# Interaction-induced two-photon edge states in extended Hubbard model realized in a cavity array

## TL;DR

This paper theoretically investigates how nonlinear interactions in a cavity array can induce topologically protected two-photon edge states, revealing new localization phenomena for bound photon pairs.

## Contribution

It demonstrates that nonlinear interactions in an extended Hubbard model enable the formation of topologically nontrivial two-photon edge states in a cavity array.

## Key findings

- Nonlinear interactions induce topological edge states for photon pairs.
- Edge states are localized and depend on the interplay of on-site and nonlocal nonlinearities.
- Analytical and numerical results confirm the existence of these bound states.

## Abstract

We study theoretically two-photon states in a periodic array of coupled cavities with both on-site and nonlocal Kerr-type nonlinearities. In the absence of nonlinearity the structure is topologically trivial and possesses no edge states. The interplay of two nonlinear interaction mechanisms described by the extended Hubbard model facilitates formation of edge states of bound photon pairs. Numerical and exact analytical results for the two-photon wave functions are presented. Our findings thus shed light onto the edge states of composite particles and their localization properties.