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In this paper, to study the effects of a nonlinear medium on the atom-fieldinteraction, we use the nonlinear coherent states approach. For this purpose,we choose the two-mode cross-Kerr as the our nonlinear optical phenomena andwith the use of it's algebra, we show that it can be described equivalently bya deformed oscillator algebra and also, by a deformed (su(2)) algebra. Then, weconstruct the associated coherent states and investigate their statisticalproperties. After that, as an example of applicability of the constructedtwo-mode nonlinear coherent states, we investigate the nonlinear effects of themedium on the dynamics of atom-field interaction within the framework of thecoherent states. By using the time-dependent Schr\"odinger equation, we firstobtain the atom-field state and then study the effect of the nonlinear mediumon the occupation probabilities of the atomic levels. In the following, weconsider the relation between the revival time of the atomic occupationprobabilities and the nonlinear parameter of the medium. Then, to study thenonlinear effects on the dynamical properties of the cavity field, we considerphoton distribution, correlation function, Mandel parameters of the field, thevon Neumann entropy and the squeezing. Particularly, the nonlinearity of themedia on the nonclassical properties of two modes is clarified.

Nonlinear optical effects on the atom-field interaction based on the nonlinear coherent states approach