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

Journal Article · Tue Mar 01 00:00:00 EST 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.71.033622· OSTI ID:20650473

Seaman, B T; Carr, L D; Holland, M J ^[1]

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1. JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440 (United States)

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 Schroedinger, 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.

• OSTI ID: 20650473
• Journal Information: Physical Review. A, Vol. 71, Issue 3; Other Information: DOI: 10.1103/PhysRevA.71.033622; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
ENERGY LEVELS
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
POTENTIAL ENERGY
POTENTIALS
SCHROEDINGER EQUATION
STABILITY
SUPERFLUIDITY
TRAPPING