  We consider the dynamics of atomic and field coherent states in the
non-resonant Dicke model. At weak coupling an initial product state evolves
into a superposition of multiple field coherent states that are correlated with
the atomic configuration. This process is accompanied by the buildup and decay
of atom-field entanglement and leads to the periodic collapse and revival of
Rabi oscillations. We provide a perturbative derivation of the underlying
dynamical mechanism that complements the rotating wave approximation at
resonance. The identification of two different time scales explains how the
dynamical signatures depend on the sign of detuning between the atomic and
field frequency, and predicts the generation of either atomic or field cat
states in the two opposite cases. We finally discuss the restrictions that the
buildup of atom-field entanglement during the collapse of Rabi oscillations
imposes on the validity of semi-classical approximations that neglect
entanglement.
