Abstract
Bose-Einstein condensates have been probed with expansion imaging since the first experimental realisation in 1995. Expansions of Bose-Einstein condensates have been used extensively, from thermometry, to measuring momentum distributions, to probing phase information. Expansion characteristics have been interpreted as a signature of turbulence in a condensate. Currently there is no method of simulating expansions of zero temperature Bose-Einstein condensates without large computational cost. This thesis was conducted to develop a robust numerical method for simulating expansions by deriving equations of motion that adaptively scale with the bulk dilation of the atom cloud over time. These equations of motion were solved for a systematic set of two and four vortex arrangements in a two-dimensional trapped Bose-Einstein condensate. It was found that high current flow in a direction provided a pressure that enhances expansion rate in that direction. Pressure due to current in the long direction of the trapped condensate suppressed the aspect ratio inversion during free expansion. Larger condensates with sets of random arrangements of vortices ranging in energy from dipole gas to large clusters were expanded and it was found again that large current flow in the long direction had large suppression of the aspect ratio inversion.