On the Theory of Casimir-Polder Forces

TL;DR

This paper investigates the magnetic Casimir-Polder forces on atoms near various materials, including superconductors, using quantum field theory and numerical analysis to understand how material properties influence these forces.

Contribution

It provides a theoretical framework for magnetic Casimir-Polder forces near different materials, including superconductors, and compares quantum dynamics with electric dipole interactions.

Findings

Repulsive Casimir-Polder forces are derived for various materials.

Superconductor properties are modeled using Mattis-Bardeen theory.

Numerical results show dependence of forces on geometry and material properties.

Abstract

We consider the energy shift for an atom close to a non-magnetic body with a magnetic moment coupled to a quantized magnetic field. The corresponding repulsive Casimir-Polder force is obtained for a perfect conductor, a metal, a dielectric medium, with dielectric properties modeled by a Drude formula, and a superconductor at zero temperature. The dielectric properties of the superconductor is obtained by making use of the Mattis-Bardeen linear response theory and we present some useful expressions for the low-frequency conductivity. The quantum dynamics with a given initial state is discussed in terms of the well-known Weisskopf-Wigner theory and is compared with corresponding results for a electric dipole coupling. The results obtained are compatible with a conventional master equation approach. In order to illustrate the dependence on geometry and material properties, numerical results are presented for the ground state using a two-level approximation.