Excitation band topology and edge matter waves in Bose-Einstein condensates in optical lattices

We show that Bose-Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose-Hubbard extension of the Haldane model, which can be realized with recently developed techniques of manipulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.