Influence of strong molecular vibrations on decoherence of molecular polaritons

We derive the transition rates, dephasing rates, and Lamb shifts for a system consisting of many molecules collectively coupled to a resonant cavity mode. Using a variational polaron master equation, we show that strong vibrational interactions inherent to molecules give rise to multi phonon processes and suppress the light--matter coupling. In the strong light--matter coupling limit, multi-phonon contributions to the transition and dephasing rates strongly dominate over single phonon contributions for typical molecular parameters. This leads to novel dependencies of the rates and spectral line widths on the number of molecules in the cavity. We also find that vibrational Lamb shifts can substantially modify the polariton energies in the strong light--matter coupling limit.