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

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.