1,408 research outputs found
Vortex lattices in rapidly rotating Bose-Einstein condensates: modes and correlation functions
After delineating the physical regimes which vortex lattices encounter in
rotating Bose-Einstein condensates as the rotation rate, , increases,
we derive the normal modes of the vortex lattice in two dimensions at zero
temperature. Taking into account effects of the finite compressibility, we find
an inertial mode of frequency , and a primarily transverse
Tkachenko mode, whose frequency goes from being linear in the wave vector in
the slowly rotating regime, where is small compared with the lowest
compressional mode frequency, to quadratic in the wave vector in the opposite
limit. We calculate the correlation functions of vortex displacements and
phase, density and superfluid velocities, and find that the zero-point
excitations of the soft quadratic Tkachenko modes lead in a large system to a
loss of long range phase correlations, growing logarithmically with distance,
and hence lead to a fragmented state at zero temperature. The vortex positional
ordering is preserved at zero temperature, but the thermally excited Tkachenko
modes cause the relative positional fluctuations to grow logarithmically with
separation at finite temperature. The superfluid density, defined in terms of
the transverse velocity autocorrelation function, vanishes at all temperatures.
Finally we construct the long wavelength single particle Green's function in
the rotating system and calculate the condensate depletion as a function of
temperature.Comment: 11 pages Latex, no figure
Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates
We calculate the in-plane modes of the vortex lattice in a rotating Bose
condensate from the Thomas-Fermi to the mean-field quantum Hall regimes. The
Tkachenko mode frequency goes from linear in the wavevector, , for lattice
rotational velocities, , much smaller than the lowest sound wave
frequency in a finite system, to quadratic in in the opposite limit. The
system also supports an inertial mode of frequency . The
calculated frequencies are in good agreement with recent observations of
Tkachenko modes at JILA, and provide evidence for the decrease in the shear
modulus of the vortex lattice at rapid rotation.Comment: 4 pages, 2 figure
Fluctuations and correlations in rotating Bose-Einstein condensates
We investigate the effects of correlations on the properties of the ground
state of the rotating harmonically-trapped Bose gas by adding Bogoliubov
fluctuations to the mean-field ground state of an -particle single-vortex
system. We demonstrate that the fluctuation-induced correlations lower the
energy compared to that of the mean-field ground state, that the vortex core is
pushed slightly away from the center of the trap, and that an unstable mode
with negative energy (for rotations slower than a critical frequency) emerges
in the energy spectrum, thus, pointing to a better state for slow rotation. We
construct mean-field ground states of 0-, 1-, and 2-vortex states as a function
of rotation rate and determine the critical frequencies for transitions between
these states, as well as the critical frequency for appearance of a metastable
state with an off-center vortex and its image vortex in the evanescent tail of
the cloud.Comment: Added a paragraph to Section III; Revised arguments in Section III.A,
results unchanged; Added reference
Vortex states of rapidly rotating dilute Bose-Einstein condensates
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating
dilute Bose-Einstein condensates adjust in radius as the rotation velocity,
, grows, thus precluding a phase transition associated with core
overlap at high vortex density. In both a harmonic trap and a rotating
hard-walled bucket, the core size approaches a limiting fraction of the
intervortex spacing. At large rotation speeds, a system confined in a bucket
develops, within Thomas-Fermi, a hole along the rotation axis, and eventually
makes a transition to a giant vortex state with all the vorticity contained in
the hole.Comment: 4 pages, 2 figures, RevTex4. Version as published; discussion
extended, some references added and update
Fermi liquid theory of ultra-cold trapped Fermi gases: Implications for Pseudogap Physics and Other Strongly Correlated Phases
We show how Fermi liquid theory can be applied to ultra-cold Fermi gases,
thereby expanding their "simulation" capabilities to a class of problems of
interest to multiple physics sub-disciplines. We introduce procedures for
measuring and calculating position dependent Landau parameters. This lays the
ground work for addressing important controversial issues: (i) the suggestion
that thermodynamically, the normal state of a unitary gas is indistinguishable
from a Fermi liquid (ii) that a fermionic system with strong repulsive contact
interactions is associated with either ferromagnetism or localization; this
relates as well to He and its p-wave superfluidity.Comment: 4 pages, 2 figures, revised versio
Thermal fluctuations of gauge fields and first order phase transitions in color superconductivity
We study the effects of thermal fluctuations of gluons and the diquark
pairing field on the superconducting-to-normal state phase transition in a
three-flavor color superconductor, using the Ginzburg-Landau free energy. At
high baryon densities, where the system is a type I superconductor, gluonic
fluctuations, which dominate over diquark fluctuations, induce a cubic term in
the Ginzburg-Landau free energy, as well as large corrections to quadratic and
quartic terms of the order parameter. The cubic term leads to a relatively
strong first order transition, in contrast with the very weak first order
transitions in metallic type I superconductors. The strength of the first order
transition decreases with increasing baryon density. In addition gluonic
fluctuations lower the critical temperature of the first order transition. We
derive explicit formulas for the critical temperature and the discontinuity of
the order parameter at the critical point. The validity of the first order
transition obtained in the one-loop approximation is also examined by
estimating the size of the critical region.Comment: 12 pages, 4 figures, final version published in Phys. Rev.
The transition temperature of the dilute interacting Bose gas for internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and the scattering length. This
result is non-perturbative, and a direct perturbative calculation of the
amplitude is impossible due to infrared divergences familiar from the study of
the superfluid helium lambda transition. Therefore we introduce here another
standard expansion scheme, generalizing the initial model which depends on one
complex field to one depending on real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large result agrees remarkably well with
recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter
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