Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2004-10-13
Phys. Rev. A 71, 033622 (2005)
Physics
Condensed Matter
Other Condensed Matter
Version 2. Fixed typos, added reference
Scientific paper
10.1103/PhysRevA.71.033622
All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schr\"odinger, 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 experimental phenomena.
Carr Lincoln D.
Holland Murray J.
Seaman B. T.
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