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

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