Fig. presents the population dynamics of the vibrational states outside the cavity (dashed lines) and coupled to a resonant cavity for ω c = ω 0 = 1172 cm -1 (solid lines). The temperature is T = 300 K, the light-matter coupling strength is η c = 0.1, the characteristic frequency of the photon-loss bath is γ c → ∞, and the cavity lifetime is set to be τ c = 200 fs (in line with the cavity used in the typical VCS experiments ). The initial condition is described in Eq. 33, which corresponds to a thermally activated process of the system by the environment. The populations of the six lowest vibrational states are presented, including |ν L (golden) in panel a, as well as |ν R (blue) |ν L (red), |ν R (green), |ν 4 (dark gray), |ν 5 (light gray) in panel b. Fig. presents the population dynamics of |ν L state (the initially populated state). One can clearly see that when the resonant cavity mode (ω c = ω 0 = 1172 cm -1 ) is coupled to the molecular vibrations (solid line), the population of |ν L decays much faster than the cavity-free case (dashed line). Fig. shows the population dynamics of the other five vibrational states, with the lower panel zooms into the short-time dynamics.