Atom-photon, two-mode entanglement and two-mode squeezing in the presence of cross-Kerr nonlinearity

The interaction of two quantized fields and three-level quantum system in a lambda-type configuration is investigated in the presence of cross-Kerr nonlinearity. We consider three models of coupling for the atom-photon interaction. First, we study the dynamical behavior of the atom-photon entanglement and show that increasing the cross-Kerr nonlinearity results in different behaviors in three considered models. Moreover, it is demonstrated that the two quantized modes can be entangled, on the other hand, by applying a classical driving field to the lower levels. Increasing the classical driving field destroys the long time atom-photon entanglement. Our results show that an oscillatory two-mode squeezing can be generated in the absence of a driving classical field and the cross-Kerr nonlinearity.