The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom-field interaction is considered to be, in general, intensitydependent. We suppose that the nonlinearity of the initial generalized coherent state of the field and the intensity-dependent coupling between atom and field are distinctly chosen. Interestingly, an exact analytical solution for the time evolution of the state of atom-field system can be found in this general regime in terms of the nonlinearity functions. Finally, the presented formalism has been applied to a few known physical systems such as Gilmore-Perelomov and Barut-Girardello coherent states of SU (1, 1) group, as well as a few special cases of interest. Mean photon number and atomic population inversion will be calculated, in addition to investigating particular non-classicality features such as revivals, sub-Poissonian statistics and quadratures squeezing of the obtained states of the entire system. Also, our results will be compared with some of the earlier works in this particular subject.

A theoretical scheme is presented for generating Gazeau-Klauder coherent states (GKCSs) via the generalization of degenerate Raman interaction with coupling constant to intensity-dependent coupling. Firstly, we prove that in the intensitydependent degenerate Raman interaction, under particular conditions, the modified effective Hamiltonian can be used instead of Hamiltonian in the interaction picture, for describing the atom-field interaction. We suppose that the cavity field is initially prepared in a nonlinear CS, which is not temporally stable. As we will observe, after the occurrence of the interaction between atom and field, the generated state involves a superposition of GKCSs which are temporally stable and initial nonlinear CS. Under specific conditions which may be prepared, the generated state just includes GKCS. So, in this way we produced the GKCS, successfully.

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