rates in donor-bridge-acceptor (DBA) systems. We derive the rate for DBA electron transfer when the molecules are coupled to cavity modes, emphasizing novel cavity-induced pathway interferences with the molecular electronic coupling pathways, as these interferences allow a new kind of ET rate tuning. The interference between the cavity-induced coupling pathways and the intrinsic molecular coupling pathway is dependent on the cavity properties. Thus, manipulating the interference between the cavity-induced DA coupling and the bridge-mediated coupling offers an approach to direct and manipulate charge flow at the nanoscale.

Cavity-Free Quantum-Electrodynamic Electron Transfer Reactions

Richard Feynman stated that "The theory behind chemistry is quantum electrodynamics". However, harnessing quantum-electrodynamic (QED) effects to modify chemical reactions is a grand challenge and currently has only been reported in experiments using cavities due to the limitation of strong light-matter coupling. In this article, we demonstrate that QED effects can significantly enhance the rate of electron transfer (ET) by several orders of magnitude in the absence of cavities, which is implicitly supported by experimental reports. To understand how cavity-free QED effects are involved in ET reactions, we incorporate the effect of infinite one-photon states into Marcus theory, derive an explicit expression for the rate of radiative ET, and develop the concept of "electron transfer overlap". Moreover, QED effects may lead to a barrier-free ET reaction whose rate is dependent on the energy-gap power law. This study thus provides new insights into fundamental chemical principles, with promising prospects for QED-based chemical reactions.

Collective response in light-matter interactions: The interplay between strong coupling and local dynamics

Strong molecule-radiation field coupling is often reached when a large number N of molecules respond collectively to the radiation field. In electronic strong coupling, molecular nuclear dynamics following polariton excitation reflects (a) the timescale separation between the fast electronic and photonic dynamics and the slow nuclear motion on one hand, and (b) the interplay between the collective nature of the molecule-field coupling and the local nature of the molecules nuclear response on the other. The first implies that the electronic excitation takes place, in the spirit of the Born approximation, at an approximately fixed nuclear configuration. The second can be rephrased as the intriguing question, can the collective nature of the optical excitation lead to collective nuclear motion following polariton formation, resulting in so-called polaron decoupled dynamics. We address this issue by studying the dynamical properties of a simplified Holstein-Tavis-Cummings type model, in which boson modes representing molecular vibrations are replaced by two-level systems while the boson frequency and the vibronic coupling are represented by the coupling between these levels (that induces Rabi oscillations between them) and electronic state dependence of this coupling. We investigate the short-time behavior of this model following polariton excitation as well as its response to CW driving and its density of states spectrum. We find that, while some aspects of the dynamical behavior appear to adhere to the polaron decoupling picture, the observed dynamics mostly reflect the local nature of the nuclear configuration of the electronic polariton rather than this picture.

Coupling, lifetimes, and "strong coupling" maps for single molecules at plasmonic interfaces

The interaction between excited states of a molecule and excited states of a metal nanostructure (e.g., plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency, an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when 2|⟨U⟩|/ℏΓ > 1, where ⟨U⟩ and Γ are the molecule-plasmon coupling and the spectral width of the optical transition, respectively. Because both ⟨U⟩ and Γ strongly increase with decreasing distance between a molecule and a plasmonic structure, it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work, we investigate the behavior of ⟨U⟩ and Γ for several geometries. Surprisingly, we find that if the only contributions to Γ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion 2|⟨U⟩|/ℏΓ > 1 is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.

Not dark yet for strong light-matter coupling to accelerate singlet fission dynamics

Polaritons are unique hybrid light-matter states that offer an alternative way to manipulate chemical processes. In this work, we show that singlet fission dynamics can be accelerated under strong light-matter coupling. For superexchange-mediated singlet fission, state mixing speeds up the dynamics in cavities when the lower polariton is close in energy to the multiexcitonic state. This effect is more pronounced in non-conventional singlet fission materials in which the energy gap between the bright singlet exciton and the multiexcitonic state is large ( > 0.1 eV). In this case, the dynamics is dominated by the polaritonic modes and not by the bare-molecule-like dark states, and, additionally, the resonant enhancement due to strong coupling is robust even for energetically broad molecular states. The present results provide a new strategy to expand the range of suitable materials for efficient singlet fission by making use of strong light-matter coupling.

Cooperative molecular structure in polaritonic and dark states

The interaction of quantum light with matter is known to give rise to mixed light-matter states. An ensemble of identical molecules is discussed. The resulting hybrid light-matter states exhibit complex structure even if only a single vibrational coordinate per molecule is considered. Starting from the uniform situation where all molecules possess the same value of this coordinate, polaritons and dark states follow like in atoms, but are functions of this coordinate. It is proven that any point on a resulting polariton energy curve is a (local) minimum or maximum for distorting molecules perpendicular to this curve. It is shown how to explicitly compute the impact of distortion solely based on the data of a free molecule. The structure of the dark states and their behavior upon distortion is analyzed as well. Useful techniques are introduced and general results on, for example, minimum energy path, symmetry breaking and restoration, are obtained. The developed strategy is transferred to include several or even many nuclear degrees of freedom per molecule and it is demonstrated that the interplay of several vibrational degrees of freedom in a single molecule of the ensemble is expected to lead to qualitatively different physics. General consequences are discussed.

Driving chemical reactions with polariton condensates

When molecular transitions strongly couple to photon modes, they form hybrid light-matter modes called polaritons. Collective vibrational strong coupling is a promising avenue for control of chemistry, but this can be deterred by the large number of quasi-degenerate dark modes. The macroscopic occupation of a single polariton mode by excitations, as observed in Bose-Einstein condensation, offers promise for overcoming this issue. Here we theoretically investigate the effect of vibrational polariton condensation on the kinetics of electron transfer processes. Compared with excitation with infrared laser sources, the vibrational polariton condensate changes the reaction yield significantly at room temperature due to additional channels with reduced activation barriers resulting from the large accumulation of energy in the lower polariton, and the many modes available for energy redistribution during the reaction. Our results offer tantalizing opportunities to use condensates for driving chemical reactions, kinetically bypassing usual constraints of fast intramolecular vibrational redistribution in condensed phase.

An Accurate Linearized Semiclassical Approach for Calculating Cavity-Modified Charge Transfer Rate Constants

We show that combining the linearized semiclasscial approximation with Fermi's golden rule (FGR) rate theory gives rise to a general-purpose cost-effective and scalable computational framework that can accurately capture the cavity-induced rate enhancement of charge transfer reactions that occurs when the molecular system is placed inside a microcavity. Both partial linearization with respect to the nuclear and photonic degrees of freedom and full linerization with respect to nuclear, photonic, and electronic degrees of freedom (the latter within the mapping Hamiltonian approach) are shown to be highly accurate, provided that the Wigner transforms of the product (WoP) of operators at the initial time is not replaced by the product of their Wigner transforms. We also show that the partial linearization method yields the quantum-mechanically exact cavity-modified FGR rate constant for a model system in which the donor and acceptor potential energy surfaces are harmonic and identical except for a shift in the equilibrium energy and geometry, if WoP is applied.

Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces

The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

Molecular Polaritonics: Chemical Dynamics Under Strong Light-Matter Coupling

Chemical manifestations of strong light-matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light-matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light-matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes

Light-matter coupling strength and optical loss are two key physical quantities in cavity quantum electrodynamics (CQED), and their interplay determines whether light-matter hybrid states can be formed or not in chemical systems. In this study, by using macroscopic quantum electrodynamics (MQED) combined with a pseudomode approach, we present a simple but accurate method, which allows us to quickly estimate the light-matter coupling strength and optical loss without free parameters. Moreover, for a molecular emitter coupled with photonic modes (including cavity modes and plasmon polariton modes), we analytically and numerically prove that the dynamics derived from the MQED-based wavefunction approach is mathematically equivalent to the dynamics governed by the CQED-based Lindblad master equation when the Purcell factor behaves like Lorentzian functions.

Theory of molecular emission power spectra. II. Angle, frequency, and distance dependence of electromagnetic environment factor of a molecular emitter in plasmonic environments

Our previous study [S. Wang et al., J. Chem. Phys. 153, 184102 (2020)] has shown that in a complex dielectric environment, molecular emission power spectra can be expressed as the product of the lineshape function and the electromagnetic environment factor (EEF). In this work, we focus on EEFs in a vacuum-NaCl-silver system and investigate molecular emission power spectra in the strong exciton-polariton coupling regime. A numerical method based on computational electrodynamics is presented to calculate the EEFs of single-molecule emitters in a dispersive and lossy dielectric environment with arbitrary shapes. The EEFs in the far-field region depend on the detector position, emission frequency, and molecular orientation. We quantitatively analyze the asymptotic behavior of the EFFs in the far-field region and qualitatively provide a physical picture. The concept of EEF should be transferable to other types of spectra in a complex dielectric environment. Finally, our study indicates that molecular emission power spectra cannot be simply interpreted by the lineshape function (quantum dynamics of a molecular emitter), and the effect of the EEFs (photon propagation in a dielectric environment) has to be carefully considered.

Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis

Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and co-workers [Flick et al., ACS Photonics 6, 2757-2778 (2019)], we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions to QED-TDDFT electron-photon eigenstates. This leads to a Hermitian QED-TDDFT coupling matrix that is expected to facilitate the future development of analytic derivatives. Through a Gaussian atomic basis implementation of the QED-TDDFT method, we examined the effect of dipole self-energy, rotating-wave approximation, and the Tamm-Dancoff approximation on the QED-TDDFT eigenstates of model compounds (ethene, formaldehyde, and benzaldehyde) in an optical cavity. We highlight, in the strong coupling regime, the role of higher-energy and off-resonance excited states with large transition dipole moments in the direction of the photonic field, which are automatically accounted for in our QED-TDDFT calculations and might substantially affect the energies and compositions of polaritons associated with lower-energy electronic states.

Polaritonic States of Matter in a Rotating Cavity

The interaction of quantum light with matter like that inside a cavity is known to give rise to mixed light-matter states called polaritons. We discuss the impact of rotation of the cavity on the polaritons. It is shown that the number of polaritons increases because of this rotation. The structure of the original polaritons is modified, and new ones are induced by the rotation that strongly depend on the angular velocity and the choice of axis of rotation. In molecules the rotation can change the number of light-induced conical intersections and their dimensionality and hence strongly impact their quantum dynamics. General consequences are discussed.

Impact of cavity on interatomic Coulombic decay

The interatomic Coulombic decay (ICD) is an efficient electronic decay process of systems embedded in environment. In ICD, the excess energy of an excited atom A is efficiently utilized to ionize a neighboring atom B. In quantum light, an ensemble of atoms A form polaritonic states which can undergo ICD with B. Here we investigate the impact of quantum light on ICD and show that this process is strongly altered compared to classical ICD. The ICD rate depends sensitively on the atomic distribution and orientation of the ensemble. It is stressed that in contrast to superposition states formed by a laser, forming polaritons by a cavity enables to control the emergence and suppression, as well as the efficiency of ICD.

Molecular Polaritons Generated from Strong Coupling between CdSe Nanoplatelets and a Dielectric Optical Cavity

We demonstrate the formation of CdSe nanoplatelet (NPL) exciton-polaritons in a distributed Bragg reflector (DBR) cavity. The molecule-cavity hybrid system is in the strong coupling regime with an 83 meV Rabi splitting, characterized from angle-resolved reflectance and photoluminescence measurements. Mixed quantum-classical dynamics simulations are used to investigate the polariton photophysics of the hybrid system by treating the electronic and photonic degrees of freedom (DOF) quantum mechanically and the nuclear phononic DOF classically. Our numerical simulations of the angle-resolved photoluminescence (PL) agree extremely well with the experimental data, providing a fundamental explanation of the asymmetric intensity distribution of the upper and lower polariton branches. Our results also provide mechanistic insights into the importance of phonon-assisted nonadiabatic transitions among polariton states, which are reflected in the various features of the PL spectra. This work proves the feasibility of coupling nanoplatelet electronic states with the photon states of a dielectric cavity to form a hybrid system and provides a new platform for investigating cavity-mediated physical and chemical processes.

Ground state properties and infrared spectra of anharmonic vibrational polaritons of small molecules in cavities

Recent experiments and theory suggest that ground state properties and reactivity of molecules can be modified when placed inside a nanoscale cavity, giving rise to strong coupling between vibrational modes and the quantized cavity field. This is commonly thought to be caused either by a cavity-distorted Born-Oppenheimer ground state potential or by the formation of light-matter hybrid states, vibrational polaritons. Here, we systematically study the effect of a cavity on ground state properties and infrared spectra of single molecules, considering vibration-cavity coupling strengths from zero up to the vibrational ultrastrong coupling regime. Using single-mode models for Li-H and O-H stretch modes and for the NH₃ inversion mode, respectively, a single cavity mode in resonance with vibrational transitions is coupled to position-dependent molecular dipole functions. We address the influence of the cavity mode on polariton ground state energies, equilibrium bond lengths, dissociation energies, activation energies for isomerization, and on vibro-polaritonic infrared spectra. In agreement with earlier work, we observe all mentioned properties being strongly affected by the cavity, but only if the dipole self-energy contribution in the interaction Hamiltonian is neglected. When this term is included, these properties do not depend significantly on the coupling anymore. Vibro-polaritonic infrared spectra, in contrast, are always affected by the cavity mode due to the formation of excited vibrational polaritons. It is argued that the quantized nature of vibrational polaritons is key to not only interpreting molecular spectra in cavities but also understanding the experimentally observed modification of molecular reactivity in cavities.

Nonequilibrium effects of cavity leakage and vibrational dissipation in thermally activated polariton chemistry

In vibrational strong coupling (VSC), molecular vibrations strongly interact with the modes of an optical cavity to form hybrid light-matter states known as vibrational polaritons. Experiments show that the kinetics of thermally activated chemical reactions can be modified by VSC. Transition-state theory, which assumes that internal thermalization is fast compared to reactive transitions, has been unable to explain the observed findings. Here, we carry out kinetic simulations to understand how dissipative processes, namely, those introduced by VSC to the chemical system, affect reactions where internal thermalization and reactive transitions occur on similar timescales. Using the Marcus-Levich-Jortner type of electron transfer as a model reaction, we show that such dissipation can change reactivity by accelerating internal thermalization, thereby suppressing nonequilibrium effects that occur in the reaction outside the cavity. This phenomenon is attributed mainly to cavity decay (i.e., photon leakage), but a supporting role is played by the relaxation between polaritons and dark states. When nonequilibrium effects are already suppressed in the bare reaction (the reactive species are essentially at internal thermal equilibrium throughout the reaction), we find that reactivity does not change significantly under VSC. Connections are made between our results and experimental observations.

Cavity frequency-dependent theory for vibrational polariton chemistry

Recent experiments demonstrate the control of chemical reactivities by coupling molecules inside an optical microcavity. In contrast, transition state theory predicts no change of the reaction barrier height during this process. Here, we present a theoretical explanation of the cavity modification of the ground state reactivity in the vibrational strong coupling (VSC) regime in polariton chemistry. Our theoretical results suggest that the VSC kinetics modification is originated from the non-Markovian dynamics of the cavity radiation mode that couples to the molecule, leading to the dynamical caging effect of the reaction coordinate and the suppression of reaction rate constant for a specific range of photon frequency close to the barrier frequency. We use a simple analytical non-Markovian rate theory to describe a single molecular system coupled to a cavity mode. We demonstrate the accuracy of the rate theory by performing direct numerical calculations of the transmission coefficients with the same model of the molecule-cavity hybrid system. Our simulations and analytical theory provide a plausible explanation of the photon frequency dependent modification of the chemical reactivities in the VSC polariton chemistry.

Controlling the Photostability of Pyrrole with Optical Nanocavities

Strong light-matter coupling provides a new strategy to manipulate the non-adiabatic dynamics of molecules by modifying potential energy surfaces. The vacuum field of nanocavities can couple strongly with the molecular degrees of freedom and form hybrid light-matter states, termed as polaritons or dressed states. The photochemistry of molecules possessing intrinsic conical intersections can be significantly altered by introducing cavity couplings to create new conical intersections or avoided crossings. Here, we explore the effects of optical cavities on the photo-induced hydrogen elimination reaction of pyrrole. Wave packet dynamics simulations have been performed on the two-state, two-mode model of pyrrole, combined with the cavity photon mode. Our results show how the optical cavities assist in controlling the photostability of pyrrole and influence the reaction mechanism by providing alternative dissociation pathways. The cavity effects have been found to be intensely dependent on the resonance frequency. We further demonstrate the importance of the vibrational cavity couplings and dipole-self interaction terms in describing the cavity-modified non-adiabatic dynamics.

Ring polymer quantization of the photon field in polariton chemistry

We use the ring polymer (RP) representation to quantize the radiation field inside an optical cavity to investigate polariton quantum dynamics. Using a charge transfer model coupled to an optical cavity, we demonstrate that the RP quantization of the photon field provides accurate rate constants of the polariton mediated electron transfer reaction compared to Fermi's golden rule. Because RP quantization uses extended phase space to describe the photon field, it significantly reduces the computational costs compared to the commonly used Fock state description of the radiation field. Compared to the other quasi-classical descriptions of the photon field, such as the classical Wigner based mean-field Ehrenfest model, the RP representation provides a much more accurate description of the polaritonic quantum dynamics because it alleviates the potential quantum distribution leakage problem associated with the photonic degrees of freedom (DOF). This work demonstrates the possibility of using the ring polymer description to treat the quantized radiation field in polariton chemistry, offering an accurate and efficient approach for future investigations in cavity quantum electrodynamics.

Polarized Fock States and the Dynamical Casimir Effect in Molecular Cavity Quantum Electrodynamics

We present a new theoretical framework, polarized Fock states (PFSs), to describe the coupled molecule-cavity hybrid system in quantum electrodynamics. Through the quantum light-matter interactions under the dipole Gauge, the molecular permanent dipoles polarize the photon field by displacing the photonic coordinate. Hence, it is convenient to use these shifted Fock states (termed the PFSs) to describe light-matter interactions under the strong coupling regimes. These PFSs are nonorthogonal to each other and are light-matter entangled states. They allow an intuitive understanding of several phenomena that go beyond the prediction of the quantum Rabi model, while also offering numerical convenience to converge the results with much fewer states. With this powerful new theoretical framework, we explain how molecular permanent dipoles lead to the generation of multiple photons from a single electronic excitation (down-conversion), effectively achieving the dynamical Casimir effect through the nuclear vibration instead of cavity mirror oscillations.

Virial Relations for Electrons Coupled to Quantum Field Modes

In this work, we present a set of virial relations for many electron systems coupled to both classical and quantum fields, described by the Pauli-Fierz Hamiltonian in dipole approximation and using length gauge. Currently, there is growing interest in solutions of this Hamiltonian because of its relevance for describing molecular systems strongly coupled to photonic modes in cavities and in the possible modification of chemical properties of such systems compared to the ones in free space. The relevance of such virial relations is demonstrated by showing a connection to mass renormalization and by providing an exact way to obtain total energies from potentials in the framework of quantum electrodynamical density functional theory.

Resolution of Gauge Ambiguities in Molecular Cavity Quantum Electrodynamics

This work provides the fundamental theoretical framework for molecular cavity quantum electrodynamics by resolving the gauge ambiguities between the Coulomb gauge and the dipole gauge Hamiltonians under the electronic state truncation. We conjecture that such ambiguity arises because not all operators are consistently constrained in the same truncated electronic subspace for both gauges. We resolve this ambiguity by constructing a unitary transformation operator that properly constrains all light-matter interaction terms in the same subspace. We further derive an equivalent and yet convenient expression for the Coulomb gauge Hamiltonian under the truncated subspace. We finally provide the analytical and numerical results of a model molecular system coupled to the cavity to demonstrate the validity of our theory.

Controllable Frequency Dependence of Resonance Energy Transfer Coupled with Localized Surface Plasmon Polaritons

We investigate the intrinsic characteristics of resonance energy transfer (RET) coupled with localized surface plasmon polaritons (LSPPs) from the perspective of macroscopic quantum electrodynamics. To quantify the effect of LSPPs, we propose a numerical scheme that allows us to accurately calculate the rate of RET between a donor-acceptor pair near a nanoparticle. Our study shows that LSPPs can be used to enhance the RET rate significantly and control its frequency dependence by modifying a core/shell structure, which indicates the possibility of RET rate optimization. Moreover, we systematically explore the angle (distance) dependence of the RET rate and analyze its origin. According to different frequency regimes, the angle dependence of RET is dominated by different mechanisms, such as LSPPs, surface plasmon polaritons (SPPs), and anti-resonance. For the proposed core/shell structure, the characteristic distance of RET coupled with LSPPs (approximately 0.05 emission wavelength) is shorter than that of RET coupled with SPPs (approximately 0.1 emission wavelength), which may provide promising applications in energy science.

Polariton-Mediated Electron Transfer via Cavity Quantum Electrodynamics

We investigate the polariton-mediated electron transfer reaction in a model system with analytic rate constant theory and direct quantum dynamical simulations. We demonstrate that the photoinduced charge transfer reaction between a bright donor state and dark acceptor state can be significantly enhanced or suppressed by coupling the molecular system to the quantized radiation field inside an optical cavity. This is because the quantum light-matter interaction can influence the effective driving force and electronic couplings between the donor state, which is the hybrid light-matter excitation, and the molecular acceptor state. Under the resonance condition between the photonic and electronic excitations, the effective driving force can be tuned by changing the light-matter coupling strength; for an off-resonant condition, the same effect can be accomplished by changing the molecule-cavity detuning. We further demonstrate that using both the electronic coupling and light-matter coupling helps to extend the effective couplings across the entire system, even for the dark state that carries a zero transition dipole. Theoretically, we find that both the counter-rotating terms and the dipole self-energy in the quantum electrodynamics Hamiltonian are important for obtaining an accurate polariton eigenspectrum as well as the polariton-mediated charge transfer rate constant, especially in the ultrastrong coupling regime.

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light-matter systems, the presented results also indicate conditions under which those effects might become accessible.

Resonant catalysis of thermally activated chemical reactions with vibrational polaritons

Interaction between light and matter results in new quantum states whose energetics can modify chemical kinetics. In the regime of ensemble vibrational strong coupling (VSC), a macroscopic number [Formula: see text] of molecular transitions couple to each resonant cavity mode, yielding two hybrid light-matter (polariton) modes and a reservoir of [Formula: see text] dark states whose chemical dynamics are essentially those of the bare molecules. This fact is seemingly in opposition to the recently reported modification of thermally activated ground electronic state reactions under VSC. Here we provide a VSC Marcus-Levich-Jortner electron transfer model that potentially addresses this paradox: although entropy favors the transit through dark-state channels, the chemical kinetics can be dictated by a few polaritonic channels with smaller activation energies. The effects of catalytic VSC are maximal at light-matter resonance, in agreement with experimental observations.

Investigating New Reactivities Enabled by Polariton Photochemistry

We perform quantum dynamics simulations to investigate new chemical reactivities enabled by cavity quantum electrodynamics. The quantum light-matter interactions between the molecule and the quantized radiation mode inside an optical cavity create a set of hybridized electronic-photonic states, so-called polaritons. The polaritonic states adapt the curvatures from both the ground and the excited electronic states, opening up new possibilities to control photochemical reactions by exploiting intrinsic quantum behaviors of light-matter interactions. With quantum dynamics simulations, we demonstrate that the selectivity of a model photoisomerization reaction can be controlled by tuning the photon frequency of the cavity mode or the light-matter coupling strength, providing new ways to manipulate chemical reactions via the light-matter interaction. We further investigate collective quantum effects enabled by coupling the quantized radiation mode to multiple molecules. Our results suggest that in the resonance case, a photon is recycled among molecules to enable multiple excited state reactions, thus effectively functioning as a catalyst. In the nonresonance case, molecules emit and absorb virtual photons to initiate excited state reactions through fundamental quantum electrodynamics processes. These results from quantum dynamics simulations reveal basic principles of polariton photochemistry as well as promising reactivities that take advantage of intrinsic quantum behaviors of photons.