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Conference on Lasers and Electro-Optics

Flow of a weakly-interacting Bose condensate

B. Jackson, J F McCann, Charles S. Adams

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.The experimental observation of Bose condensation using magnetically trapped alkali vapours has stimulated considerable interest in the understanding of weakly-interacting Bose fluids. Experiments have confirmed that the Gross-Pitaevskii equation gives an accurate description of condensate dynamics in the limit T/spl rarr/0, and that the principal effect of finite temperature is condensate depletion. We solve the two-dimensional time-dependent, Gross-Pitaevskii equation, including the effect of gravity, to simulate the flow of a weakly-interacting condensate. We have modeled the output coupling of an atom laser, and the flow of a condensate through a constriction.

DOI
10.1109/iqec.1998.680108

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Summary form only given.The experimental observation of Bose condensation using magnetically trapped alkali vapours has stimulated considerable interest in the understanding of weakly-interacting Bose fluids. Experiments have confirmed that the Gross-Pitaevskii equation gives an accurate description of condensate dynamics in the limit T/spl rarr/0, and that the principal effect of finite temperature is condensate depletion. We solve the two-dimensional time-dependent, Gross-Pitaevskii equation, including the effect of gravity, to simulate the flow of a weakly-interacting condensate. We have modeled the output coupling of an atom laser, and the flow of a condensate through a constriction.
We solve the Gross-Pitaevskii equation to model the behaviour of a weakly-interacting Bose condensate. Solutions are presented for the eigenstates in one- and two-dimensional harmonic traps. We include the effect of gravity and coupling to a second condensate to simulate an output coupler for Bose condensed atoms, and find that the output pulse shape is in qualitative agreement with experiment. We also model flow under gravity through a constriction, demonstrating excitation and separation of eigenmodes in the condensate.
In this thesis we solve the Gross-Pitaevskii equation numerically in order to model the response of trapped Bose-Einstein condensed gases to perturbations by electromagnetic fields. First, we simulate output coupling of pulses from the condensate and compare our results to experiments. The excitation and separation of eigenmodes on flow through a constriction is also studied. We then move on to the main theme of this thesis: the important subject of quantised vortices in Bose condensates, and the relation between Bose-Einstein condensation and superfluidity. We propose methods of producing vortex pairs and rings by controlled motion of objects. Full three-dimensional simulations under realistic experimental conditions are performed in order to test the validity of these ideas. We link vortex formation to drag forces on the object, which in turn is connected with energy transfer to the condensate. We therefore argue that vortex formation by moving objects is intimately related to the onset of dissipation in superfluids. We discuss this idea in the context of a recent experiment, using simulations to provide evidence of vortex formation in the experimental scenario. Superfluidity is also manifest in the property of persistent currents, which is linked to vortex stability and dynamics. We simulate vortex line and ring motion, and find in both cases precessional motion and thermodynamic instability to dissipation. Strictly speaking, the Gross-Pitaevskii equation is valid only for temperatures far below the BEC transition. We end the thesis by describing a simple finite-temperature model to describe mean-field coupling between condensed and non-condensed components of the gas. We show that our hybrid Monte-Carlo/FFT technique can describe damping of the lowest energy excitations of the system. Extensions to this model and future research directions are discussed in the conclusion. (author)
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. This article offers a short survey on mathematical models and theories as well as numerical methods for BEC based on the mean field theory. We start with the Gross-Pitaevskii equation (GPE) in three dimensions (3D) for modeling one-component BEC of the weakly interacting bosons, scale it to obtain a three-parameter model and show how to reduce it to two dimensions (2D) and one dimension (1D) GPEs in certain limiting regimes. Mathematical theories and numerical methods for ground states and dynamics of BEC are provided. Extensions to GPE with an angular momentum rotation term for a rotating BEC, to GPE with long-range anisotropic dipole-dipole interaction for a dipolar BEC and to coupled GPEs for spin-orbit coupled BECs are discussed. Finally, some conclusions are drawn and future research perspectives are discussed.
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form ${V}_{\mathrm{ext}}{(x)=V}_{0}(|x|{/a)}^{\ensuremath{\gamma}},$ in which $\ensuremath{\gamma}<2,$ by solving the Gross-Pitaevskii equation within the semiclassical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for a finite number of particles at low temperature, indicating a phase transition for weakly interacting systems.
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.