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The nonlinear Dirac equation in Bose-Einstein condensates: II. relativistic soliton stability analysis

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 c...

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Main Authors: Haddad, Laith H. (Author) , Carr, Lincoln D. (Author)
Format: Article (Journal)
Language:English
Published: 25 June 2015
In: New journal of physics
Year: 2015, Volume: 17, Issue: 6, Pages: 1-22
ISSN:1367-2630
DOI:10.1088/1367-2630/17/6/063034
Online Access:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1088/1367-2630/17/6/063034
Verlag, lizenzpflichtig, Volltext: https://iopscience.iop.org/article/10.1088/1367-2630/17/6/063034/meta
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Author Notes:L.H. Haddad and Lincoln D. Carr

MARC

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520 |a 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. 
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