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arXiv:cond-mat/9804038 · Journal of Physics B Atomic Molecular and Optical Physics

Output coupling and flow of a dilute Bose-Einstein condensate

B Jackson, J F McCann, Charles S. Adams

Published Oct 28, 1998• 28 citations
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Abstract

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.

DOI
10.1088/0953-4075/31/20/008

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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.
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.
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)
In this Thesis we apply the Gross-Pitaevskii equation (GPE) to describe properties of a dilute, near zero temperature Bose gas for various confining geometries. We start by reviewing some basic information about the density, the chemical potential and elementary excitations of a dilute atomic condensate confined in a single harmonic trap for a Bose condensate with repulsive and attractive interactions and we also discuss the stability in the case of attractive interactions. We extend our study to a one and three dimensional double-well trap. We investigate the eigenenergy levels and show that the nonlinearity leads to triangular structures which appear either in the ground or excited states for the case of a Bose condensate with attractive or repulsive interactions respectively. We apply the eigenenergy level picture to analyse Josephson effects induced when the barrier IS moved at a constant velocity across the trapping potential or by the application of a time-dependent potential gradient. The GPE simulations are compared to the predictions of a nonlinear two state model. Above a critical velocity there is a transition to a superposition of ground and excited states which leads to sudden changes in the population difference. The direction of Josephson flow depends critically on the initial state of the system and we discuss the feasibility of experimental control of the atomic flow using phase-imprinting. The stability of a low temperature Bose-Einstein condensate with attract interactions in one and three dimensional double-well potentiate is discussed. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. Finally we investigate the stability and tunnelling effects in a multi-well system.
A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.
The coherent characteristics of four trapped Bose-Einstein condensates (BEC) conjunct one by one in a ring shape which is divided by two far off-resonant lasers, are studied. Four coupled Gross-Pitaevskii equations are used to describe the dynamics of the system. Two kinds of self-trapping effects are discussed in the coupled BECs, and the phase diagrams for different initial conditions and different coupling strengths are discussed. This study can be used to determine interaction parameters between atoms in BEC.
The evolution of a two component Bose-Einstein condensate, consisting of atoms in two distinct hyperfine states, is modeled using a generalization of the Gross-Pitaevskii equation. Coherent coupling of the components by a microwave or RF field gives rise to a range of spatiotemporal behaviors, controlled by the strength and detuning of the applied field. From an initial trapped single component state, a second component can be generated which may escape from the trapping region or remain trapped within the first component. The initiating mechanism is identified and characterized.