Exact Casimir-Polder potentials: interaction of an atom with a conductor-patched dielectric surface

TL;DR

This paper provides exact solutions for the Casimir-Polder interaction between an atom and complex conductor-patched dielectric surfaces, including a disc and a bowl, relevant for precision experiments and theoretical understanding.

Contribution

It introduces exact formulas for atom-surface interactions with conductor patches, extending previous approximations and enabling detailed analysis of force behaviors.

Findings

Exact formula for atom near a conducting disc

Intricate behavior of Casimir-Polder force on polarized atoms

Exact expression for atom-bowl interaction

Abstract

We study the interaction between a neutral atom or molecule and a conductor-patched dielectric surface. We model this system by a perfectly reflecting disc lying atop of a non-dispersive dielectric half-space, both interacting with the neutral atom or molecule. We assume the interaction to be non-retarded and at zero temperature. We find an exact solution to this problem. In addition we generate a number of other useful results. For the case of no substrate we obtain the exact formula for the van der Waals interaction energy of an atom near a perfectly conducting disc. We show that the Casimir-Polder force acting on an atom that is polarized in the direction normal to the surface of the disc displays intricate behaviour. This part of our results is directly relevant to recent matter-wave experiments in which cold molecules are scattered by a radially symmetric object in order to study diffraction patterns and the so-called Poisson spot. Furthermore, we give an exact expression for the non-retarded limit of the Casimir-Polder interaction between an atom and a perfectly-conducting bowl.