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Optics and Spectroscopy

On stability of spatially periodic structures of an atomic Bose-Einstein condensate

Nikolai N Rozanov

Published Sep 1, 2006• 0 citations
Publisher

Abstract

The stability of spatially periodic structures, including vortex lattices, in a dilute atomic Bose-Einstein condensate is analyzed. By using the approximate solution of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevskiĭ equation), it is shown that, in the limit of low concentrations, such structures are stable.

DOI
10.1134/s0030400x0609013x

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The stability of spatially periodic structures, including vortex lattices, in a dilute atomic Bose-Einstein condensate is analyzed. By using the approximate solution of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevskiĭ equation), it is shown that, in the limit of low concentrations, such structures are stable.
The conditions providing the formation of periodic vortex lattices of an interference nature in an atomic Bose-Einstein condensate (i.e., in the absence of rotation of the condensate) are determined. Spatially periodic exact solutions of the nonlocal nonlinear Schrödinger equation (the generalized Gross-Pitaevskii equation) that describes the Bose-Einstein condensate of a dilute gas of alkali metal atoms with due regard for the nonlocality of interatomic interactions are obtained in the form of a set of two or three plane waves. It is shown that periodic vortex lattices can be produced in interference experiments with a Bose-Einstein condensate of a dilute gas of alkali metal atoms.
The cubic nonlinear Schrodinger equation with repulsive nonlinearity and elliptic function potential in two-dimensions models a repulsive dilute gas Bose--Einstein condensate in a lattice potential. A family of exact stationary solutions is presented and its stability is examined using analytical and numerical methods. All stable trivial-phase solutions are off-set from the zero level. Our results imply that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Key words: Bose-Einstein condensates, two-dimensional nonlinear Schrodinger equation, periodic potential, elliptic functions PACS: 65.65 1 Introduction The cubic nonlinear Schrodinger equation with attractive or repulsive nonlinearity and a potential is used as a mean-field model for the dynamics of a dilute-gas Bose Einstein condensate (BEC) [1,2]. In this case, the equation is often referred to as the Gross-Pitaevskii equation. These BECs are of interest in both the theoretical and experim...
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case.
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We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions.