Dynamics of entanglement of atoms with two-photon transitions induced by a thermal field

In this paper, we investigate the entanglement between two two-level atoms non-resonantly interacting with a thermal field of a lossless one-mode resonator via degenerate two-photon transitions. On the basis of the exact solution of the time-dependent density matrix we calculate the negativity as a measure of atomic entanglement. We show that for separable initial atomic states a slight atom-field detuning may generate the high amount of atom-atom entanglement. The results also show that for non-resonant atom-field interaction the entanglement induced by nonlinear two-photon interaction is smaller than that induced by one-photon interaction in contrast to the resonant interaction situation. For a Bell-type entangled initial atomic state we obtain that if the detuning increases, there is an appreciable decrease in the amplitudes of the negativity oscillations. The results also show that elimination of the sudden death of entanglement for non-resonant two-photon atom-field interaction may take place.