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Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory

K. Osterloh·M. Baig·L. Santos·P. Zoller·M. Lewenstein
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Abstract

We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs $n$ internal states of atoms and laser assisted state sensitive tunneling. Thus, dynamics are communicated by unitary $n\times n$-matrices. By experimental control of the tunneling parameters, the system can be made truly non-Abelian. We show that single particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex ``moth''-like structure. We discuss the possibility to employ non-Abelian interferometry (Aharonov-Bohm effect) and address methods to realize matter dynamics in specific classes of lattice gauge fields.

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K. Osterloh, M. Baig, L. Santos, P. Zoller, M. Lewenstein. 2005-02-09. Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory. https://doi.org/10.1103/physrevlett.95.010403

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