atom-photon thermal entanglement in onlinear jaynes-cummings models

in this work we investigate the thermal entanglement between two-level atoms and photons in a nonlinear cavity. we consider intensity-dependent couplings and calculate the negativity, as a measure of atom-photonentanglement. the cavity is assumed to be at a temperature t, so that all number of photons, and at the same time, both atomic states, with definite probabilities, are present. we then demonstrate a condition under which the intensity-dependent coupling leads to entanglement. it is also shown that, as in the case of linear jaynes- cummings model, the thermal states of atoms and photons are never separable.