100 research outputs found
Shape oscillation of a rotating Bose-Einstein condensate
We present a theoretical and experimental analysis of the transverse monopole
mode of a fast rotating Bose-Einstein condensate. The condensate's rotation
frequency is similar to the trapping frequency and the effective confinement is
only ensured by a weak quartic potential. We show that the non-harmonic
character of the potential has a clear influence on the mode frequency, thus
making the monopole mode a precise tool for the investigation of the fast
rotation regime
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.
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
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
Vortex Rings in Fast Rotating Bose-Einstein Condensates
When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex
phase appears, that is the condensate becomes annular with no vortices in the
bulk but a macroscopic phase circulation around the central hole. In a former
paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have
studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii
energy on the unit disc. In particular we computed an upper bound to the
critical speed for the transition to the giant vortex phase. In this paper we
confirm that this upper bound is optimal by proving that if the rotation speed
is taken slightly below the threshold there are vortices in the condensate. We
prove that they gather along a particular circle on which they are evenly
distributed. This is done by providing new upper and lower bounds to the GP
energy.Comment: to appear in Archive of Rational Mechanics and Analysi
The transverse breathing mode of an elongated Bose-Einstein condensate
We study experimentally the transverse monopole mode of an elongated rubidium
condensate. Due to the scaling invariance of the non-linear Schr\"odinger
(Gross-Pitaevski) equation, the oscillation is monochromatic and sinusoidal at
short times, even under strong excitation. For ultra-low temperatures, the
quality factor can exceed 2000, where and
are the mode angular frequency and damping rate. This value is much
larger than any previously reported for other eigenmodes of a condensate. We
also present the temperature variation of and .Comment: 4 pages, 4 figures, submitted to PR
Phase field approach to optimal packing problems and related Cheeger clusters
In a fixed domain of we study the asymptotic behaviour of optimal
clusters associated to -Cheeger constants and natural energies like the
sum or maximum: we prove that, as the parameter converges to the
"critical" value , optimal Cheeger clusters
converge to solutions of different packing problems for balls, depending on the
energy under consideration. As well, we propose an efficient phase field
approach based on a multiphase Gamma convergence result of Modica-Mortola type,
in order to compute -Cheeger constants, optimal clusters and, as a
consequence of the asymptotic result, optimal packings. Numerical experiments
are carried over in two and three space dimensions
Excitations of a Bose-Einstein condensate in a one-dimensional optical lattice
We investigate the low-lying excitations of a stack of weakly-coupled
two-dimensional Bose-Einstein condensates that is formed by a one-dimensional
optical lattice. In particular, we calculate the dispersion relations of the
monopole and quadrupole modes, both for the ground state as well as for the
case in which the system contains a vortex along the direction of the lasers
creating the optical lattice. Our variational approach enables us to determine
analytically the dispersion relations for an arbitrary number of atoms in every
two-dimensional condensate and for an arbitrary momentum. We also discuss the
feasibility of experimentally observing our results.Comment: 16 pages, 5 figures, minor changes,accepted for publication in Phys.
Rev.
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
Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap
The collective modes of a rotating Bose-Einstein condensate confined in an
attractive quadratic plus quartic trap are investigated. Assuming the presence
of a large number of vortices we apply the diffused vorticity approach to the
system. We then use the sum rule technique for the calculation of collective
frequencies, comparing the results with the numerical solution of the
linearized hydrodynamic equations. Numerical solutions also show the existence
of low-frequency multipole modes which are interpreted as vortex oscillations.Comment: 10 pages, 4 figure
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