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, [\hat{A},\hat{A}⁺]=(\hat{N}+1)f²(\hat{N}+1)-\hat{N}f²(\hat{N}) in which f(\hat{N}) as a function of number operator \hat{N} 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(\hat{N}), 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.