  The purpose of this paper is to investigate some properties through a
three-level $\Xi$-type atom interacting with a two-mode field. We test this
system in the presence of the photon assisted atomic phase damping, detuning
parameter and Kerr nonlinearity. Also, the coupling parameter modulated to be
time-dependent. The problem solution of this model is given by using the
Schr\H{o}dinger equation when the atom and the field are initially prepared in
the excited state and coherent state, respectively. We used the results to
calculate some aspects such as atomic population inversion and concurrence. The
results show that the time-dependent coupling parameter and the detuning
parameter can be considered as a quantum control parameters of the atomic
population inversion and quantum entanglement in the considered model.
