Influence of Stark shift on entanglement of two atoms with degenerate two-photon transitions for entangled and disentangled initial states

Considering two-atom degenerate two-photon Jaynes–Cummings model, we investigate the atom–atom entanglement when (a) atoms and field are prepared initially in the entangled atom-field W- or GHZ state, (b) two atoms are prepared initially in the coherent disentangled state and the cavity field is prepared in a few-photon Fock state, and study the effect of the Stark shift on entanglement. The results show that the atom–atom negativity evolves periodically with time and the periods are affected by the Stark shift and the degree of the initial atomic coherence. Considering different initial states we derived that the atom–atom entanglement can be greatly increased or decreased due to the presence of the Stark shift. In addition, the entanglement sudden death effect vanishes due to the presence of Stark shift for some initial states.