Enhanced repulsively and attractively bound atom pairs in topological optical lattice ladders

Inspired by the growing interest in using cold-atoms in optical lattices to explore the effects of strong interactions in topological band structures, we investigate phases in the Cruetz ladder and Lieb lattice which are both characterised by flat energy bands. By investigating realistic experimental implementations of the Creutz ladder, we understand how the lattice topology enhances the properties of interacting bound pairs giving rise to large pair-tunnelling which can lead to robust pair superfluidity. We also investigate fermions in a Lieb ladder at half filling where we show that pair correlations are also enhanced even when there is strong mixing with dispersive bands. We identify schemes for preparation of these phases via time-dependent parameter variation and look at ways to detect and characterise these systems in an experiment. This work provides a starting point for investigating the interplay between the effects of topology, interactions and pairing in more general systems, with potential future connections to quantum simulation of topological materials.