Casimir-Polder interaction between a polarizable particle and a plate with a hole

TL;DR

This paper calculates the exact non-retarded Casimir-Polder interaction between a polarizable particle and a reflecting sheet with a hole, revealing orientation-dependent potential features that could enable particle trapping.

Contribution

It provides the first exact analysis of the Casimir-Polder interaction involving a surface with a hole, highlighting orientation effects and potential trapping applications.

Findings

Interaction depends strongly on dipole orientation.

Two saddle points for perpendicular polarization.

Single saddle point at the aperture center for parallel polarization.

Abstract

We determine exactly the non-retarded Casimir-Polder interaction between a neutral but polarizable particle and a perfectly reflecting sheet containing a circular hole. The calculation reveals a strong dependence of the interaction on the orientation of the particle's electric dipole moment with respect to the surface. For a dipole moment that is polarized perpendicularly to the surface the interaction potential has two saddle points lying above and below the plane of the surface, on a line through the centre of the aperture. For a dipole moment that is polarized parallel to the surface there is only one saddle point right in the middle of the aperture. Provided the particles' motion could be confined to a line through the middle of the aperture, this effect could potentially be used for population-sensitive trapping of particles.