where R j and P j are the "initial" nuclear configuration at time t j , c j ≡ {c a (t j )} and cj ≡ {c a (t j )} are the complex forward and backward coefficients at time t j . Here, the time t j (for t j ∈ {t 1 , t 2 , t 3 }) are the times at which the system is perturbed with a laser. The quantity ρ(j) represents the reduced system density matrix after applying the perturbation at time t j-1 , with an initial state of ρ(j-1) = c nj-1 |n j-1 ⟩⟨ñ j-1 |c * ñj-1 , and evolved during the time t ∈ [t j-1 , t j ]. The evolved density matrix elements can be expressed as