Rydberg atoms and beams of ultracold polar molecules have become highly useful experimental tools in recent years. There is therefore a need for accessible calculations of interaction potentials between such particles and nearby surfaces and structures, bearing in mind that the particles are far out of thermal equilibrium with their environment and that their interaction is predominantly nonretarded. Based on a new perturbative expansion with respect to the inverse speed of light and the inverse conductivity, we derive a simple, closed-form expression for the interaction potential (i.e., the particle energy level shifts) of a particle and a metallic sphere that is accurate at better than the 1$\%$ level for typical experimental setups at room temperature and above and off by no more than a few percent at any temperature including zero. Our result illuminates the influence of retardation and imperfect conductivity and the interplay of these effects with geometry. The method developed for the present study may be applied to other, more complex geometries.

• Received 12 July 2011

DOI:https://doi.org/10.1103/PhysRevA.85.022503