is the α th electronic adiabatic wavefunction parameterized by the nuclear positions at time t , R(t ), and |n ⟩ is the time-independent photonic Fock state. The time-dependent electronic-photonic wavefunction |Φ (t ) ⟩ is evolved by approximating the time-dependent Schrödinger equation (TDSE), i ∂ ∂t |Ψ(t ) ⟩ = ĤPF |Ψ(t ) ⟩ (see Eqs. 13 and 18), as the following set of differential equations for the expansion coefficients in the adiabatic-Fock basis,