Eigenstates of the Atom-Field Interaction and the Binding of Light in Photonic Crystals

TL;DR

This paper derives exact eigenstates for an atom interacting with a quantized field in a cavity, revealing complex bound states and light localization phenomena in photonic crystals, with implications for quantum optics.

Contribution

It introduces a novel mapping of the atom-field problem onto the anisotropic Kondo model, providing exact solutions and insights into light localization in photonic crystals.

Findings

Rich bound state spectrum beyond rotating wave approximation

Recovery of Jaynes-Cummings states in weak coupling limit

Non-perturbative Lamb shifts and decay rates computed

Abstract

We solve for the exact atom-field eigenstates of a single atom in a three dimensional spherical cavity, by mapping the problem onto the anisotropic Kondo model. The spectrum has a rich bound state structure in comparison with models where the rotating wave approximation is made. It is shown how to obtain the Jaynes-Cummings model states in the limit of weak coupling. Non-perturbative Lamb shifts and decay rates are computed. The massive Kondo model is introduced to model light localization in the form of photon-atom bound states in photonic crystals.