L. H. Haddad, K. M. O'Hara, Lincoln D. Carr
We present 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 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 find that most vortices are stable with a lifetime between 1 and 10 seconds.
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http://arxiv.org/abs/1210.2114
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