Geometric phase acquired by the two-level atom with different trajectories in cosmic string scalar field

We consider the geometric phase induced by the two-level atom with inertial and uniformly accelerated motion, which is coupled to massless scalar field in cosmic string spacetime. Our result shows that when the atom is very close to the string, the geometric phase of cosmic string spacetime is ν times that of Minkowski spacetime. By comparing phase difference induced by the inertial and accelerated motion, we find the sensitive dependence of the phase difference on deficit angle parameter, transition frequencies of the atom, atomic acceleration and the initial state parameter. We also obtain phase difference increases with deficit angle parameter and the atomic acceleration. Although reaching the measurable magnitude of geometric phase requires extremely high acceleration, the detection experiment may be implemented in the future. Our work may suggest a possible way to detect cosmic string scalar field by using geometric phase.