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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.
The implementation of the fractional quantum Hall effect in ultracold atomic quantum gases remains, despite substantial advances in the field, a major challenge. Since atoms are electrically neutral, a key ingredient is the generation of sufficiently
In this article we present a pedagogical discussion of some of the optomechanical properties of a high finesse cavity loaded with ultracold atoms in laser induced synthetic gauge fields of different types. Essentially, the subject matter of this arti
Neutral atomic Bose condensates and degenerate Fermi gases have been used to realize important many-body phenomena in their most simple and essential forms, without many of the complexities usually associated with material systems. However, the charg
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest leng
Using a numerical implementation of the truncated Wigner approximation, we simulate the experiment reported by Ramanathan et al. in Phys. Rev. Lett. 106, 130401 (2011), in which a Bose-Einstein condensate is created in a toroidal trap and set into ro