field: Intensity-dependent coupling, deformed Kerr medium and detuning effects'
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Introduction {#sec-intro}
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The Jaynes-Cummings model (JCM) which is extensively used to perform a full quantum mechanical description of the atom-field interaction [@JCM1; @JCM2], gives a pattern to solve the interaction between the single-mode quantized electromagnetic field and the two-level atom in the rotating wave approximation (RWA). Relative facility of this model, in addition to appearing some non-trivial phenomena and remarkable properties such as Rabi oscillations of population inversion (which indicate the energy exchanges between field and matter), the collapses and revivals of these oscillations [@shore] etc gets the model in the core of this field of researches. Moreover, experimental observation of the collapse and subsequent revival, Rabi oscillations and a single-mode two-photon maser has been reported [@walther]. To expand and modify the JCM, many generalizations have been proposed in recent decades. Intensity-dependent (nonlinear) JCM was suggested in [@suk1; @suk2] where the dependence of atom-field coupling on the light intensity is described, and then has been used by others [@selective1; @selective2; @selective3]. Dynamical behavior of the JCM beyond the RWA has been studied in [@naderi] in which the effects of the counter-rotating terms on various dynamical properties such as the 