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

TL;DR

This paper details an experimental approach to create and analyze relativistic vortices governed by the nonlinear Dirac equation in a 2D Bose-Einstein condensate with a honeycomb lattice, identifying stable vortex types and their properties.

Contribution

It introduces a practical method for preparing relativistic vortices in BECs and characterizes their stability and spectral properties, advancing the understanding of relativistic quantum fluids.

Findings

Seven vortex types identified, including skyrmions and half-quantum vortices.

Most vortices predicted to be stable for 1-10 seconds.

Physical parameters for experimental realization are specified.

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.