Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

Abstract

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.

11 pages, 5 figures. Updated references

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Cited by in corpus (8)

• Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
• Rotational properties of dipolar Bose-Einstein condensates confined in anisotropic harmonic potentials
• A general theory of flattened dipolar condensates
• Two-dimensional Bose gas of tilted dipoles: roton instability and condensate depletion
• Self trapping of a dipolar Bose-Einstein condensate in a double well
• Dissipation effect in the double-well Bose-Einstein Condensate
• Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions
• Vortices in fermion droplets with repulsive dipole-dipole interactions