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The Journal of Physical Chemistry Letters

Simulation of the Pump–Probe Spectra and Bright State Dynamics of Molecular Polaritons

Yulong Ding, Chun Hui Huang, Yinjia Chen, Shuming Bai, Qiang Shi

Published Dec 26, 2025• 2 citations
Publisher

Abstract

We employed the Tavis-Cummings model to study the pump-probe spectra of molecular polaritons. To describe the dissipative effects caused by the environment, the population decays of the photon mode and the two level states (TLSs), as well as the fast component of the dephasing of TLSs, are described by using the Lindblad equation. The effect of static disorder in the TLS transition frequency is incorporated into the equation of motion of the density matrix. The pump-probe spectra of the model system are calculated using the optical response function approach. Pronounced Rabi oscillations are observed in the pump-probe spectra, which are signatures of the strong light-matter coupling between the cavity mode and the collective bright state of the TLSs. To help understand the pump-probe spectra, we also simulate the laser pulse induced dynamics of the bright state of the molecular polaritons. The results show that the bright state lifetime is primarily determined by the dephasing time of the TLSs, consistent with the fast decay of the Rabi oscillations observed in the pump-probe spectra. Once the coherence decays, the long-time pump-probe response is dominated by the excited state population of the dark state manifold.

DOI
10.1021/acs.jpclett.5c03570

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We employed the Tavis-Cummings model to study the pump-probe spectra of molecular polaritons. To describe the dissipative effects caused by the environment, the population decays of the photon mode and the two level states (TLSs), as well as the fast component of the dephasing of TLSs, are described by using the Lindblad equation. The effect of static disorder in the TLS transition frequency is incorporated into the equation of motion of the density matrix. The pump-probe spectra of the model system are calculated using the optical response function approach. Pronounced Rabi oscillations are observed in the pump-probe spectra, which are signatures of the strong light-matter coupling between the cavity mode and the collective bright state of the TLSs. To help understand the pump-probe spectra, we also simulate the laser pulse induced dynamics of the bright state of the molecular polaritons. The results show that the bright state lifetime is primarily determined by the dephasing time of the TLSs, consistent with the fast decay of the Rabi oscillations observed in the pump-probe spectra. Once the coherence decays, the long-time pump-probe response is dominated by the excited state population of the dark state manifold.
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.
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.
Davydov trial states, in combination with the Green's function method, we study the dynamics of the Tavis-Cummings model and the Holstein-Tavis-Cummings model in the presence of diagonal disorder and cavity-qubit coupling disorder. For the Tavis-Cummings model, time evolution of the photon population, the optical absorption spectra, and the hetero-entanglement between the qubits and the cavity mode are calculated by using the Green's function method to corroborate numerically exact results of Davydov's Ansätze. For the Holstein-Tavis-Cummings model, only the latter is utilized to simulate effects of disorder on the photon population dynamics and the absorption spectra. We have demonstrated that the complementary employment of analytical and numerical methods permits uncovering a fairly comprehensive picture of a variety of complex behaviors in disordered multidimensional polaritonic cavity quantum electrodynamics systems.
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light–matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis–Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
The fast dynamics of molecular polaritonics is scrutinized theoretically through the implementation of two-dimensional spectroscopy protocols. We derive conceptually simple and computationally efficient formulas to calculate two-dimensional spectra for molecules, each of them modeled as a system of two electronic states including vibrational relaxation, immersed in an optical cavity, thus coupled to quantized radiation. Cavity photon losses and molecular relaxation are incorporated into the Hamiltonian dynamics to form an open quantum system that is solved through a master equation. In the collective case, the relaxation dynamics into dark states is revealed to be the crucial factor to explain the asymmetries in both the diagonal and cross peaks of two-dimensional spectra for long waiting times between excitation and detection, a feature shown by recent experiments. Our theoretical method provides a deeper insight in those processes that yield relevant signals in multidimensional molecular spectroscopy.
Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.