Entanglement and decoherence of N atoms and a mesoscopic field in a cavity

We investigate the behavior of N atoms resonantly coupled to a single electromagnetic field mode sustained by a high quality cavity, containing a mesoscopic coherent field. We show with a simple effective hamiltonian model that the strong coupling between the cavity and the atoms produces an atom-field entangled state, involving N+1 nearly-coherent components slowly rotating at different paces in the phase plane. The periodic overlap of these components results in a complex collapse and revival pattern for the Rabi oscillation. We study the influence of decoherence due to the finite cavity quality factor. We propose a simple analytical model, based on the Monte Carlo approach to relaxation. We compare its predictions with exact calculations and show that these interesting effects could realistically be observed on a two or three atoms sample in a 15 photons field with circular Rydberg atoms and superconducting cavities