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Springer eBooks

Coherent Vortex Dynamics in Two- and Three-Dimensional Bose-Einstein Condensates

R. J. Ballagh, B. M. Caradoc-Davies

Published Nov 16, 2007• 0 citations
Publisher
DOI
10.1007/3-540-40894-0_2

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Abstract Understanding how two vortex dipoles interact with each other microscopically is helpful for understanding the dynamics of quantum turbulence in a two-dimensional Bose–Einstein condensate (BEC). We investigate the collision of two vortex dipoles propagating in opposite directions along parallel lines by numerically solving the two-dimensional Gross–Pitaevskii equation. By varying the impact parameter, we identify three general dynamical modes of the vortex dipoles in a homogeneous BEC, which are the vortex recombination mode, the encircling mode and the flyby mode. The existence of these three modes has been corroborated by numerical computations of the ordinary differential equations describing the vortex interactions. Furthermore, we show the corresponding parameter ranges for these modes.
We simulate in the mean-field limit the effects of rotationally stirring a three-dimensional trapped Bose-Einstein condensate with a Gaussian laser beam. A single vortex cycling regime is found for a range of trap geometries, and is well described as coherent cycling between the ground and the first excited vortex states. The critical angular speed of stirring for vortex formation is quantitatively predicted by a simple model. We report preliminary results for the collisions of vortex lines, in which sections may be exchanged.
We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results. An imaginary time propagation method and Crank-Nicolson scheme for discretization have been used for numerical simulation. The numerically calculated average value of the angular momentum per particle shows very clearly its dynamical relation with the time development of the vortex formation. The rotational frequency dependence of the variation of average value of the angular momentum per particle with time shows that vortices form much faster in time for higher rotational frequency. Similarly, the vortex forms much faster in time with an increase of the strength of the repulsive three-body interaction. The simulation of the vortex lattice formation in the condensate shows that the presence of the three-body interactions does not alter the vortex lattice pattern but it helps in the shape deformations of the condensate thereby leading to vortex lattice formation. Likewise, the three-body interactions enable the vortex lattice formation in Bose-Einstein condensates even with attractive two-body interactions and in purely quintic BEC.