Topological quantum matter with cold atoms

Abstract

This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different systems, which produced both fascinating physics findings and exciting opportunities for applications. Among the physical systems that have been considered to realize and probe these intriguing phases, ultracold atoms become promising platforms due to their high flexibility and controllability. Quantum simulation of topological phases with cold atomic gases is a rapidly evolving field, and recent theoretical and experimental developments reveal that some toy models originally proposed in condensed matter physics have been realized with this artificial quantum system. The purpose of this article is to introduce these developments. The article begins with a tutorial review of topological invariants and the methods to control parameters in the Hamiltonians of neutral atoms. Next, topological quantum phases in optical lattices are introduced in some detail, especially several celebrated models, such as the Su–Schrieffer–Heeger model, the Hofstadter–Harper model, the Haldane model and the Kane–Mele model. The theoretical proposals and experimental implementations of these models are discussed. Notably, many of these models cannot be directly realized in conventional solid-state experiments. The newly developed methods for probing the intrinsic properties of the topological phases in cold-atom systems are also reviewed. Finally, some topological phases with cold atoms in the continuum and in the presence of interactions are discussed, and an outlook on future work is given.

Keywords:

• Topological matter
• cold atoms
• Chern number and topological invariants
• optical lattices
• artificial gauge fields

PACS:

• 67.85.-d Ultracold gases
• trapped gases
• 03.75.Ss Degenerate Fermi gases
• 73.43.Nq Quantum phase transitions
• 71.10.Fd Lattices Fermi models
• 03.75.Lm TunnelingJosephson effect
• Boson-Einstein condensates in periodic potentials
• solitons
• vortices
• and topological excitations
• 03.65.Vf Phases: geometric
• dynamic ortopological

Acknowledgments

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the NKRDP of China [grant no. 2016YFA0301803], the NSFC [grant nos. 11604103, 11474153, 91636218, and 11874201], the NSAF [grant nos. U1830111 and U1801661], the NSF of Guangdong Province [grant no. 2016A030313436], the KPST of Guangzhou [grant no. 201804020055], and the Startup Foundation of SCNU.