Geometric phase for a static two-level atom in cosmic string spacetime

We investigate the geometric phase of a static two-level atom immersed in a bath of fluctuating vacuum electromagnetic field in the background of a cosmic string. Our results indicate that due to the existence of the string, the geometric phase depends crucially on the position and the polarizability of the atom relative to the string. This can be ascribed to the fact that the presence of the string profoundly modify the distribution of electric field in Minkowski spacetime. So in principle, we can detect the cosmic string by experiments involving geometric phase.