Temperature dependence of the energy-level shift induced by the Bose-Einstein condensation of photons

We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose-Einstein condensation of photons. It is found that below the critical temperature Tc, the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.