Topological Bands for Ultracold Atoms

TL;DR

This paper reviews recent experimental advances in creating and characterizing topological and geometrical bandstructures in ultracold atomic gases, highlighting methods, observables, and potential many-body phases.

Contribution

It provides a comprehensive overview of the physical principles, experimental techniques, and future directions for topological bands in ultracold atoms, integrating single-particle and many-body perspectives.

Findings

Summary of key concepts in geometry and topology for Bloch bands

Description of methods to generate topological bandstructures in cold atoms

Discussion of physical observables and many-body phases in these systems

Abstract

There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. We describe the different methods that have been used to generate these novel bandstructures for cold atoms, as well as the physical observables that have allowed their characterization. We focus on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. However, we also describe how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, we describe the forms of inter-particle interactions that emerge when atoms are subjected to these energy bands, and some of the many-body phases that may be sought in future experiments.