Dressed emitters as impurities

TL;DR

This paper introduces a unified, impurity-based theoretical framework for analyzing dressed states of quantum emitters coupled to photonic baths, enabling model-independent insights and extension to multiple emitters with effective Hamiltonians.

Contribution

It develops a resolvent-based, impurity analogy approach for dressed states, generalizes to multiple emitters, and formalizes properties previously limited to specific models.

Findings

Explicit connection between dressed states and impurity problems.

Model-independent formulation of dressed state properties.

Derivation of dissipationless effective Hamiltonians for multiple emitters.

Abstract

Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular dispersive effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle in a model-independent context a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.