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Bose-Einstein Condensates in Non-abelian Gauge Fields

The recent success of the NIST group in generating abelian gauge field in cold atoms has created opportunities to simulate electronic transports in solids using atomic gases. Very recently, the NIST group has also announced in a DARPA Meeting the creation of non-abelian gauge fields in a pseudo spin-1/2 Bose gas. While there have been considerable theoretical activities in synthetic gauge fields, non-abelian fields have not been generated until now. Here, we show that in a non-abelian gauge field, a spinor condensate will develop a spontaneous stripe structure in each spin component, reflecting a ground state made up of two non-orthogonal dressed states with different momenta. Depending on interactions, this ground state can reduce back to a single dressed state. These momentum carrying stripes are the {\em macroscopic} bosonic counterpart of the spin-orbit phenomena in fermions that are being actively studied in electron physics today.