Identifying Vibrations that Control Non-adiabatic Relaxation of Polaritons in Strongly Coupled Molecule-Cavity Systems

Optical-cavity manipulation strategies of singlet fission systems mediated by conical intersections: Insights from fully quantum simulations

We offer a theoretical perspective on simulation and engineering of polaritonic conical-intersection-driven singlet-fission (SF) materials. We begin by examining fundamental models, including Tavis-Cummings and Holstein-Tavis-Cummings Hamiltonians, exploring how disorder, non-Hermitian effects, and finite temperature conditions impact their dynamics, setting the stage for studying conical intersections and their crucial role in SF. Using rubrene as an example and applying the numerically accurate Davydov Ansatz methodology, we derive dynamic and spectroscopic responses of the system and demonstrate key mechanisms capable of SF manipulation, viz. cavity-induced enhancement/weakening/suppression of SF, population localization on the singlet state via engineering cavity-mode excitation, polaron/polariton decoupling, and collective enhancement of SF. We outline unsolved problems and challenges in the field and share our views on the development of the future lines of research. We emphasize the significance of careful modeling of cascades of polaritonic conical intersections in high excitation manifolds and envisage that collective geometric phase effects may remarkably affect the SF dynamics and yield. We argue that the microscopic interpretation of the main regulatory mechanisms of polaritonic conical-intersection-driven SF can substantially deepen our understanding of this process, thereby providing novel ideas and solutions for improving conversion efficiency in photovoltaics.

Radiative pumping vs vibrational relaxation of molecular polaritons: a bosonic mapping approach

We present a formalism to study molecular polaritons based on the bosonization of molecular vibronic states. This formalism accommodates an arbitrary number of molecules N, excitations and internal vibronic structures, making it ideal for investigating molecular polariton processes accounting for finite N effects. We employ this formalism to rigorously derive radiative pumping and vibrational relaxation rates. We show that radiative pumping is the emission from incoherent excitons and divide its rate into transmitted and re-absorbed components. On the other hand, the vibrational relaxation rate in the weak linear vibronic coupling regime is composed of a O ( 1 / N ) contribution already accounted for by radiative pumping, and a O ( 1 / N 2 ) contribution from a second-order process in the single-molecule light-matter coupling that we call polariton-assisted Raman scattering. This scattering is enhanced when the difference between fluorescence and lower polariton frequencies matches a Raman-active excitation.

Trajectory-based non-adiabatic simulations of the polariton relaxation dynamics

We benchmark the accuracy of various trajectory-based non-adiabatic methods in simulating the polariton relaxation dynamics under the collective coupling regime. The Holstein-Tavis-Cummings Hamiltonian is used to describe the hybrid light-matter system of N molecules coupled to a single cavity mode. We apply various recently developed trajectory-based methods to simulate the population relaxation dynamics by initially exciting the upper polariton state and benchmark the results against populations computed from exact quantum dynamical propagation using the hierarchical equations of motion approach. In these benchmarks, we have systematically varied the number of molecules N, light-matter detunings, and the light-matter coupling strengths. Our results demonstrate that the symmetrical quasi-classical method with γ correction and spin-mapping linearized semi-classical approaches yield more accurate polariton population dynamics than traditional mixed quantum-classical methods, such as the Ehrenfest and surface hopping techniques.

Role of Vibronic Coupling for the Dynamics of Intersystem Crossing in Eu3+ Complexes: an Avenue for Brighter Compounds

Understanding the dynamics of photophysical processes in Ln3+ complexes remains challenging due to the intricate nature involving the metallic center, where sensitization (antenna effect) plays a pivotal role. Current studies have often overlooked the vibronic coupling within the antenna effect, leading to incomplete insights into excited-state dynamics. To address these shortcomings, we introduce a novel theoretical and computational approach that leverages the impact of the vibrational modes of the S1 and T1 states in this effect through the correlation function formalism, offering a comprehensive view of intersystem crossing (ISC). Our approach achieves a desirable alignment between empirical and theoretical rates, outperforming previously employed semiclassical methods. A groundbreaking finding is that vibronic coupling with vibrations in the 700-1600 cm-1 energy range is crucial for higher ISC, and local vibrational mode analysis identified that this process is driven by delocalized vibrations across the molecule. These results shed light on the key molecular fragments responsible for vibronic coupling, opening an avenue for harnessing faster ISC by tailoring the ligand scaffold. Overall, it also demonstrates how ISC dynamics can serve as a bridge between theory and experiment, furnishing detailed mechanistic insights and a roadmap for the development of brighter compounds.

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

Simulations of photoinduced processes with the exact factorization: state of the art and perspectives

This perspective offers an overview of the applications of the exact factorization of the electron-nuclear wavefunction to the domain of theoretical photochemistry, where the aim is to gain insights into the ultrafast dynamics of molecular systems via simulations of their excited-state dynamics beyond the Born-Oppenheimer approximation. The exact factorization offers an alternative viewpoint to the Born-Huang representation for the interpretation of dynamical processes involving the electronic ground and excited states as well as their coupling through the nuclear motion. Therefore, the formalism has been used to derive algorithms for quantum molecular-dynamics simulations where the nuclear motion is treated using trajectories and the electrons are treated quantum mechanically. These algorithms have the characteristic features of being based on coupled and on auxiliary trajectories, and have shown excellent performance in describing a variety of excited-state processes, as this perspective illustrates. We conclude with a discussion on the authors' point of view on the future of the exact factorization.

Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics

We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories. The analysis of the time-dependent potentials of the theory along with the assessment of the performance of CTMQC allows us to point out some limitations of the current approximations used in CTMQC. Meanwhile, comparing CTMQC with other trajectory-based algorithms, namely multi-trajectory Ehrenfest and Tully surface hopping, demonstrates the better quality of CTMQC predictions.

Thermal disorder prevents the suppression of ultra-fast photochemistry in the strong light-matter coupling regime

Strong coupling between molecules and confined light modes of optical cavities to form polaritons can alter photochemistry, but the origin of this effect remains largely unknown. While theoretical models suggest a suppression of photochemistry due to the formation of new polaritonic potential energy surfaces, many of these models do not account for the energetic disorder among the molecules, which is unavoidable at ambient conditions. Here, we combine simulations and experiments to show that for an ultra-fast photochemical reaction such thermal disorder prevents the modification of the potential energy surface and that suppression is due to radiative decay of the lossy cavity modes. We also show that the excitation spectrum under strong coupling is a product of the excitation spectrum of the bare molecules and the absorption spectrum of the molecule-cavity system, suggesting that polaritons can act as gateways for channeling an excitation into a molecule, which then reacts normally. Our results therefore imply that strong coupling provides a means to tune the action spectrum of a molecule, rather than to change the reaction.

Photochemical initiation of polariton-mediated exciton propagation

Placing a material inside an optical cavity can enhance transport of excitation energy by hybridizing excitons with confined light modes into polaritons, which have a dispersion that provides these light-matter quasi-particles with low effective masses and very high group velocities. While in experiments, polariton propagation is typically initiated with laser pulses, tuned to be resonant either with the polaritonic branches that are delocalized over many molecules, or with an uncoupled higher-energy electronic excited state that is localized on a single molecule, practical implementations of polariton-mediated exciton transport into devices would require operation under low-intensity incoherent light conditions. Here, we propose to initiate polaritonic exciton transport with a photo-acid, which upon absorption of a photon in a spectral range not strongly reflected by the cavity mirrors, undergoes ultra-fast excited-state proton transfer into a red-shifted excited-state photo-product that can couple collectively with a large number of suitable dye molecules to the modes of the cavity. By means of atomistic molecular dynamics simulations we demonstrate that cascading energy from a photo-excited donor into the strongly coupled acceptor-cavity states via a photo-chemical reaction can indeed induce long-range polariton-mediated exciton transport.

Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities

The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.

Theory and modeling of light-matter interactions in chemistry: current and future

Light-matter interaction not only plays an instrumental role in characterizing materials' properties via various spectroscopic techniques but also provides a general strategy to manipulate material properties via the design of novel nanostructures. This perspective summarizes recent theoretical advances in modeling light-matter interactions in chemistry, mainly focusing on plasmon and polariton chemistry. The former utilizes the highly localized photon, plasmonic hot electrons, and local heat to drive chemical reactions. In contrast, polariton chemistry modifies the potential energy curvatures of bare electronic systems, and hence their chemistry, via forming light-matter hybrid states, so-called polaritons. The perspective starts with the basic background of light-matter interactions, molecular quantum electrodynamics theory, and the challenges of modeling light-matter interactions in chemistry. Then, the recent advances in modeling plasmon and polariton chemistry are described, and future directions toward multiscale simulations of light-matter interaction-mediated chemistry are discussed.

Tuning the Coherent Propagation of Organic Exciton-Polaritons through the Cavity Q-factor

Transport of excitons in organic materials can be enhanced through polariton formation when the interaction strength between these excitons and the confined light modes of an optical resonator exceeds their decay rates. While the polariton lifetime is determined by the Q(uality)-factor of the optical resonator, the polariton group velocity is not. Instead, the latter is solely determined by the polariton dispersion. Yet, experiments suggest that the Q-factor also controls the polariton propagation velocity. To understand this observation, the authors perform molecular dynamics simulations of Rhodamine chromophores strongly coupled to Fabry-Pérot cavities with various Q-factors. The results suggest that propagation in the aforementioned experiments is initially dominated by ballistic motion of upper polariton states at their group velocities, which leads to a rapid expansion of the wavepacket. Cavity decay in combination with non-adiabatic population transfer into dark states, rapidly depletes these bright states, causing the wavepacket to contract. However, because population transfer is reversible, propagation continues, but as a diffusion process, at lower velocity. By controlling the lifetime of bright states, the Q-factor determines the duration of the ballistic phase and the diffusion coefficient in the diffusive regime. Thus, polariton propagation in organic microcavities can be effectively tuned through the Q-factor.

Multi-scale molecular dynamics simulations of enhanced energy transfer in organic molecules under strong coupling

Exciton transport can be enhanced in the strong coupling regime where excitons hybridize with confined light modes to form polaritons. Because polaritons have group velocity, their propagation should be ballistic and long-ranged. However, experiments indicate that organic polaritons propagate in a diffusive manner and more slowly than their group velocity. Here, we resolve this controversy by means of molecular dynamics simulations of Rhodamine molecules in a Fabry-Pérot cavity. Our results suggest that polariton propagation is limited by the cavity lifetime and appears diffusive due to reversible population transfers between polaritonic states that propagate ballistically at their group velocity, and dark states that are stationary. Furthermore, because long-lived dark states transiently trap the excitation, propagation is observed on timescales beyond the intrinsic polariton lifetime. These insights not only help to better understand and interpret experimental observations, but also pave the way towards rational design of molecule-cavity systems for coherent exciton transport.

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.

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.

Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models

We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.