We also compared the population dynamics of different vibrational states outside and inside a resonant cavity, as shown in Fig. . For the molecule outside the cavity, after a transient fluctuation due to the establishment of the molecule-solvent entanglement, the population in various states reaches a steady distribution in the long-time regime, where the flux-side correlation function plateaus. Placing the molecule inside a resonant cavity leads to a strong oscillation in the intermediate time period (100fs < t < 1000fs). The long-time population is unaffected by the cavity mode.