Dynamical properties of a two-level atom in three variants of the two-photon q-deformed Jaynes-Cummings model

Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three variants of the two-photon q-deformed Jaynes-Cummings model. The model is based on the generalized deformed oscillator algebra, [(A) over cap,(A) over cap (+)] = ((N) over cap + 1)f(2)((N) over cap + 1) - (N) over capf(2)((N) over cap) in which f((N) over cap) as a function of number operator (N) over cap determines not only the intensity dependence of atom-field coupling, when the model Hamiltonian is expressed in terms of non-deformed field operators, but also the structure of initial state of the radiation field. With the field initially being in three different types of q-deformed coherent states, each of them corresponding to a particular form of the function f (1), the quantum collapse and revival effects as well as atomic dipole squeezing are studied for both on- and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures, which are absent in the non-deformed Jaynes-Cummings model, and the magnitude of dipole squeezing may be increased.