The aim of this study is to investigate an effective two-level atom coupled to a two-mode f-deformed cavity field with and without the rotating wave approximation. The first section discusses the theoretical model of the interaction between a two-mode cavity-field and an effective two-level atom within the framework of an f-DJCM without the rotating wave approximation. After that, we obtain the reduced density matrix of the atom with and without the rotating-wave approximation. Then, we have investigated the effect of the counter-term on temporal evolution of various non-classical properties of the atom, i.e., atomic population inversion, atomic dipole squeezing and atom-field entanglement. Particularly, we compare the numerical result for three different values of the deformation parameter q (q=1, q=1.1, q=1) with and without the rotating wave approximation.
