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

Quantum Control of the Time-Dependent Interaction between a Three-Level $\Xi$-Type Atom and a Two-Mode Field with Damping Term