Periodic behavior of collapse–revival phenomenon in the full nonlinear interaction between a three-level atom and a single-mode field

In this paper based on a generalization of the Jaynes–Cummings model we solve the dynamical Hamiltonian describing the interaction between a (ΛΛ or V-type) three-level atom and a single-mode field in the “full nonlinear regime” and then the analytical form of state vector of the system is explicitly obtained. In this manner, we encountered with “intensity-dependent detuning” as well as “intensity-dependent atom–field coupling” in our two models. Via choosing an appropriate deformation function (which imposes nonlinearity to the system) we consider the influence of Kerr-like medium from which the resonance condition for a selected number of quanta is achieved (selective transition is occurred). Furthermore, by these considerations, we may find the optimum values for atom–field coupling constants which provide a regular periodic behavior of probability amplitudes for the two considered atomic systems. Moreover, to show this periodic time behavior, the temporal evolution of the probability of the allowed atomic transitions as well as the Mandel parameter (as a non-classical sign) is depicted for various circumstances. As is observed, complete revivals may appear in some particular situations.