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

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.