248 research outputs found
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 , mode.Comment: 2 figures. Submitted to Physical Review A. v2 contains more
references. No change in the main resul
Self-similar expansion of the density profile in a turbulent Bose-Einstein condensate
In a recent study we demonstrated the emergence of turbulence in a trapped
Bose-Einstein condensate of Rb-87 atoms. An intriguing observation in such a
system is the behavior of the turbulent cloud during free expansion.The aspect
ratio of the cloud size does not change in the way one would expect for an
ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous
expansion can be understood, at least qualitatively, in terms of the presence
of vorticity distributed throughout the cloud, effectively counteracting the
usual reversal of the aspect ratio seen in free time-of-flight expansion of
non-rotating condensates.Comment: 8 pages, 4 figure
Effective Lagrangian and Quantum Screening in Charged Condensate
A condensate of charged scalars in a neutralizing background of fermions
(e.g., condensed helium-4 nuclei in an electron background in white dwarf
cores) is investigated further. We discuss an effective Lagrangian approach to
this system and show that the strong screening of an electric charge found
previously in arXiv:0806.3692 in a mean-field approximation, is a consequence
of a cancellation due to a phonon. The resulting propagators contain terms that
strongly modify their infrared behavior. Furthermore, we evaluate a one-loop
fermion quantum correction to the screened potential, and find that it is also
suppressed by the phonon subtraction. Therefore, charged impurities (e.g.,
hydrogen or helium-3 nuclei) will be screened efficiently by the condensate.Comment: 1+16 pages; v2: typos & minor improvements; v3: one reference and one
footnote added; two comments streamline
The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating
Bose-Einstein condensate on the unit disc in two dimensions. Writing the
coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps
\to 0 with the angular velocity proportional to
(\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0
(\eps^2|\log\eps|)^{-1} and then a minimizer of
the GP energy functional has no zeros in an annulus at the boundary of the disc
that contains the bulk of the mass. The vorticity resides in a complementary
`hole' around the center where the density is vanishingly small. Moreover, we
prove a lower bound to the ground state energy that matches, up to small
errors, the upper bound obtained from an optimal giant vortex trial function,
and also that the winding number of a GP minimizer around the disc is in accord
with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To
be published in Commun. Math. Phy
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
Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate
We present a detailed theoretical analysis of Bragg spectroscopy from a
Bose-Einstein condensate at T=0K. We demonstrate that within the linear
response regime, both a quantum field theory treatment and a meanfield
Gross-Pitaevskii treatment lead to the same value for the mean evolution of the
quasiparticle operators. The observable for Bragg spectroscopy experiments,
which is the spectral response function of the momentum transferred to the
condensate, can therefore be calculated in a meanfield formalism. We analyse
the behaviour of this observable by carrying out numerical simulations in
axially symmetric three-dimensional cases and in two dimensions. An approximate
analytic expression for the observable is obtained and provides a means for
identifying the relative importance of three broadening and shift mechanisms
(meanfield, Doppler, and finite pulse duration) in different regimes. We show
that the suppression of scattering at small values of q observed by
Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the
meanfield treatment, and can be interpreted in terms of the interference of the
u and v quasiparticle amplitudes. We also show that, contrary to the
assumptions of previous analyses, there is no regime for trapped condensates
for which the spectral response function and the dynamic structure factor are
equivalent. Our numerical calculations can also be performed outside the linear
response regime, and show that at large laser intensities a significant
decrease in the shift of the spectral response function can occur due to
depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published
version: minors changes and an additional figure. (To appear in Phys. Rev. A
Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
We derive and discuss the equations of motion for the condensate and its
fluctuations for a dilute, weakly interacting Bose gas in an external potential
within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation.
Account is taken of the depletion of the condensate and the anomalous Bose
correlations, which are important at finite temperatures. We give a critical
analysis of the self-consistent HFB approximation in terms of the
Hohenberg--Martin classification of approximations (conserving vs gapless) and
point out that the Popov approximation to the full HFB gives a gapless
single-particle spectrum at all temperatures. The Beliaev second-order
approximation is discussed as the spectrum generated by functional
differentiation of the HFB single--particle Green's function. We emphasize that
the problem of determining the excitation spectrum of a Bose-condensed gas
(homogeneous or inhomogeneous) is difficult because of the need to satisfy
several different constraints.Comment: plain tex, 19 page
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