Relative Energy Shift of a Two-Level Atom in a Cylindrical Spacetime

We investigate the evolution dynamics of a two-level atom system interacting with the massless scalar field in a Cylindrical spacetime. We find that both the energy shifts of ground state and excited state can be separated into two parts due to the vacuum fluctuations. One is the corresponding energy shift for a rest atom in four-dimensional Minkowski space without spatial compactification, the other is just the modification of the spatial compactified periodic length. It will reveal that the influence of the presence of one spatial compactified dimension can not be neglected in Lamb shift as the relative energy level shift of an atom.