where [ρ pl R l (t))] is the reduced density matrix in the polariton basis along a given nuclear trajectory R l (t), with l as the label of the trajectory. Further, U(R l (t)) is the matrix that diagonalize the matrix [V (R l (t))] as shown in Eq. 19, along the same trajectory R l (t). The adiabatic-Fock state population is then obtained from trajectory average as follows