Lamb shift multipolar analysis

TL;DR

This paper derives an exact multipole expression for calculating the Lamb shift caused by resonant scatterers on quantum emitters, using multi-scattering theory and Quasi-Normal Modes, with applications to plasmonic nanospheres and dimers.

Contribution

It introduces a novel multipole formula for Lamb shift calculation in complex environments and demonstrates its application to plasmonic nanoparticles and dimers.

Findings

Lamb shift resonance can be blue-shifted by increasing nanoparticle size.

The multipole expression accurately predicts the Lamb shift in various configurations.

Nanoparticles can be used to tune the Lamb shift resonance.

Abstract

It is now well established that radiative decay of quantum emitters can be strongly modified by their environment. In this paper we present an exact, within the weak-coupling approximation, multipole expression to compute the Lamb (frequency) shift induced by an arbitrary set of resonant scatterers on a nearby quantum emitter, using multi-scattering theory. We also adopt a Quasi-Normal Mode description to account for the line shape of the Lamb shift spectrum in the near-field of a plasmonic nanosphere. It is then shown that the Lamb shift resonance can be blue-shifted as the size of the nanoparticle increases, suggesting that nanoparticles may be used to tune this resonant interaction. Finally, a realistic calculation of the Lamb shift is made for a dimer configuration.