Tuning quantum-classical correspondence for atomic and molecular systems in a cavity

We show that the correspondence between quantum and classical mechanics can be tuned by varying the coupling strength between an atom or a molecule and the modes of a cavity. In the acceleration gauge (AG) representation, the cavity-matter system is described by an effective Hamiltonian, with a non-trivial coupling appearing in the potential, and with renormalized masses. Importantly, and counterintuitively, the AG coupling changes non-monotonically with the strength of the cavity-matter interaction. As a result, one obtains an effective (approximately decoupled) cavity-matter dynamics both for the case of weak and strong interactions. In the weak coupling regime, the effective mass parameters essentially coincide with their standard interaction free counterparts. In contrast, the renormalized atomic/molecular mass increases as the cavity-matter interaction is increased. This results in AG dynamics of matter governed by a conventionally looking atomic/molecular Hamiltonian, whose effective Planck constant is reduced when the cavity-matter interaction is increased.