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Phys. Rev. A 71, 033618 (2005) [12 pages]

Exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

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Claudia Eberlein1, Stefano Giovanazzi2, and Duncan H. J. O’Dell1
1Department of Physics & Astronomy, University of Sussex, Falmer, Brighton BN1 9QH, England
2School of Physics & Astronomy, University of St Andrews, North Haugh, St. Andrews KY16 9SS, Scotland

Received 20 August 2004; published 15 March 2005

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate (BEC) which has dipole-dipole interactions as well as the usual s -wave contact interaction, in a harmonic trap. Remarkably, despite the nonlocal anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s -wave case, but with a different aspect ratio. We explain in detail the mathematical tools necessary to describe dipolar BECs with or without cylindrical symmetry. Various properties such as electrostriction and stability are discussed.


©2005 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.71.033618
DOI: 10.1103/PhysRevA.71.033618
PACS: 03.75.Hh, 34.20.Cf, 32.80.Qk, 75.80.+q

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