Fluctuation induced quantum interactions between compact objects and a plane mirror

TL;DR

This paper develops a comprehensive method to calculate quantum fluctuation-induced interactions, including Casimir forces, between compact objects and a mirror plane, applicable to scalar and electromagnetic fields across all distances.

Contribution

It generalizes a recent approach to include arbitrary boundary conditions and dielectric objects, providing accurate interaction calculations over all separations.

Findings

Derived interaction formulas using scattering matrices.

First all-separation results for electromagnetic Casimir force between sphere and mirror.

Extended Casimir-Polder potential to dielectric spheres with multipole polarizabilities.

Abstract

The interaction of compact objects with an infinitely extended mirror plane due to quantum fluctuations of a scalar or electromagnetic field that scatters off the objects is studied. The mirror plane is assumed to obey either Dirichlet or Neumann boundary conditions or to be perfectly reflecting. Using the method of images, we generalize a recently developed approach for compact objects in unbounded space [1,2] to show that the Casimir interaction between the objects and the mirror plane can be accurately obtained over a wide range of separations in terms of charge and current fluctuations of the objects and their images. Our general result for the interaction depends only on the scattering matrices of the compact objects. It applies to scalar fields with arbitrary boundary conditions and to the electromagnetic field coupled to dielectric objects. For the experimentally important electromagnetic Casimir interaction between a perfectly conducting sphere and a plane mirror we present the first results that apply at all separations. We obtain both an asymptotic large distance expansion and the two lowest order correction terms to the proximity force approximation. The asymptotic Casimir-Polder potential for an atom and a mirror is generalized to describe the interaction between a dielectric sphere and a mirror, involving higher order multipole polarizabilities that are important at sub-asymptotic distances.