Quantum Entropy of a Nonlinear Two-level Atom with Atomic Motion

The wave function of a system governed by the time-dependent nonlinear Jaynes-Cummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.