Casimir interaction between a dielectric nanosphere and a metallic plane

TL;DR

This paper calculates the Casimir interaction between a dielectric nanosphere and a metallic plane using multiple scattering theory, providing exact results and asymptotic forms relevant for quantum nanosphere-surface studies.

Contribution

It offers the first exact calculations of Casimir forces for dielectric nanospheres near metallic surfaces using realistic models, extending previous approximate formulas.

Findings

Exact Casimir interaction results for dielectric nanospheres and metallic planes.

Asymptotic expressions for small spheres and various distances.

Recovery of the Casimir-Polder formula in the small sphere limit.

Abstract

We study the Casimir interaction between a dielectric nanosphere and a metallic plane, using the multiple scattering theory. Exact results are obtained with the dielectric described by a Sellmeier model and the metal by a Drude model. Asymptotic forms are discussed for small spheres, large or small distances. The well-known Casimir-Polder formula is recovered at the limit of vanishingly small spheres, while an expression better behaved at small distances is found for any finite value of the radius. The exact results are of particular interest for the study of quantum states of nanospheres in the vicinity of surfaces.