  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, intensity-dependent. 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.
