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

Abstract

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, [Â,Â+] = (N̂ + 1)f2(N + 1) - N̂f2(N̂) in which f(N̂) as a function of number operator N̂ 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(N̂), 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. © 2004 The Physical Society of Japan.