Abstract
In this paper, we study the time evolution of the geometric phase and nonlocal correlations for a three-level atom interacting with the quantum field emerged in a nonlinear Kerr medium. We discuss the dependence of the physical quantifiers on the phase damping effect. We examine the effects of the initial state and different system parameters on the evolution of the nonlocal correlation and geometric phase with and without the phase damping effect. Furthermore, we explore the link between the geometric phase and the nonlocal correlation during the time evolution. Finally, we show that the model proposed will be very useful to avoid the phase damping effect by a proper choice of the physical parameters in the field for both cases of the initial pure and mixed states of the three-level atom.