Entropy and entanglement in the mixed state for a dispersive JC model in a phase-damped cavity

Temporal evolution is studied for total entropy, the entropy difference and the sum of negative eigenvalues of the partially transposed density matrix as quantitative entanglement measurements for JC model in a phase-damped cavity in the dispersive approximation. The cavity field is assumed to be coupled to a reservoir with a phase-damping coupling. The case of a statistical mixture (SM) of coherent states is considered as initial field state. The effects of cavity phase damping on the entanglement between the field and the atom are studied.