Classification of three-photon states in waveguide quantum electrodynamics

TL;DR

This paper classifies three-photon eigenstates in a waveguide quantum electrodynamics system, revealing complex hierarchical structures, entanglement features, and unique localized states like trimers and corner states.

Contribution

It provides the first classification of three-photon eigenstates in a finite atomic array coupled to a waveguide, highlighting new localized states and structural hierarchies.

Findings

Hierarchical eigenstate structure in the complex plane

Existence of interaction-induced localized states like trimers and corner states

Extension of two-photon effects to three-photon systems

Abstract

We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the complex plane. The main characteristic eigenstates are explored using entanglement entropy as a distinguishing feature. We show that the rich interplay of effects from order, chaos to localisation found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localised states unique to three-photon systems such as bound trimers, corner states and trimer edge states.