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

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.

12 pages, 9 figures

References in corpus (5)

• Quantized Rotation of Atoms From Photons with Orbital Angular Momentum
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Dynamical Creation of Fractionalized Vortices and Vortex Lattices
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates

Cited by in corpus (11)

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• The nonlinear Dirac equation in Bose-Einstein condensates: Vortex solutions and spectra in a weak harmonic trap
• The nonlinear Dirac equation in Bose-Einstein condensates: Superfluid fluctuations and emergent theories from relativistic linear stability equations
• Solitary waves in the Nonlinear Dirac Equation
• The nonlinear Dirac equation in Bose-Einstein condensates: II. Relativistic soliton stability analysis
• Solitary waves in a two-dimensional nonlinear Dirac equation: from discrete to continuum
• Speed-of-light pulses in a nonlinear Weyl equation
• Bose-Einstein condensate of Dirac magnons: Pumping and collective modes
• Investigation of 3D-Quantized Ring Vortices in Rotating Coupled Atom-Molecular BEC