The influence of a surface in the non-retarded interaction between two atoms

TL;DR

This paper derives analytical formulas for non-additive dispersive interactions between two atoms near arbitrary conducting surfaces in the non-retarded regime, revealing how surfaces influence atomic forces with potential experimental relevance.

Contribution

It introduces a mapping of a three-body quantum problem into a two-body electrostatic problem, providing new analytical tools for surface-atom interaction analysis.

Findings

Non-additivity effects can be significant near surfaces.

Surface shape and configuration alter atomic interaction strength.

Interactions are suppressed in certain geometries like plate capacitors.

Abstract

In this work we obtain analytical expressions for the non-additivity effects in the dispersive interaction between two atoms and perfectly conducting surface of arbitrary shape in the non-retarded regime. We show that this three bodies quantum-mechanical problem can be solved by mapping it into a two-bodies electrostatic one. We apply the general formulas developed in this paper in several examples. Firstly we re-derive the London interaction as a particular case of our formalism. Then we treat two atoms in the presence of a plane, re-obtained the result displayed in the literature. After we add some new examples. A particularly interesting one is two atoms inside a plate capacitor, a situation where non-additivity is very manifest since the plates lead to the exponentially suppression of the interaction of the atoms, provided the atoms are separated by a distance of the order of the distance between the plates or greater. Our results holds even in the presence of other atoms inside the plate capacitor. As a last example we deal with two atoms in the presence of a sphere, both grounded and isolated. We show that for realistic experimental parameters the non-additivity may be relevant for the force in each atom.