The time-evolution of entanglement in the interacting System of the atom and coherence field with phase decoherence

We investigate the time evolution of the entanglement in the interacting system of a single two-level atom and a single mode coherence field with phase decoherence and discuss the influences of the coupling constant of light and atoms,mean photon number of light and detuning.The results show that the oscillating frequency of the entanglement of the system will increase with the increasing of the coupling constant of light and atoms and the mean photon number of light.The influence of the detuning on time evolution of the entanglement is obvious without phase decoherence and the quantum state of the field and atom will stay in a most entangled state for a long time when the detuning is proper.The phase decoherence causes the fading of entanglement when the system is resonant and it will fade to zero at last.The entanglement of the system is a fading oscillation at first with phase decoherence.The detuning restrains the phase decoherence with the time evolution.In this case the entanglement of the system will not fade to zero at last.The oscillating amplitude of the entanglement is lessening at first and the entanglement will quickly become a constant value with the increasing of detuning.The system will stay in an entangled state with phase decoherence if the detuning is proper.