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.

Dropping an impurity into a Chern insulator: A polaron view on topological matter

“…In parallel to the identification of novel topological properties in single-particle band structures [4][5][6], intense efforts are dedicated to the rich interplay of topological bands and inter-particle interactions [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In addition to condensed-matter systems, topological band structures have also been studied in the context of ultracold gases [21][22][23]. These atomic systems are particularly well suited to investigate the role of interactions in topological phases [24][25][26][27][28][29][30], since the interaction strength between neutral atoms can be easily tuned experimentally [31].…”

Topological gapless matters in three-dimensional ultracold atomic gases

“…Compared with solid-state materials, cold atoms provide a clean and highly controllable platform to simulate Hamiltonians. In the context of topology, there has been remarkable progress made in cold atoms in both topological insulators and topological gapless matters 111,112 . For topological insulators, the Zak phase was observed in a 1D dimerized optical lattice 113 , and the Haldane model, the Chern band and the Harper Hamiltonian were experimentally realized in cold atoms [114][115][116][117][118][119][120] .…”

Polaron in a p+ip Fermi topological superfluid

“…The study of topological matter has attracted much attention in recent years [1][2][3][4][5][6][7][8]. Whereas topological bands and phases in noninteracting systems are well understood by now, the interplay of interaction and topological bands is still under extensive study [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”