期刊
NEW JOURNAL OF PHYSICS
卷 17, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/17/11/113011
关键词
vortices; Bose-Einstein condensates; relativistic nonlinear equations
资金
- National Science Foundation [PHY-1067973, PHY-1011156]
- Air Force Office of Scientific Research [FA9550-08-1-0069]
- Alexander von Humboldt foundation
- Heidelberg Center for Quantum Dynamics
- Direct For Mathematical & Physical Scien
- Division Of Physics [1306638] Funding Source: National Science Foundation
We analyze the vortex solution space of the (2 + 1)-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with s-wave scattering for bosons leads to a large number of vortex solutions characterized by different functional forms for the internal spin and overall phase of the order parameter. We present a detailed derivation of these solutions which include skyrmions, half-quantum vortices, Mermin-Ho and Anderson-Toulouse vortices for vortex winding l = 1. For l >= 2 we obtain topological as well as non-topological solutions defined by the asymptotic radial dependence. For arbitrary values of l the non-topological solutions include bright ring-vortices which explicitly demonstrate the confining effects of the Dirac operator. We arrive at solutions through an asymptotic Bessel series, algebraic closed-forms, and using standard numerical shooting methods. By including a harmonic potential to simulate a finite trap we compute the discrete spectra associated with radially quantized modes. We demonstrate the continuous spectral mapping between the vortex and free particle limits for all of our solutions.
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