  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.
