Classification of three-photon states in waveguide quantum electrodynamics

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 order, chaos and localization found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localized states unique to three-photon systems such as bound trimers, corner states, and trimer edge states.