Modification of energy shifts of atoms by the presence of a boundary in a thermal bath and the Casimir-Polder force

We study the modification by the presence of a plane wall of energy-level shifts of two-level atoms which are in multipolar coupling with quantized electromagnetic fields in a thermal bath in a formalism which separates the contributions of thermal fluctuations and radiation reaction and allows a distinct treatment to atoms in the ground and excited states. The position-dependent energy shifts give rise to an induced force acting on the atoms. We are able to identify three different regimes where the force shows distinct features and examine, in all regimes, the behaviors of this force in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, thus providing some physical insights into the atom-wall interaction at finite temperature. In particular, we show that both the magnitude and the direction of the force acting on an atom may have a clear dependence on the atomic polarization directions. In certain cases, a change in relative ratio of polarizations in different directions may result in a change in direction of the force.