Nonlinear band structure in Bose-Einstein condensates: Nonlinear Schrödinger equation with a Kronig-Penney potential

B. T. Seaman, L. D. Carr, and M. J. Holland
Phys. Rev. A 71, 033622 – Published 21 March 2005

Abstract

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one-dimensional lattice are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schrödinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential. Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for understanding experimental phenomena.

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  • Received 13 October 2004

DOI:https://doi.org/10.1103/PhysRevA.71.033622

©2005 American Physical Society

Authors & Affiliations

B. T. Seaman, L. D. Carr, and M. J. Holland

  • JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA

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Vol. 71, Iss. 3 — March 2005

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