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arXiv · 1210.2114

The nonlinear Dirac equation: Preparation and stability of relativistic vortices in Bose-Einstein condensates

L. H. Haddad·K. M. O'Hara·Lincoln D. Carr
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Abstract

We propose a detailed experimental procedure for preparing relativistic vortices, governed by the nonlinear Dirac equation, in a two-dimensional Bose-Einstein condensate (BEC) in a honeycomb optical lattice. Our setup contains Dirac points, in direct analogy to graphene. We determine a range of practical values for all relevant physical parameters needed to realize relativistic vortices in a BEC of $^{87}\mathrm{Rb}$ atoms. Seven distinct vortex types, including Anderson-Toulouse and Mermin-Ho skyrmion textures and half-quantum vortices, are obtained, and their discrete spectra and stability properties are calculated in a weak harmonic trap. We predict that most vortices are stable with a lifetime between $1$ and $10$ seconds.

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L. H. Haddad, K. M. O'Hara, Lincoln D. Carr. 2015-02-06. The nonlinear Dirac equation: Preparation and stability of relativistic vortices in Bose-Einstein condensates. https://doi.org/10.1103/physreva.91.043609

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