Atomic multipole relaxation rates near surfaces

TL;DR

This paper derives formulas for atomic multipole relaxation rates near surfaces, revealing how these rates depend on distance and material properties, with implications for quantum optics and surface science.

Contribution

It provides a comprehensive theoretical framework for calculating atomic relaxation rates of various multipole orders near absorbing surfaces using electromagnetic Green functions.

Findings

Decay rates depend on atom-surface distance with specific scaling laws.

Explicit formulas for electric and magnetic multipole relaxation rates are derived.

Hierarchy of relaxation rate behaviors near dielectric surfaces is established.

Abstract

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface we find a hierarchy of scaling laws depending on the atom-surface distance z.