When Do Classical Fields Mimic Quantum-Light-Induced Molecular-Dynamics?

By using the Feshbach projection formalism, the problem on wether quantum-cavity chemistry can be mimicked by classical fields is addressed. Specifically, the following theorem is shown:

Consider a molecular system described by the Hamiltonian $H_m$ , with support on the Hilbert space $\mathcal{H}_m$, in interaction with a photon field characterized by the Hamiltonian $H_{bph}$, with support on the Hilbert space $H\mathcal{bph}$. If the state of the photon field is aimed not to be measured, then, up to second order in the interaction, it is not posible to distinguish between the dynamics induced by a classical electric field having the same statistics as the quantum electric field and the actual quantum photon field.

This theorem allows for understanding recent results on quantum-cavity chemistry and provides a solid ground for exploring genuinely quantum dynamics assisted by quantum-cavity states.