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      Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions

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          Abstract

          We derive rigorously one- and two-dimensional mean-field equations for cigar- and pancake-shaped Bose-Einstein condensates (BEC) with higher order interactions (HOI). We show how the higher order interaction modifies the contact interaction of the strongly confined particles. Surprisingly, we find that the usual Gaussian profile assumption for the strongly confining direction is inappropriate for the cigar-shaped BEC case, and a Thomas-Fermi type profile should be adopted instead. Based on the derived mean field equations, the Thomas-Fermi densities are analyzed in presence of the contact interaction and HOI. For both box and harmonic traps in one, two and three dimensions, we identify the analytical Thomas-Fermi densities, which depend on the competition between the contact interaction and the HOI.

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          Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow

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            Validity of the shape-independent approximation for Bose-Einstein condensates

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              Near Resonant Spatial Images of Confined Bose-Einstein Condensates in the '4D' Magnetic Bottle

              We present quantitative measurements of the spatial density profile of Bose-Einstein condensates of sodium atoms confined in a new '4D' magnetic bottle. The condensates are imaged in transmission with near resonant laser light. We demonstrate that the Thomas-Fermi surface of a condensate can be determined to better than 1%. More generally, we obtain excellent agreement with mean-field theory. We conclude that precision measurements of atomic scattering lengths and interactions between phase separated cold atoms in a harmonic trap can be measured with high precision using this method.
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                Author and article information

                Journal
                1511.00141

                Quantum gases & Cold atoms
                Quantum gases & Cold atoms

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