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Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states

Ruseckas, J. and Juzeliunas, G. and Ohberg, P. and Fleischhauer, M. (2005) Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states. Physical Review Letters, 95 (1). 010404. ISSN 0031-9007

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We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.