  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.
