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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonground stationary states of Bose condensate of trapped neutral atoms

Vladislav Viktorovich Serov, Vladimir Leonardovich Derbov, Sergue Il'ich Vinitsky, Vyacheslav I. Yukalov

Published Jun 4, 2002• 2 citations
Publisher

Abstract

Small deviations from the stationary solutions of the Gross_Pitaevskii equation describing non-ground states of Bose-Einstein condensate of atoms in a harmonic trap are analyzed basing on the Bogoliubov equations and using both perturbation theory and direct numerical calculations. Non- vortex excited stationary that were not studied before are shown to possess new and unexpected features.

DOI
10.1117/12.469592

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Small deviations from the stationary solutions of the Gross_Pitaevskii equation describing non-ground states of Bose-Einstein condensate of atoms in a harmonic trap are analyzed basing on the Bogoliubov equations and using both perturbation theory and direct numerical calculations. Non- vortex excited stationary that were not studied before are shown to possess new and unexpected features.
Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large-amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.
We investigate the recently found stationary vortex cluster states in dilute atomic Bose-Einstein condensates confined by a nonrotating trap, and also present a stationary three-vortex cluster. We find the stationary states by minimizing directly an error norm for the stationary Gross-Pitaevskii equation, and study the dynamic and energetic stability of the resulting states by solving the corresponding Bogoliubov equations for the elementary excitations. The results are verified by integrating the time-dependent Gross-Pitaevskii equation. Contrary to previously reported results, the stationary states were observed to be both energetically and dynamically unstable. The dynamical decay rate of the clusters is typically very slow, but it should be experimentally observable. The most promising circumstances to experimentally generate and observe these structures and their dynamics is in weakly dissipative condensate systems, using phase-imprinting techniques.
We study the conservative dynamics and stationary configurations of a vortex-antivortex pair in a harmonically trapped two-dimensional Bose-Einstein condensate. We establish the conceptual framework for understanding the stationary states and the topological defect trajectories, through considerations of different mechanisms of vortex motion and the bifurcation of solitonlike stationary solutions. Our insights are based on Lagrangian-based variational calculations, numerical solutions of both the time-dependent and time-independent Gross-Pitaevskii equations, and exact solutions for the noninteracting case.
The theory of Bose-Einstein condensation in a two-dimensional(2D) harmonic trap is developed from 2D Gross-Pitaevskii equation. The 2D interaction strength is obtained from a 2D collision theory. We show the realization of 2D condensation of trapped Bose atoms directly by obtaining the stable solutions for the condensate wave function from the 2D Gross-Pitaevskii equation. We calculate the ground-state energy of the 2D system, and also the wave function of the 2D vortex state. In particular, the 2D energy state becomes less stable than the 3D case with the number of trapped atoms. The results of the 2D Bose condensation are also compared with those of the well-known 3D case.