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

Yongyong Cai, Matthias Rosenkranz, Zhen Lei, and Weizhu Bao
Phys. Rev. A 82, 043623 – Published 26 October 2010

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.

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  • Received 25 June 2010

DOI:https://doi.org/10.1103/PhysRevA.82.043623

©2010 American Physical Society

Authors & Affiliations

Yongyong Cai1, Matthias Rosenkranz1,*, Zhen Lei2,3,4, and Weizhu Bao1,5,†

  • 1Department of Mathematics, National University of Singapore, 119076, Singapore
  • 2School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • 3Key Laboratory of Nonlinear Mathematical Models and Methods of Ministry of Education, Fudan University, Shanghai 200433, China
  • 4Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China
  • 5Center for Computational Science and Engineering, National University of Singapore, 117543, Singapore

  • *matrm@nus.edu.sg
  • bao@math.nus.edu.sg; [http://www.math.nus.edu.sg/~bao/]

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Issue

Vol. 82, Iss. 4 — October 2010

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