Classification of three-photon states in waveguide quantum electrodynamics

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