Casimir-Polder potential and transition rate in resonating cylindrical cavities

We consider the Casimir-Polder potential of particles placed inside a metallic cylindrical cavity at finite temperatures, taking account of thermal nonequilibrium effects. In particular, we study how the resonant ( thermal nonequilibrium) potential and transition rates can be enhanced by fine tuning the radius of the cavity to match the transition wavelength of the dominant transitions of the particle. Numerical calculations show that the cavity-induced energy-level shift of atoms prepared in low-lying Rydberg states can be enhanced beyond 30 kHz, which is within the range of observability of modern experiments. Because the magnitude of the resonance peaks depends sensitively on the low-frequency dissipation of the cavity metal, experiments in this setup could be a critical test of the disputed thermal correction to the Casimir force between metal plates.