Interaction-induced topological states of photon pairs

To date, the concept of topological order relies heavily on the properties of single-particle bands. Only recently it has been realized that interactions can have a dramatic impact on topological properties not only modifying the topology of the bands but also creating a topological order in an otherwise trivial system. Applying an extended version of the Bose-Hubbard model, we investigate a system which, being topologically trivial in the single-particle regime, harbors topologically nontrivial edge and interface states of repulsively bound photon pairs. Whereas binding of the photons in this model is captured by a standard local interaction term, an additional direct two-photon hopping renders the system topologically non-trivial. Besides their interaction-induced origin, predicted two-photon edge states exhibit a range of other unexpected features, including the robustness to collapse of the corresponding bulk band and the ability to coexist with the continuum of two-photon scattering states forming a bound state in the continuum. Performing rigorous calculation of the Zak phase for bound photon pairs, we prove the topological origin of the two-photon edge states.