Disordered vortex arrays in a two-dimensional condensate

We suggest a method to create turbulence in a Bose-Einstein condensate. The method consists in, firstly, creating an ordered vortex array, and, secondly, imprinting a phase difference in different regions of the condensate. By solving numerically the two-dimensional Gross-Pitaevskii equation we show that the motion of the resulting positive and negative vortices is disordered.Comment: 14 pages, 18 figures, accepted by Geophysical and Astrophysical Fluid Dynamic

Ballistic propagation of thermal excitations near a vortex in superfluid He3-B

Andreev scattering of thermal excitations is a powerful tool for studying quantized vortices and turbulence in superfluid He3-B at very low temperatures. We write Hamilton's equations for a quasiparticle in the presence of a vortex line, determine its trajectory, and find under wich conditions it is Andreev reflected. To make contact with experiments, we generalize our results to the Onsager vortex gas, and find values of the intervortex spacing in agreement with less rigorous estimates

Quantum vortex reconnections

We study reconnections of quantum vortices by numerically solving the governing Gross-Pitaevskii equation. We find that the minimum distance between vortices scales differently with time before and after the vortex reconnection. We also compute vortex reconnections using the Biot-Savart law for vortex filaments of infinitesimal thickness, and find that, in this model, reconnection are time-symmetric. We argue that the likely cause of the difference between the Gross-Pitaevskii model and the Biot-Savart model is the intense rarefaction wave which is radiated away from a Gross-Pitaeveskii reconnection. Finally we compare our results to experimental observations in superfluid helium, and discuss the different length scales probed by the two models and by experiments.Comment: 23 Pages, 12 Figure

Turbulent superfluid profiles in a counterflow channel

We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page

Instability of vortex array and transitions to turbulent states in rotating helium II

We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson {\it et al.}, who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow

Vortex Waves in a Cloud of Bose Einstein - Condensed, Trapped Alkali - Metal Atoms

We consider the vortex state solution for a rotating cloud of trapped, Bose Einstein - condensed alkali atoms and study finite temperature effects. We find that thermally excited vortex waves can distort the vortex state significantly, even at the very low temperatures relevant to the experiments.Comment: to appear in Phys. Rev.

Matter-wave dark solitons in boxlike traps

Motivated by the experimental development of quasihomogeneous Bose-Einstein condensates confined in boxlike traps, we study numerically the dynamics of dark solitons in such traps at zero temperature. We consider the cases where the side walls of the box potential rise either as a power law or a Gaussian. While the soliton propagates through the homogeneous interior of the box without dissipation, it typically dissipates energy during a reflection from a wall through the emission of sound waves, causing a slight increase in the soliton's speed. We characterize this energy loss as a function of the wall parameters. Moreover, over multiple oscillations and reflections in the boxlike trap, the energy loss and speed increase of the soliton can be significant, although the decay eventually becomes stabilized when the soliton equilibrates with the ambient sound field

Vortex reconnections in atomic condensates at finite temperature

The study of vortex reconnections is an essential ingredient of understanding superfluid turbulence, a phenomenon recently also reported in trapped atomic Bose-Einstein condensates. In this work we show that, despite the established dependence of vortex motion on temperature in such systems, vortex reconnections are actually temperature independent on the typical length/time scales of atomic condensates. Our work is based on a dissipative Gross-Pitaevskii equation for the condensate, coupled to a semiclassical Boltzmann equation for the thermal cloud (the Zaremba-Nikuni-Griffin formalism). Comparison to vortex reconnections in homogeneous condensates further show reconnections to be insensitive to the inhomogeneity in the background density.Comment: 6 pages, 4 figure