Vortex lattice of a Bose-Einstein Condensate in a rotating anisotropic trap

We study the vortex lattices in a Bose-Einstein Condensate in a rotating anisotropic harmonic trap. We first investigate the single particle wavefunctions obtained by the exact solution of the problem and give simple expressions for these wavefunctions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.Comment: 15 pages,4 figure

Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice

Starting from the equations of rotational hydrodynamics we study the macroscopic behaviour of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al., Phys. Rev. Lett. 89, 100403 (2002).Comment: 4 pages, 4 figure

Experiments on the twisted vortex state in superfluid 3He-B

We have performed measurements and numerical simulations on a bundle of vortex lines which is expanding along a rotating column of initially vortex-free 3He-B. Expanding vortices form a propagating front: Within the front the superfluid is involved in rotation and behind the front the twisted vortex state forms, which eventually relaxes to the equilibrium vortex state. We have measured the magnitude of the twist and its relaxation rate as function of temperature above 0.3Tc. We also demonstrate that the integrity of the propagating vortex front results from axial superfluid flow, induced by the twist.Comment: prepared for proceedings of the QFS2007 symposium in Kaza

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010

Oscillations of a rapidly rotating annular Bose-Einstein condensate

A time-dependent variational Lagrangian analysis based on the Gross-Pitaevskii energy functional serves to study the dynamics of a metastable giant vortex in a rapidly rotating Bose-Einstein condensate. The resulting oscillation frequencies of the core radius reproduce the trends seen in recent experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the theoretical values are smaller by a factor approximately 0.6-0.8.Comment: 7 pages, revtex

Kelvin Modes of a fast rotating Bose-Einstein Condensate

Using the concept of diffused vorticity and the formalism of rotational hydrodynamics we calculate the eigenmodes of a harmonically trapped Bose-Einstein condensate containing an array of quantized vortices. We predict the occurrence of a new branch of anomalous excitations, analogous to the Kelvin modes of the single vortex dynamics. Special attention is devoted to the excitation of the anomalous scissors mode.Comment: 7 pages, 3 figures, submitted to Phys. Rev.

Excitation spectrum of vortex lattices in rotating Bose-Einstein condensates

Using the coarse grain averaged hydrodynamic approach, we calculate the excitation spectrum of vortex lattices sustained in rotating Bose-Einstein condensates. The spectrum gives the frequencies of the common-mode longitudinal waves in the hydrodynamic regime, including those of the higher-order compressional modes. Reasonable agreement with the measurements taken in a recent JILA experiment is found, suggesting that one of the longitudinal modes reported in the experiment is likely to be the $n=2$, $m=0$ mode.Comment: 2 figures. Submitted to Physical Review A. v2 contains more references. No change in the main resul

Tkachenko waves, glitches and precession in neutron star

Here I discuss possible relations between free precession of neutron stars, Tkachenko waves inside them and glitches. I note that the proposed precession period of the isolated neutron star RX J0720.4-3125 (Haberl et al. 2006) is consistent with the period of Tkachenko waves for the spin period 8.4s. Based on a possible observation of a glitch in RX J0720.4-3125 (van Kerkwijk et al. 2007), I propose a simple model, in which long period precession is powered by Tkachenko waves generated by a glitch. The period of free precession, determined by a NS oblateness, should be equal to the standing Tkachenko wave period for effective energy transfer from the standing wave to the precession motion. A similar scenario can be applicable also in the case of the PSR B1828-11.Comment: 6 pages, no figures, accepted to Ap&S

Periodic Vortex Structures in Superfluid 3He-A

We discuss the general properties of periodic vortex arrangements in rotating superfluids. The different possible structures are classified according to the symmetry space-groups and the circulation number. We calculate numerically several types of vortex structures in superfluid 3He-A. The calculations are done in the Ginzburg-Landau region, but the method is applicable at all temperatures. A phase diagram of vortices is constructed in the plane formed by the magnetic field and the rotation velocity. The characteristics of the six equilibrium vortex solutions are discussed. One of these, the locked vortex 3, has not been considered in the literature before. The vortex sheet forms the equilibrium state of rotating 3He-A at rotation velocities exceeding 2.6 rad/s. The results are in qualitative agreement with experiments.Comment: 13 pages, 7 figures, http://boojum.hut.fi/research/theory/diagram.htm