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
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.