Casimir-Polder repulsion: Three-body effects

TL;DR

This paper investigates three-body effects on Casimir-Polder forces, demonstrating that such effects are generally small and exploring the conditions under which repulsive forces can occur between atoms and macroscopic bodies.

Contribution

It extends the electromagnetic multiple-scattering formalism to three-body interactions and analyzes the impact of three-body effects on Casimir-Polder repulsion in various geometries.

Findings

Three-body effects are small in atom-plate interactions.

Three-body corrections do not significantly alter Casimir-Polder repulsion at large distances.

Highly anisotropic nanoparticles may be more feasible for observing repulsive Casimir-Polder forces.

Abstract

In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction of an atom with a conducting screen possessing a slit, or between two parallel wires. To this end we further extend the electromagnetic multiple-scattering formalism for three-body interactions. To test this machinery we reinvestigate the interaction of a polarizable atom between two parallel conducting plates. In that case, three-body effects are shown to be small, and are dominated by three- and four-scattering terms. The atom-wedge calculation is illustrated by an analogous scalar situation, described in the Appendix. The wedge-wedge-atom geometry is difficult to analyze because this is a scale-free problem. But it is not so hard to investigate the three-body corrections to the interaction between an anisotropic atom or nanoparticle and a pair of parallel conducting cylinders, and show that the three-body effects are very small and do not affect the Casimir-Polder repulsion at large distances between the cylinders. Finally, we consider whether such highly anisotropic atoms needed for repulsion are practically realizable. Since this appears rather difficult to accomplish, it may be more feasible to observe such effects with highly anisotropic nano particles.