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: II. relativistic soliton stability analysis
• Verf.angabe: L.H. Haddad and Lincoln D. Carr
• E-Jahr: 2015
• Jahr: 25 June 2015
• Umfang: 22 S.
• Teil: volume:17
• Teil: year:2015
• Teil: number:6
• Teil: elocationid:063034
• Teil: pages:1-22
• Teil: extent:22
• 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), 6, Artikel-ID 063034, Seite 1-22
• ISSN Quelle: 1367-2630
• DOI: doi:10.1088/1367-2630/17/6/063034
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1750196972

Abstract

The nonlinear Dirac equation for Bose–Einstein condensates (BECs) in honeycomb optical lattices gives rise to relativistic multi-component bright and dark soliton solutions. Using the relativistic linear stability equations, the relativistic generalization of the Boguliubov-de Gennes equations, we compute soliton lifetimes against quantum fluctuations and classify the different excitation types. For a BEC of 87Rb atoms, we find that oursoliton solutions are stable on time scales relevant to experiments. Excitations in the bulk region far from the core of asoliton and bound states in the core are classified as either spin waves or as a Nambu–Goldstone mode. Thus, solitons are topologically distinct pseudospin-1 2 domain walls between polarized regions of Sz = ±1 2. Numerical analysis in the presence of a harmonic trap potential reveals a discrete spectrum reflecting the number of bright soliton peaks or dark soliton notches in the condensate background. For each quantized mode the chemical potential versus nonlinearity exhibits two distinct power law regimes corresponding to the free-particle (weakly nonlinear) and soliton (strongly nonlinear) limits.