Topology and Interactions in the Photonic Creutz and Creutz‐Hubbard Ladders

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, 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—are suggested. First, 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. The inclusion of a repulsive Hubbard‐type interaction term, which can give rise to repulsively bound pairs termed doublons, is then considered. 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. The latest advances have allowed photonic quantum simulators to realize an increasing number of quantum exotic phenomena, such as topological or strongly correlated systems. In this paper, different photonic setups are suggested and numerical results are provided to analyze the interplay between flat band dynamics, topology, and Hubbard interactions in a quasi‐1D topological insulator: the Creutz ladder.