The nonlinear Dirac equation in Bose-Einstein condensates: vortex solutions and spectra in a weak harmonic trap
We analyze the vortex solution space of the -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 solution...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
29 October 2015
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| In: |
New journal of physics
Year: 2015, Jahrgang: 17, Heft: 11, Pages: 1-25 |
| ISSN: | 1367-2630 |
| DOI: | 10.1088/1367-2630/17/11/113011 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1367-2630/17/11/113011
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| Verfasserangaben: | L.H. Haddad and Lincoln D. Carr |
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| 520 | |a We analyze the vortex solution space of the -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 For 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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