Two atoms in dissipative cavities in dispersive limit: entanglement sudden death and long-lived entanglement

We investigate the entanglement dynamics and coherence of two two-level atoms interacting with two coherent fields of two spatially separated and dissipative cavities. It is in particular shown that entanglement sudden death is obtained within a short interaction time. However, after a long interaction time a long-lived entanglement is shown; that is, the initial entanglement of two atoms could be partially preserved. In addition, the coherence of the two atoms will not be lost during the evolution.