The geometric phase of a two-level atom in a narrow-bandwidth squeezed vacuum

In this paper, we derive the time dependent solution of the effective master equation for the reduced density matrix operator of a two level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum. The results show that the initial state setting, detuning parameter and Rabi frequency play important roles in the evolution of the system dynamics and geometric phase. We present a useful way for controlling the geometric phase variation for the system under consideration.