Abstract
In this paper we consider the problem of the interaction between a three-level atom and a quantized bimodal cavity field. The coupling parameter between the atom and the field is taken to be time-dependent by taking the atomic motion into consideration. In the absence of the detuning parameter Delta as well as the Kerr-like medium chi the analytic solution of the wave function is obtained. In our examination of the atomic population the phenomenon of collapses and revivals is observed, however, after a considerable period of time. It is also shown that under the effect of the acceleration parameter delta(0) the state of the system loses purity and becomes partially mixed. In the examination of the geometric phase we have observed the regularity behavior when the velocity parameter delta(1) takes place, while, in the presence of the Kerr-like medium chi, the system shows irregular behavior.