Investigations in vortex molecule dynamics and ring current generation in Bose-Einstein condensates : a dissertation presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at Massey University, Albany, New Zealand

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Massey University
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Topological excitations are a special type of long-lived excitation that are impervious to small perturbations in cold atom systems. This thesis aims to investigate properties of two different topological excitations in two-dimensional condensates using the Gross Pitaevskii equations (GPE). The majority of this thesis investigates the dynamics of a vortex molecule in coherently coupled Bose-Einstein condensates in different trap geometries. A vortex molecule consists of two vortices in separate condensates bound together by a Josephson vortex (also called a domain wall). We aim to shed light on vortex molecule dynamics using a simple point-vortex framework. Firstly, we extend the point vortex framework to account for the domain wall using a parametrized interaction energy. The interaction energy is parametrized in special boundary conditions that emulate an infinite plane. We then use this extended point vortex model to investigate the phase space and the dynamics of a vortex molecule in a flat-bottomed channel trap. Our extended model captures all the essential features of the phase space and agrees with GPE simulations of a vortex molecule in a trap. We then expand the point vortex framework further to account for the effect of the boundaries on the Josephson vortex by using a distributed vorticity model. We use this continuous vorticity model to investigate the precession frequency of a vortex molecule in an isotropic disc and find support for our model. Additionally, we investigate a protocol to create persistent supercurrents in a ring shaped single condensate. Though this protocol has been showed to adiabatically create ring currents in ideal one-dimensional rings by Fialko [Phys. Rev. Lett. 108, 250402 (2012)], we use this protocol for two-dimensional rings and find the emergence of ring currents non-adiabatically.
Bose-Einstein condensation, Condensed matter, Vortex-motion, Molecules