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Phys. Rev. E 63, 036612 (2001) [11 pages]

Stability of repulsive Bose-Einstein condensates in a periodic potential

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J. C. Bronski1, L. D. Carr2, B. Deconinck3, J. N. Kutz3 *, and K. Promislow4
1Department of Mathematics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801
2Department of Physics, University of Washington, Seattle, Washington 98195-1560
3Department of Applied Mathematics, University of Washington, Seattle, Washington 98195-2420
4Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

Received 29 September 2000; published 27 February 2001

The cubic nonlinear Schrödinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose–Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined using analytical and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schrödinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas–Fermi limit.


©2001 The American Physical Society

URL: http://link.aps.org/abstract/PRE/v63/e036612
DOI: 10.1103/PhysRevE.63.036612
PACS: 03.75.Fi, 03.65.Ge, 05.45.-a, 05.10.-a

* Author to whom correspondence should be addressed.

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