Journal of Physics A Mathematical and General

Dynamics of periodic multi-component Bose–Einstein condensates

Bernard Deconinck, J. Nathan Kutz, Matthew S Patterson, Brandon W Warner

Published May 8, 2003• 49 citations

Abstract

The cubic vector nonlinear Schrödinger equation with an external trigonometric potential models a quasi-one-dimensional multi-component Bose–Einstein condensate trapped in a standing light wave. We construct families of exact stationary solutions for the more general case of an elliptic function potential. Some of these solutions degenerate to zero as the effect of the external potential disappears, whereas others limit to solutions of the free vector nonlinear Schrödinger equation. The stability of these solutions is examined both analytically and numerically. The stability results depend on the nature of the atomic interactions not only within the components but also between components. As in the scalar case (one component) with repulsive interaction, all linearly stable solutions are deformations of the ground state of the linear Schrödinger equation. Unlike the scalar case with attractive interaction, no solutions are found to be stable if there is any attractive interaction present.

DOI: 10.1088/0305-4470/36/20/306

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