Atom-atom interactions at and between metal surfaces at nonzero temperature

We have investigated the temperature-dependent Casimir-Polder interaction between two oscillators in the proximity of metal surfaces. The interaction near a single metal surface has much in common with the interaction in free space. However, at any finite temperature the long-range asymptote is equal to the high-temperature asymptote. This asymptote, which originates not from the n=0 term in the Matsubara summation but from thermal population of the n>0 terms, is F(R)=-2k_BTα₀²/R⁶. This should be compared with the more rapidly decaying zero-temperature Casimir-Polder asymptote, F(R)≈-13ħcα₀²/(2πR⁷). The interaction in the midplane between two metallic surfaces is very different. The nonretarded interaction decreases exponentially and the interaction is dominated by an enhanced Casimir-Polder-like asymptote. At large separations this asymptote also decays exponentially. For any relevant temperatures the long-range asymptote is no longer equal to the high-temperature limit. In other words crossover to a classical limit found for the long-range interaction in free space, and on a metal surface, is not always valid in a narrow cavity.