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    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
    (Massey University, 2023) Choudhury, Sarthak
    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 et.al. [Phys. Rev. Lett. 108, 250402 (2012)], we use this protocol for two-dimensional rings and find the emergence of ring currents non-adiabatically.
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    Icy tornadoes in the quantum world - Josephson junctions of Bose-Einstein condensates : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematical Physics at Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University, Albany, New Zealand
    (Massey University, 2012) Jaritz, Gabriele
    This thesis presents a theoretical study of ultra-cold gases in, or close to a Bose- Einstein condensed phase. A system of two coupled Bose-Einstein condensates shows strong resemblance to Josephson junctions, consisting of two superconductors linked via a thin insulating barrier. In these systems quantised ring currents across the barrier (Josephson vortices) have been detected. We concentrate on similar macroscopic quantum states in our systems of linear and annular coupled Bose-Einstein condensates, and test them towards their potential for showing macroscopic quantum tunnelling. For the linear system we present a very detailed stability analysis of the stationary solutions, the vortex and the soliton, using Bogoliubov-de Gennes theory. An analytic approximation of the unstable mode is provided. We show that the transition between vortices rotating in opposite directions is possible and propose an effective potential separating these two states. For the annular system of two coupled ring shaped condensates of different radii, we review the parameter regimes for finding vortices in the ground state. We show that pinning of vortices via a repulsive external potential is possible and suggest further steps towards the detection of macroscopic quantum tunnelling.