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Vortex Dynamics in Bose-Einstein CondensatesBenjamin Michael Caradoc-DaviesDoctor of Philosophy at the University of Otago, Dunedin, New Zealand.
July 2000 AbstractWe investigate in the mean field limit the dynamics of vortices in trapped Bose-Einstein condensates, using numerical simulations of the Gross-Pitaevskii equation in two and three dimensions. Vortices are found to be readily generated by a variety of mechanisms, including collisions between condensates or with an aperture, or by mechanically disturbing the condensate with a perturber. In particular, we study the rotational stirring of a condensate with a repulsive Gaussian potential, representing a far-blue-detuned laser. We find that for a condensate rotationally stirred just below a critical angular frequency, given by the energy difference between the ground and vortex eigenstates, a single vortex cycles into the centre of the condensate and then out. We analyse this behaviour in terms of a two state model, and show that it can be understood as nonlinear Rabi cycling between the ground and vortex states of the condensate. The single vortex cycling regime occurs both in two dimensions, and in three dimensions for a range of trap geometries. We show how this dynamical behaviour can be used to prepare a central vortex state in a parameter regime accessible to current experiments. We also show (in two and three dimensions) that a singly quantised central vortex is dynamically stable to a perturbation, while a doubly quantised central vortex immediately dissociates into two unit vortices upon perturbation. We give a simple geometrical explanation for this instability. We find that a central vortex remains in the condensate if a perturber is inserted and left in place: the condensate exhibits persistent flow past the obstruction, as is characteristic of a superfluid. Rotationally stirring a condensate in a spherically symmetric trap can form vortex lines which collide and exchange sections, an example of the rich dynamical behaviour of these structures.DownloadCopyright (c) 2000 Benjamin Michael Caradoc-DaviesPermission is granted to make and distribute verbatim copies of this thesis in any medium. All other rights reserved.
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PrintingNote that Appendix E contains 5 colour plates, intended to be printed single-sided. The remainder of the thesis should be printed two-sided in greyscale on A4 paper. Some pages are intentionally left blank, as chapters begin on a recto page.The content of this page was last modified by Ben Caradoc-Davies on 29 November 2000. | ||||||||||||||||||||||||||||||||||||||||||||||
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