Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

Mitchell J. Knight; Thomas Bland; Nick G. Parker; Andy M. Martin

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arXiv · 1908.02395

Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

Mitchell J. Knight·Thomas Bland·Nick G. Parker·Andy M. Martin

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Abstract

Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einstein condensates, and gives strong agreement with the three-dimensional results, even as the trapping is relaxed away from the strict quasi-one- and quasi-two-dimensional regimes. This approach offers a significant improvement over the standard one- and two-dimensional reduction.

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Mitchell J. Knight, Thomas Bland, Nick G. Parker, Andy M. Martin. 2019-08-06. Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates. https://arxiv.org/abs/1908.02395

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