Instead of a quantum harmonic oscillator description, the cavity photonic mode is now characterized by the continuous phase-space variables p t c and x t c . Classical trajectories are generated based on Hamilton's equations of motion, as in the Ehrenfest method, where the nuclear force is approximated under the mean-field assumption, obtained by tracing over the time-dependent density matrix ρ(p t c ,x t c ,t). In this approach, the cavity photonic dynamics are governed by