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We demonstrate how to create artificial external non-Abelian gauge potentialsacting on cold atoms in optical lattices. The method employs $n$ internalstates of atoms and laser assisted state sensitive tunneling. Thus, dynamicsare communicated by unitary $n\times n$-matrices. By experimental control ofthe tunneling parameters, the system can be made truly non-Abelian. We showthat single particle dynamics in the case of intense U(2) vector potentialslead to a generalized Hofstadter butterfly spectrum which shows a complex``moth''-like structure. We discuss the possibility to employ non-Abelianinterferometry (Aharonov-Bohm effect) and address methods to realize matterdynamics in specific classes of lattice gauge fields.Comment: 5 pages, 3 figure

Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory