Topological bands for ultracold atoms

There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence…

• NS
  National Science Foundation
• SF
  Simons Foundation
• NI
  National Institute of Standards and Technology
• EA
  Engineering and Physical Sciences Research Council

  Awards: EP/K030094/1, EP/P009565/1, EP/P009565/1, EP/K030094/1
• AF
  Air Force Office of Scientific Research
• AR
  Army Research Office
• HE
  H2020 European Research Council