Excited state contribution to the Casimir-Polder force at finite temperature

Abstract

Using the master equation we calculate the contribution of the excited state of a two-level atom to its interacting potential with a perfectly conducting wall at finite temperature. For low temperature, $\hbar \omega_0/k_B T = k_0 \lambda_T\gg 1$, where $\omega_0 = k_0 c$ is the transition frequency of the atom and $\lambda_T$ is the thermal wavelength, we show that this contribution is very small $(\propto e^{-k_0\lambda_T})$. In the opposite limit $(k_0\lambda_T \ll 1)$, however, we show that the expression for the interacting potential, for all relevant distance regimes, becomes exactly the same as that for very short distances $(k_0 z \ll 1)$ and with the field in the vacuum state.