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Localized gap-soliton trains of Bose-Einstein condensates in an optical lattice

D. L. Wang1,2,3, X. H. Yan1, and W. M. Liu3

  • 1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 2Department of Physics, Xiangtan University, Xiangtan 411105, China
  • 3Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China

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Phys. Rev. E 78, 026606 – Published 14 August, 2008

DOI: https://doi.org/10.1103/PhysRevE.78.026606

Abstract

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu’s functions cen−1 and sen; and the Bloch wave in the nth band gap is a linear superposition of cen and sen. For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons—fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann et al., Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.

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Phys. Rev. E 78, 026606– Published 14 August, 2008
  • Received 28 August 2007

© 2008 American Physical Society

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