Three-dimensional vortex dynamics in Bose-Einstein condensates

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.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review A (6 March 2000

Fourier transforming a trapped Bose-Einstein condensate by waiting a quarter of the trap period: simulation and applications

We investigate the property of isotropic harmonic traps to Fourier transform a weakly interacting Bose–Einstein condensate (BEC) every quarter of a trap period. We solve the Gross–Pitaevskii equation numerically to investigate the time evolution of interacting BECs in the context of the Fourier transform, and we suggest potential applications

Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates

Simulations of a rotationally stirred condensate show that a regime of simple behaviour occurs in which a single vortex cycles in and out of the condensate. We present a simple quantitative model of this behaviour, which accurately describes the full vortex dynamics, including a critical angular speed of stirring for vortex formation. A method for experimentally preparing a condensate in a central vortex state is suggested.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review Letters (5 February 1999); See http://www.physics.otago.ac.nz/research/bec/vortex for MPEG movies and further information; Accepted for Physical Review Letters (24 June 1999); Changes: updated Figs 1 and 2 (new style), minor typos fixed, more discussion at en

Observation of Superfluid Flow in a Bose-Einstein Condensed Gas

We have studied the hydrodynamic flow in a Bose-Einstein condensate stirred by a macroscopic object, a blue detuned laser beam, using nondestructive {\em in situ} phase contrast imaging. A critical velocity for the onset of a pressure gradient has been observed, and shown to be density dependent. The technique has been compared to a calorimetric method used previously to measure the heating induced by the motion of the laser beam.Comment: 4 pages, 5 figure

Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation

Pade approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in two and three dimensions. These approximations are used to establish a new mechanism of vortex nucleation as a result of solitary wave interactions.Comment: In press by Journal of Physics: Mathematics and Genera

Vortices in a Bose-Einstein Condensate

We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.Comment: 4 pages with 3 figure

Dynamic instability of a rotating Bose-Einstein condensate

We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the non-linear Schr\"odinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.Comment: 4 pages, 3 figures, last version including comparison with experiment

Stable and unstable vortices in multicomponent Bose-Einstein condensates

We study the stability and dynamics of vortices in two-species condensates as prepared in the recent JILA experiment (M. R. Andrews {\em et al.}, Phys. Rev. Lett. 83 (1999) 2498). We find that of the two available configurations, in which one specie has vorticity $m=1$ and the other one has $m=0$, only one is linearly stable, which agrees with the experimental results. However, it is found that in the unstable case the vortex is not destroyed by the instability, but may be transfered from one specie to the other or display complex spatiotemporal dynamics.Comment: 4 EPS figures, now features a three-dimensional stud

Vortex Nucleation in a Stirred Bose-Einstein Condensate

We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. We observed the vortex cores using time-of-flight absorption imaging. By varying the size of the stirrer, we observed either discrete resonances or a broad response as a function of the frequency of the stirrer's motion. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization. This is consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.Comment: 5 pages, two embedded figures. To appear in Phys. Rev. A (RC