Recoherence in the entanglement dynamics and classical orbits in theN-atom Jaynes-Cummings model

The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation $J_z.$ Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase-space projection associated with the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase-space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase-space borderline) is, in general, responsible for oscillations in the entanglement properties.