Non-Abelian Gauge Potentials for Ultracold Atoms with Degenerate Dark States

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.

Figure 1

(a) $j=2\to j=1$ transition with two degenerate dark states in the manifolds $\{|1⟩,|3⟩,|5⟩\}$ and $\{|2⟩,|4⟩\}$ which are not coupled by nonadiabatic transitions. (b) Tripod-coupling scheme forming two degenerate dark states with nonadiabatic coupling.