Bose-Einstein Condensates in Standing Waves: The Cubic Nonlinear Schrödinger Equation with a Periodic Potential
Jared C. BronskiDepartment of Mathematics, University of Illinois Urbana-Champaign, 61801, USALincoln D. CarrDepartment of Physics, University of Washington, Seattle, Washington 98195-1560Bernard DeconinckDepartment of Applied Mathematics, University of Washington, Seattle, Washington 98195-2420J. Nathan KutzDepartment of Applied Mathematics, University of Washington, Seattle, Washington 98195-2420
2001en
ABI
Abstract
We present a new family of stationary solutions to the cubic nonlinear Schrödinger equation with an elliptic function potential. In the limit of a sinusoidal potential our solutions model a quasi-one-dimensional dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided that the ratio of the height of the variations of the condensate to its dc offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Recent developments allow for experimental investigation of these predictions.
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