Theoretical methods based on linear response theory to simulate dynamics and absorption spectra of molecular polaritons

In this work, we first derive path integral expressions for the dynamics of molecular polaritons in microcavities. For systems with a large number of molecules in the cavity, i.e., in the thermodynamic limit, it is shown that linear response theory can be employed to describe the molecular response, which can be further modeled by an effective harmonic bath. This leads to analytical path integral expressions for the Dicke model, as well as its extensions that incorporate effects of static disorder and coupling to intramolecular vibrational degrees of freedom. The hierarchical equations of motion are then derived to simulate polariton dynamics and absorption spectra. By further taking advantage of the harmonic nature of both the system and the effective bath, an efficient exact diagonalization method is also obtained. Similar results are also obtained for the Tavis-Cummings model, the rotating-wave approximation of the Dicke model. Utilizing these theoretical findings, we simulate the polariton dynamics and absorption spectra and analyze the critical coupling strength for the superradiant transition in the presence of static disorder and coupling to intramolecular vibrational motion.