Dynamical behaviour of the entanglement between two spatially separated atoms under the influence of dissipation

We consider two two-level atoms, which are located in two independent dissipative cavities. The two atoms are initially prepared in the singlet state. We investigate the influence of dissipation on the entanglement between the two atoms. In the case of resonance the degree of the entanglement can fall abruptly to zero, which is the so-called sudden death of entanglement. It is noted that when two atoms are in a common environment, the singlet state is a decoherence-free state. When the dispersive limit is fulfilled, the degree of entanglement between the two atoms is oscillating at first, then it arrives at a steady value, which increases with the increase of the damping constant κ; when both fields are initially in the vacuum state, the entanglement between the two atoms will not decay.