Synthetic Gauge Fields for Ultra Cold Atoms: A Primer

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.

Invited Review Article for the Journal of the Indian Institute of Science, Bangalore ( Available online at the url http://journal.iisc.ernet.in) entitled "COLD ATOM QUANTUM EMULATORS: FROM CONDENSED MATTER TO FIELD THEORY TO OPTICAL CLOCKS"