where the laser excitation is applied at time t = 0, and one detects the system response at time t 1 . The trace is performed for all DOFs. In addition, ρ0 represents the initial density matrix of the entire system in equilibrium ground state at t = -∞, (ρ 0 = ρ(-∞)). Further, ρ0 is assumed to be a separable state between the polariton and the phonon bath DOFs as follows