56 research outputs found
Ultracold dipolar gases - a challenge for experiments and theory
We present a review of recent results concerning the physics of ultracold
trapped dipolar gases. In particular, we discuss the Bose-Einstein condensation
for dipolar Bose gases and the BCS transition for dipolar Fermi gases. In both
cases we stress the dominant role of the trap geometry in determining the
properties of the system. We present also results concerning bosonic dipolar
gases in optical lattices and the possibility of obtaining variety of different
quantum phases in such case. Finally, we analyze various possible routes
towards achieving ultracold dipolar gases.Comment: This paper is based on the lecture given by M. Lewenstein at the
Nobel Symposium ''Coherence and Condensation in Quantum Systems'',
Gothesburg, 4-7.12.200
BCS pairing in a trapped dipolar Fermi gas
We present a detailed study of the BCS pairing transition in a trapped polarized dipolar Fermi gas. In the case of a shallow nearly spherical trap, we find a decrease in the transition temperature as a function of the trap aspect ratio and predict the existence of the optimal trap geometry. The latter corresponds to the highest critical temperature of the BCS transition for a given number of particles. We also derive the phase diagram for an ultracold trapped dipolar Fermi gas in the situation where the trap frequencies can be of the order of the critical temperature of the BCS transition in the homogeneous case, and determine the critical value of the dipole - dipole interaction energy below which the BCS transition ceases to exist. The critical dipole strength is obtained as a function of the trap aspect ratio. Alternatively, for a given dipole strength, there is a critical value of the trap anisotropy for the BCS state to appear. The order parameter calculated at criticality exhibits novel non-monotonic behaviour resulting from the combined effect of the confining potential and the anisotropic character of the interparticle dipole - dipole interaction.DFGRTN Cold Quantum GasesESF PESC BEC2000+Russian Foundation for Basic ResearchQUDEDISINTASAlexander von Humboldt Foundatio
BCS pairing in a trapped dipolar Fermi gase
We present a detailed study of the BCS pairing transition in a trapped
polarized dipolar Fermi gas. In the case of a shallow nearly spherical trap, we
find the decrease of the transition temperature as a function of the trap
aspect ratio and predict the existence of the optimal trap geometry. The latter
corresponds to the highest critical temperature of the BCS transition for a
given number of particles. We also derive the phase diagram for an ultracold
trapped dipolar Fermi gases in the situation, where the trap frequencies can be
of the order of the critical temperature of the BCS transition in the
homogeneous case, and find the critical value of the dipole-dipole interaction
energy, below which the BCS transition ceases to exist. The critical dipole
strength is obtained as a function of the trap aspect ratio. Alternatively, for
a given dipole strength there is a critical value of the trap anisotropy for
the BCS state to appear. The order parameter calculated at criticality,
exhibits nover non-monotonic behavior resulted from the combined effect of the
confining potential and anisotropic character of the interparticle
dipole-dipole interation.Comment: 14 pages, 3 figure
Interferometric detection of a single vortex in a dilute Bose-Einstein condensate
Using two radio frequency pulses separated in time we perform an amplitude
division interference experiment on a rubidium Bose-Einstein condensate. The
presence of a quantized vortex, which is nucleated by stirring the condensate
with a laser beam, is revealed by a dislocation in the fringe pattern.Comment: 4 pages, 4 figure
Images of the Dark Soliton in a Depleted Condensate
The dark soliton created in a Bose-Einstein condensate becomes grey in course
of time evolution because its notch fills up with depleted atoms. This is the
result of quantum mechanical calculations which describes output of many
experimental repetitions of creation of the stationary soliton, and its time
evolution terminated by a destructive density measurement. However, such a
description is not suitable to predict the outcome of a single realization of
the experiment were two extreme scenarios and many combinations thereof are
possible: one will see (1) a displaced dark soliton without any atoms in the
notch, but with a randomly displaced position, or (2) a grey soliton with a
fixed position, but a random number of atoms filling its notch. In either case
the average over many realizations will reproduce the mentioned quantum
mechanical result. In this paper we use N-particle wavefunctions, which follow
from the number-conserving Bogoliubov theory, to settle this issue.Comment: 8 pages, 6 figures, references added in version accepted for
publication in J. Phys.
Scattering of light and atoms in a Fermi-Dirac gas with BCS pairing
We theoretically study the optical properties of a Fermi-Dirac gas in the
presence of a superfluid state. We calculate the leading quantum-statistical
corrections to the standard column density result of the electric
susceptibility. We also consider the Bragg diffraction of atoms by means of
light-stimulated transitions of photons between two intersecting laser beams.
Bardeen-Cooper-Schrieffer pairing between atoms in different internal levels
magnifies incoherent scattering processes. The absorption linewidth of a
Fermi-Dirac gas is broadened and shifted. Bardeen-Cooper-Schrieffer pairing
introduces a collisional local-field shift that may dramatically dominate the
Lorentz-Lorenz shift. For the case of the Bragg spectroscopy the static
structure function may be significantly increased due to superfluidity in the
nearforward scattering.Comment: 13 pages, 6 figures; to appear in PR
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
Optical Generation of Vortices in trapped Bose-Einstein Condensates
We demonstrate numerically the efficient generation of vortices in
Bose-Einstein condensates (BEC) by using a ``phase imprinting'' method. The
method consist of passing a far off resonant laser pulse through an absorption
plate with azimuthally dependent absorption coefficient, imaging the laser beam
onto a BEC, and thus creating the corresponding non-dissipative Stark shift
potential and condensate phase shift. In our calculations we take into account
experimental imperfections. We also propose an interference method to detect
vortices by coherently pushing part of the condensate using optically induced
Bragg scattering.Comment: 8 pages, 4 figure
Dynamics of a Vortex in a Trapped Bose-Einstein Condensate
We consider a large condensate in a rotating anisotropic harmonic trap. Using
the method of matched asymptotic expansions, we derive the velocity of an
element of vortex line as a function of the local gradient of the trap
potential, the line curvature and the angular velocity of the trap rotation.
This velocity yields small-amplitude normal modes of the vortex for 2D and 3D
condensates. For an axisymmetric trap, the motion of the vortex line is a
superposition of plane-polarized standing-wave modes. In a 2D condensate, the
planar normal modes are degenerate, and their superposition can result in
helical traveling waves, which differs from a 3D condensate. Including the
effects of trap rotation allows us to find the angular velocity that makes the
vortex locally stable. For a cigar-shape condensate, the vortex curvature makes
a significant contribution to the frequency of the lowest unstable normal mode;
furthermore, additional modes with negative frequencies appear. As a result, it
is considerably more difficult to stabilize a central vortex in a cigar-shape
condensate than in a disc-shape one. Normal modes with imaginary frequencies
can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection
with recent JILA experiments, we consider the motion of a straight vortex line
in a slightly nonspherical condensate. The vortex line changes its orientation
in space at the rate proportional to the degree of trap anisotropy and can
exhibit periodic recurrences.Comment: 19 pages, 6 eps figures, REVTE
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