The nonlinear Dirac equation in Bose-Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices

We present a thorough analysis of soliton solutions to the quasi-one-dimensional (quasi-1D) nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair geometry. Our NLDE corresponds to a quasi-1D reduction of the honeycomb lattice along the zigzag direction,...

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Bibliographic Details
Published in:	New journal of physics 2015-06, Vol.17 (6), p.63033
Main Authors:	Haddad, L H, Weaver, C M, Carr, Lincoln D
Format:	Article
Language:	eng
Subjects:	05.45.-a 67.85.Hj 67.85.Jk Asymptotic methods Bose-Einstein condensate Bose-Einstein condensates Chemical potential Dirac equation Graphene Invariance Nanoribbons Nonlinearity Optical lattices Organic chemistry Physics Series expansion Solitary waves soliton Solution space Tensors
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Summary:	We present a thorough analysis of soliton solutions to the quasi-one-dimensional (quasi-1D) nonlinear Dirac equation (NLDE) for a Bose-Einstein condensate in a honeycomb lattice with armchair geometry. Our NLDE corresponds to a quasi-1D reduction of the honeycomb lattice along the zigzag direction, in direct analogy to graphene nanoribbons. Excitations in the remaining large direction of the lattice correspond to the linear subbands in the armchair nanoribbon spectrum. Analytical as well as numerical soliton Dirac spinor solutions are obtained. We analyze the solution space of the quasi-1D NLDE by finding fixed points, delineating the various regions in solution space, and through an invariance relation which we obtain as a first integral of the NLDE. We obtain spatially oscillating multi-soliton solutions as well as asymptotically flat single soliton solutions using five different methods: by direct integration; an invariance relation; parametric transformation; a series expansion; and by numerical shooting. By tuning the ratio of the chemical potential to the nonlinearity for a fixed value of the energy-momentum tensor, we can obtain both bright and dark solitons over a nonzero density background.
ISSN:	1367-2630 1367-2630