The nonlinear Dirac equation in Bose-Einstein condensates

• Verfasst von: Haddad, Laith H. [VerfasserIn]
• Verfasst von: Carr, Lincoln D. [VerfasserIn]
• Titel: The nonlinear Dirac equation in Bose-Einstein condensates
• Titelzusatz: vortex solutions and spectra in a weak harmonic trap
• Verf.angabe: L.H. Haddad and Lincoln D. Carr
• E-Jahr: 2015
• Jahr: 29 October 2015
• Umfang: 25 S.
• Teil: volume:17
• Teil: year:2015
• Teil: number:11
• Teil: elocationid:113011
• Teil: pages:1-25
• Teil: extent:25
• Fussnoten: Gesehen am 03.03.2021
• Titel Quelle: Enthalten in: New journal of physics
• Ort Quelle: [Bad Honnef] : Dt. Physikalische Ges., 1999
• Jahr Quelle: 2015
• Band/Heft Quelle: 17(2015), 11, Artikel-ID 113011, Seite 1-25
• ISSN Quelle: 1367-2630
• DOI: doi:10.1088/1367-2630/17/11/113011
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1750185970

Abstract

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.