Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli-Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis-Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.
Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli-Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis-Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.
The field of Polaritonic Chemistry studies molecules strongly coupled to the light field of optical cavities. The resulting modification of the potential energy landscape has been demonstrated to enable control over the chemical and physical properties of materials and molecular ensembles. This thesis extends the Tavis–Cummings model to describe molecules under strong light–matter coupling, incorporating static dipole moments and dipole self-energy contributions derived from the Pauli–Fierz Hamiltonian. These additional terms are shown to be essential for reproducing cavity-modified molecular dynamics and spectra. Simulations on the nuclear wavefunction propagation of MgH+ molecules demonstrate the impact of these terms, while an effective two-level system model accurately captures the behavior of large ensembles. Beyond single excitations, the thesis also explores the higher excitation manifolds of the Tavis-Cummings model, which reveals that allowing for more than a single excitation makes the reaction of the involved polaritons entropically more favorable. Open-system simulations highlight how the coherence of the system's initial state governs decay pathways and enables long-lived energy storage. Finally, a multilevel vibrational model coupled to a two-mode cavity is introduced, where a Raman scheme enables selective mixing of vibrational states. The simulation results show that continuous pumping can drive molecules into specific vibrational states while suppressing electronic excitation, both for single molecules and small ensembles. Together, these results provide new theoretical insights into the mechanisms by which optical cavities reshape molecular energy landscapes. The results suggest approaches for controlling photonic, electronic, and vibrational dynamics in strongly coupled systems, contributing to the theoretical foundation of polariton chemistry.
Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of N anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ${\mathrm{\ensuremath{\Omega}}}_{R}$ is approximately equal to the molecular anharmonic shift $2\mathrm{\ensuremath{\Delta}}$. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible ${S}_{0}\ensuremath{\rightarrow}{S}_{1}\ensuremath{\rightarrow}{S}_{2}$ transitions) and strongly interact with a UV-visible cavity.
We analyze vibrational dynamics in a toy model for polaritonic chemistry under collective electronic strong coupling. In a Holstein-Tavis-Cummings model, incoherently excited by a photon, we show that disorder leads to non-Gaussian states of vibrational modes on short time scales at the single-molecule level. Using exact matrix product state simulations, we demonstrate that this effect can remain robust for larger molecule numbers, implying that nuclear wave packets cannot be effectively described by thermal states. Furthermore, we compare simulations of the exact quantum dynamics with semiclassical approximations. We find that the Ehrenfest approximation can only well reproduce ensemble-averaged observables for very large system sizes. Also simulations in the truncated Wigner approximation fail to capture the non-Gaussian effects. Our work highlights the importance of disorder and genuine quantum effects in cavity-modified nuclear dynamics in polaritonic chemistry.
Modifications of chemical reaction rates via strong light-matter coupling at mid-infrared regime has attracted significant interest in physics and chemistry in recent years. However, despite numerous efforts, there is currently no general theory that can fully describe the available experimental evidence. We implement an open quantum system model to describe the suppression of the intracavity reaction rate for alcoholysis of phenyl isocyanate with cyclohexanol in infrared Fabry-Perot cavities. The model considers the three molecular modes observed in the infrared absorption spectrum of phenyl isocyanate in the region of interest. The results point out that suppression of intracavity reaction rates is modified when a cavity is resonant with specific molecular modes of the reactant [1]. We derive analytical expressions using a reduced model that explains the role of light-matter coherences and molecular disorder in the modifications of intracavity chemical processes. Our findings significantly improve our understanding of cavity-modified chemistry by tuning cavity modes with different molecular modes. [1] W.Ahn, J.F. Triana, F. Recabal, F. Herrera, B.S. Simpkins . Chemrxiv, wb6vs (2022)
Harnessing strong light-matter interactions to control chemical reactions in confined electromagnetic fields offers a promising route toward deepening our understanding of chemical dynamics at the collective quantum-mechanical level, with potential implications for future chemical synthesis paradigms. Achieving this goal, however, requires an in-depth mechanistic understanding of underlying dynamical processes. As a step in this direction, we present a systematic and numerically exact quantum dynamical study of cooperative reaction dynamics inside an optical microcavity. Using a hierarchy of model systems with increasing complexity, we elucidate how cavity-modified reactivity emerges from-and is highly sensitive to-subtle structural and environmental variations. Our models consist of optically dark reactive molecules, each represented by a symmetric double well potential, coupled to infrared-active non-reactive intramolecular or solvent vibrational modes, as well as their respective dissipative environments. Our results demonstrate that cavity-induced rate modifications arise from a delicate interplay among mode hybridization in strong-coupling regimes, the dynamical balance of all participating energy exchange processes, and quantum interference between multiple fluctuation-dissipation-mediated reaction pathways enabled by collective cavity coupling. By continuously tuning a single system parameter or introducing molecular collectivity, we observe qualitatively distinct rate modification profiles as functions of the cavity frequency, including resonant rate enhancement, resonant rate suppression, hybridization-induced peak splitting, and, notably, asymmetric Fano-type line shapes in which enhancement peaks and suppression dips coexist within a narrow resonance window, highlighting the important role of quantum interference in cavity-modified chemical reactivity.
Harnessing strong light-matter interactions to control chemical reactions in confined electromagnetic fields offers a promising route toward deepening our understanding of chemical dynamics at the collective quantum-mechanical level, with potential implications for future chemical synthesis paradigms. Achieving this goal, however, requires an in-depth mechanistic understanding of the underlying dynamical processes. As a step in this direction, we present a systematic and numerically exact quantum dynamical study of cooperative reaction dynamics inside an optical microcavity. Using a hierarchy of model systems with increasing complexity, we elucidate how cavity-modified reactivity emerges from-and is highly sensitive to-subtle structural and environmental variations. Our models consist of optically dark reactive molecules, each represented by a symmetric double well potential, coupled to infrared-active non-reactive intramolecular or solvent vibrational modes, as well as their respective dissipative environments. Our results demonstrate that cavity-induced rate modifications arise from a delicate interplay among mode hybridization in strong-coupling regimes, the dynamical balance of all participating energy exchange processes, and quantum interference between multiple fluctuation-dissipation-mediated reaction pathways enabled by collective cavity coupling. By continuously tuning a single system parameter or introducing molecular collectivity, we observe qualitatively distinct rate modification profiles as functions of the cavity frequency, including resonant rate enhancement, resonant rate suppression, hybridization-induced peak splitting, and, notably, asymmetric Fano-type line shapes in which enhancement peaks and suppression dips coexist within a narrow resonance window, highlighting the important role of quantum interference in cavity-modified chemical reactivity.