  In this paper, we investigate the possibility of the entanglement swapping
between two independent nonperfect cavities consisting of an atom with finite
lifetime of atomic levels (as two independent sources of dissipation) which
interacts with a quantized electromagnetic field in the presence of detuning
and Kerr medium. In fact, there is no direct interaction between the two atoms,
therefore, no entanglement exists between them. We use the Bell state
measurement performing on the photons leaving the cavities to swap the
entanglement stored between the atom-fields in each cavity into atom-atom. Our
motivation is arisen from the fact that two-qubit entangled states are of
enough interest for quantum information science and technologies. We discuss
the effect of initial state of the system, detuning parameter, the Kerr medium
and the two dissipation sources on the swapped entanglement to atom-atom. We
interestingly find that when the atomic decay rates and photonic leakages from
the cavities are equal, our system behaves as an ideal system with no
dissipation. Our results show that it is possible to create a long-living
atom-atom maximally entangled state in the presence of Kerr effect and
dissipation; we determine these conditions in detail and also establish the
final atom-atom Bell state.
