Dynamics of a single vortex line in a Bose-Einstein condensate

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 seconds. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.Comment: 4 pages, 4 figures, submitted to PR

Quadrupole Oscillation of a Single-Vortex Condensate: Evidence for Kelvin Modes

We study the two transverse quadrupole modes of a cigar-shaped Bose-Einstein condensate with a single centered vortex. We show that the counter-rotating mode is more strongly damped than in the absence of a vortex, whereas the co-rotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counter-rotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the wiggling vortex line.Comment: 4 pages, 3 figure

Vortex oscillations in confined Bose-Einstein condensate interacting with 1D optical lattice

We study Bose-Einstein condensate of atomic Boson gases trapped in a composite potential of a harmonic potential and an optical lattice potential. We found a series of collective excitations that induces localized vortex oscillations with a characteristic wavelength. The oscillations might be observed experimentally when radial confinement is tight. We present the excitation spectra of the vortex oscillation modes and propose a way to experimentally excite the modes.Comment: 5 pages, 7 figures. Title, abstract and references are update

From Rotating Atomic Rings to Quantum Hall States

Considerable efforts are currently devoted to the preparation of ultracold neutral atoms in the emblematic strongly correlated quantum Hall regime. The routes followed so far essentially rely on thermodynamics, i.e. imposing the proper Hamiltonian and cooling the system towards its ground state. In rapidly rotating 2D harmonic traps the role of the transverse magnetic field is played by the angular velocity. For particle numbers significantly larger than unity, the required angular momentum is very large and it can be obtained only for spinning frequencies extremely near to the deconfinement limit; consequently, the required control on experimental parameters turns out to be far too stringent. Here we propose to follow instead a dynamic path starting from the gas confined in a rotating ring. The large moment of inertia of the fluid facilitates the access to states with a large angular momentum, corresponding to a giant vortex. The initial ring-shaped trapping potential is then adiabatically transformed into a harmonic confinement, which brings the interacting atomic gas in the desired quantum Hall regime. We provide clear numerical evidence that for a relatively broad range of initial angular frequencies, the giant vortex state is adiabatically connected to the bosonic $\nu=1/2$ Laughlin state, and we discuss the scaling to many particles.Comment: 9 pages, 5 figure

The Impact of Heat Islands on Mortality in Paris during the August 2003 Heat Wave

Background: Heat waves have a drastic impact on urban populations, which could increase with climate change

Critical rotation of a harmonically trapped Bose gas

We study experimentally and theoretically a cold trapped Bose gas under critical rotation, i.e. with a rotation frequency close to the frequency of the radial confinement. We identify two regimes: the regime of explosion where the cloud expands to infinity in one direction, and the regime where the condensate spirals out of the trap as a rigid body. The former is realized for a dilute cloud, and the latter for a Bose-Einstein condensate with the interparticle interaction exceeding a critical value. This constitutes a novel system in which repulsive interactions help in maintaining particles together.Comment: 4 pages, 4 figures, submitted to PR

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all figures, in text (especially in Sec III) and in Reference

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions.Comment: Review article, 38 pages, 7 figs. To appear in Int. Jour. of Bif. and Chao

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp