  We investigate the behavior of a circuit QED device when the resonator is
initially populated with a mesoscopic coherent field. The strong coupling
between the cavity and the qubit produces an entangled state involving
mesoscopic quasi-pointer states with respect to cavity dissipation. The overlap
of the associated field components results in collapse and revivals for the
Rabi oscillation. Although qubit relaxation and dephasing do not preserve these
states, a simple analytical description of the dissipative dynamics of the
circuit QED device including cavity relaxation as well as qubit dissipation is
obtained from the Monte-Carlo approach. Explicit predictions for the
spontaneous and induced Rabi oscillation signals are derived and sucessfully
compared with exact calculations. We show that these interesting effects could
be observed with a 10 photon field in forthcoming circuit QED experiments.
