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

Shunsuke Furukawa,Masahito Ueda

doi:10.1088/1367-2630/17/11/115014

Abstract

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 periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be 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.

Highlights

While the main focus of the studies of topological phases has been placed on fermionic systems, atomic systems offer unique opportunities to study their bosonic counterparts in a controllable manner
It is interesting to ask how the topological properties of Bloch bands are carried over to Bogoliubov excitation bands, which are the elementary excitations of weakly interacting Bose-Einstein condensates (BEC) in optical lattices
We show that the topological properties of Bloch bands for the noninteracting case are smoothly carried over to Bogoliubov excitation bands for the interacting case, and that the parameter ranges displaying topological bands extend with increasing the Hubbard interaction or the particle density

Summary

Introduction

Topological insulators and superconductors have attracted great attention in recent years for their rich variety of quantized responses and robust gapless edge states which originate from nontrivial topology of bulk Bloch bands. Ultracold atomic systems have recently joined as a new platform for exploring the physics of topological phases, especially due to ongoing experimental developments for engineering synthetic gauge fields required to produce such phases.

Results

Conclusion