Lamb shift multipolar analysis

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.