Topological Quantum Matter with Ultracold Gases in Optical Lattices

Abstract

Since the discovery of topological insulators, many topological phases have been predicted and realized in a range of different systems, providing both fascinating physics and exciting opportunities for devices. And although new materials are being developed and explored all the time, the prospects for probing exotic topological phases would be greatly enhanced if they could be realized in systems that were easily tuned. The flexibility offered by ultracold atoms could provide such a platform. Here, we review the tools available for creating topological states using ultracold atoms in optical lattices, give an overview of the theoretical and experimental advances and provide an outlook towards realizing strongly correlated topological phases.

10 pages, 4 figures. Author-produced version of a Progress Article published in Nature Physics

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• Optical Flux Lattices for Ultracold Atomic Gases
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Topology of density matrices
• Dissipative preparation of Chern insulators
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
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