Casimir repulsion beyond the dipole regime

TL;DR

This paper investigates Casimir forces beyond the dipole approximation, revealing an intermediate regime of strong repulsion that transitions to attraction at very close distances, with potential enhancements but still below detectable levels.

Contribution

It extends previous Casimir repulsion results to more complex geometries and analyzes the force behavior beyond the dipole regime through numerical methods.

Findings

Intermediate repulsive regime with increased force at certain distances

Rapid transition from repulsion to attraction as separation decreases

Enhanced repulsive force with extended conductor geometries by a factor of ~1000

Abstract

We extend a previous result [Phys. Rev. Lett. 105, 090403 (2010)] on Casimir repulsion between a plate with a hole and a cylinder centered above it to geometries in which the central object can no longer be treated as a point dipole. We show through numerical calculations that as the distance between the plate and central object decreases, there is an intermediate regime in which the repulsive force increases dramatically. Beyond this, the force rapidly switches over to attraction as the separation decreases further to zero, in line with the proximity force approximation. We demonstrate that this effect can be understood as a competition between an increased repulsion due to a larger polarizability of the central object interacting with increased fringing fields near the edge of the plate, and attractive forces due primarily to the nonzero thickness of the plate. In comparison with our previous work, we find that using the same plate geometry but replacing the single cylinder with a ring of cylinders, or more generally an extended uniaxial conductor, the repulsive force can be enhanced by a factor of approximately $10^3$. We conclude that this enhancement, although quite dramatic, is still too small to yield detectable repulsive Casimir forces.