Radiative Energy Shifts of an Atom Coupled to the Derivative of a Scalar Field near a Reflecting Boundary

We study the radiative energy level shifts of a two-level atom in dipole coupling to the derivative of a massless scalar quantum field in a spacetime with a perfectly reflecting boundary, and calculate the contributions of vacuum fluctuations and radiation reaction to the level shift. It is found that the energy level shift of the excited state is an oscillating function of the atom's distance from the boundary and it can either be positive or negative, while that of the ground state is always positive. The most remarkable feature is that the energy level shift of the ground state behaves like 1/z⁴ when the atom's distance from the boundary, z, is very large as compared to the transition wavelength of the atom, while it behaves like 1/z³ when z is very small.