Multipole expansion for dispersion forces -- watch this trace

TL;DR

This paper examines the validity of the traceless multipole assumption in light-matter interactions, revealing that higher-order multipoles like the octupole contribute to dispersion forces beyond electrostatics.

Contribution

It demonstrates that multipoles beyond the quadrupole are not always traceless and that octupole trace contributions affect Casimir-Polder interactions.

Findings

Trace of octupole moment influences Casimir-Polder forces

Higher multipoles contribute beyond electrostatic approximation

Revises understanding of multipole expansion in dispersion forces

Abstract

Light-matter interaction models invariably rely on the multipole expansion of the electromagnetic potentials generated by complex charge distributions. These multipoles are typically taken to be traceless, however, for a correct evaluation of dispersion forces at all distances, the validity of this assumption has to be checked carefully. Here, we revisit the concept of dispersion forces on an atom near a dielectric surface from the perspective of macroscopic quantum electrodynamics and find that, beyond the quadrupole, the multipoles cannot always be taken as fully traceless. In particular, we show that the trace of the octupole moment contributes to Casimir-Polder interactions beyond the electrostatic regime.