Entanglement dynamics and maintenance for two atoms in coupled cavities

We study the entanglement dynamics for two atoms held in separate cavities which are coupled. We calculate the negativity for the atoms by initially taking the atoms to be maximally entangled as well as taking the cavity fields to be in (i) maximally entangled state 12(|01〉+|10〉) or (ii) completely unentangled state |10〉|10〉. Limited to the particular two examples, we find that in both of the cases a large coupling strength between the cavities maintains the maximal entanglement for the two atoms well; when the coupling strength is small, compared with case (ii), the initially maximally entangled fields only enhance the entanglement for the two atoms at certain times instead of having a total improvement on the entanglement. We also investigate the entanglement dynamics by taking into account the dissipation.