Discussion on the geometric phase for an open two-level system in the cosmic string spacetime with torsion

We investigate the geometric phase for a two-level atom interacting with massless scalar field in the background spacetime of a cosmic string with torsion in the framework of open quantum systems. We show that the geometric phase depends on not only the inherent properties of this atom but also on the topological properties of the background spacetime. The correction to the geometric phase of the atom derives from a composite effect of the cosmic string and screw dislocation associated with the curvature and torsion, respectively. The numerical results of the correction to the geometric phase are also present. It is seen that the modification of the phase oscillates around zero and the amplitude of the correction decreases gradually, with the increase of the distance r between the atom and line defects. When the atom gets close to the line defects, the correction will increase significantly but finally tend to a finite value. The behavior of the geometric phase with the variation of the atomic position in three different types of topological defect spacetimes, i.e., the cosmic string spacetime, screw dislocation spacetime and cosmic string spacetime with torsion, are also shown. We note that the geometric phase in the case of cosmic string spacetime is different from that of other two spacetimes, which suggests that the presence of torsion can significantly affect the geometric phase of the atom, especially in the region near the topological defects. In addition, the geometric phase for the two-level atom which results from the thermal fluctuation of the thermal bath is studied. It is shown that the geometric phase increases with the growth of the temperature T. Copyright (C) EPLA, 2019