Non-Abelian gauge fields and topological insulators in shaken optical lattices

TL;DR

This paper explores how time-periodic lattice shaking can generate artificial gauge fields in optical lattices, enabling control over topological phases and non-Abelian gauge fields in various lattice geometries.

Contribution

It provides concrete proposals for creating and manipulating topological and non-Abelian gauge fields using shaken optical lattices, expanding the toolkit for quantum simulation.

Findings

Controlled creation of Dirac cones in shaken kagome lattices

Realization of topological and quantum spin Hall insulators in shaken lattices

Method to generate strong non-Abelian gauge fields in optical lattices

Abstract

Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagom\'e lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-Abelian gauge fields.