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

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.