Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions

Bradley, R. Mark
Bernard, James E.
Carr, L. D.
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Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-anti-vortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.
Comment: 22 pages, 9 figures
Condensed Matter - Other Condensed Matter