Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders

TL;DR

This paper explores how photonic systems can simulate topological and interaction effects in the Creutz ladder, including localization phenomena and bound states, advancing quantum simulation capabilities.

Contribution

It proposes experimental protocols and models for studying topology, flat band dynamics, and interactions in photonic Creutz ladders, including a scheme for implementing a two-particle bosonic model.

Findings

Observation of Aharonov-Bohm localization in noninteracting systems

Identification of regimes with localized pairs and free particles

Scheme for photonic realization of a bosonic Creutz-Hubbard model

Abstract

The latest advances in the field of photonics have enabled the simulation of an increasing number of quantum models in photonic systems, turning them into an important tool for realizing exotic quantum phenomena. In this paper we suggest different ways in which these systems can be used to study the interplay between flat band dynamics, topology and interactions in a well-known quasi-1D topological insulator: the Creutz ladder. Firstly, a simple experimental protocol is proposed to observe the Aharonov-Bohm localization in the noninteracting system, and the different experimental setups that might be used for this are reviewed. We then consider the inclusion of a repulsive Hubbard-type interaction term, which can give rise to repulsively bound pairs termed doublons. The dynamics of these quasiparticles are studied for different points of the phase diagram, including a regime in which pairs are localized and particles are free to move. Finally, a scheme for the photonic implementation of a two-particle bosonic Creutz-Hubbard model is presented.