Vortex dynamics near the surface of a Bose-Einstein condensate

Abstract

The center-of-mass dynamics of a vortex in the surface region of a Bose-Einstein condensate is investigated both analytically using a variational calculation and numerically by solving the time-dependent Gross-Pitaevskii equation. We find, in agreement with previous works, that away from the Thomas-Fermi surface, the vortex moves parallel to the surface of the condensate with a constant velocity. We obtain an expression for this velocity in terms of the distance of the vortex core from the Thomas-Fermi surface that fits accurately with the numerical results. We find also that, coupled to its motion parallel to the surface, the vortex oscillates along the direction normal to the surface around a minimum point of an effective potential.

Crossover from interaction to driven regimes in quantum vortex reconnections

“…First, in box-traps the density of the confined BEC is constant throughout the sample (exception made for a thin layer near the trap edges whose width is of the order of the healing length), while in harmonically trapped BECs the condensate density is maximum in the center of the trap and decreases parabolically when moving towards the boundaries of the trap. Second, while the role of images in both box-and harmonically trapped BECs still remains an open question [10][11][12][13][14], in box-traps vortex images with respect to boundaries are believed to be the only source of vortex motion [13]; on the contrary, in harmonic traps vortex dynamics is also determined by density gradients (arising from the inhomogeneous trapping potential) and vortex curvature [10,15,16].…”

“…Reconnections of coherent filamentary structures ( Fig. 1) play a fundamental role in the dynamics of plasmas (from astrophysics [1][2][3] to confined nuclear fusion), nematic liquid crystals [4], polymers and macromolecules [5] (including DNA [6]), optical beams [7,8], ordinary (classical) fluids [9][10][11] and quantum fluids [12,13]. In fluids, the coherent structures consist of concentrated vorticity, whose character depends on the classical or quantum nature of the fluid: in classical fluids (air, water etc.…”

Vortex dipole in a trapped two-dimensional Bose-Einstein condensate

“…Also, for large initial pair distances x 1 (0) > x s , we note that the defects first move in the −y direction for a very short time, before starting in the +y direction. These two features might be due to effects of the relatively nearby boundary [25,28].…”

“…This method for vortex dynamics in BECs was pioneered in Ref. [6] and has since been used in several vortex applications [21,22,23,24,25,26]. For the condensate shape function f c of Eq.…”

“…(A.1) can be done analytically. We also did not attempt to incorporate velocity field effects due to the boundary [25,28]. Our presented results are therefore limited to wavefunctions of the form of Eq.…”