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Effective spin-orbit coupling can be created in cold atom systems using atom-light interaction. We study Bose-Einstein condensates in an optical lattice using the Gross-Pitaevskii equation with spin-orbit coupling. Bloch states for the linear equation are numerically obtained, and compared with stationary solutions to the Gross-Pitaevskii equation with nonlinear terms. Various vortex lattice states are found when the spin-orbit coupling is strong.
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Sakaguchi et al. (2013) studied this question.
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