Synthetic Gauge Fields for Ultra Cold Atoms: A Primer

TL;DR

This paper reviews the principles of gauge invariance in quantum mechanics and explains how light-induced gauge fields can be generated in ultra cold atomic systems, enabling novel quantum simulations and phenomena.

Contribution

It provides a comprehensive primer on creating synthetic gauge fields in ultra cold atoms using light, including Abelian and Non-Abelian cases, with practical examples.

Findings

Light-induced gauge fields can be realized in ultra cold atoms.

Synthetic spin-orbit coupling can be achieved with Raman lasers.

Gauge invariance concepts underpin the generation of these fields.

Abstract

We start by reviewing the concept of gauge invariance in quantum mechanics, for Abelian and Non-Ableian cases. Then we idescribe how the various gauge potential and field can be associated with the geometrical phase acquired by a quantum mechanical wave function while adiabatically evolving in a parameter space. Subsequently we show how this concept is exploited to generate light induced gauge field for neutral ultra cold bosonic atoms. As an example of such light induced Abelian and Non Abelian gauge field for ultra cold atoms we disucss ultra cold atoms in a rotating trap and creation of synthetic spin orbit coupling for ultra cold atomic systems using Raman lasers.