30 research outputs found
Collective excitations of degenerate Fermi gases in anisotropic parabolic traps
The hydrodynamic low-frequency oscillations of highly degenerate Fermi gases
trapped in anisotropic harmonic potentials are investigated. Despite the lack
of an obvious spatial symmetry the wave-equation turns out to be separable in
elliptical coordinates, similar to a corresponding result established earlier
for Bose-condensates. This result is used to give the analytical solution of
the anisotropic wave equation for the hydrodynamic modes.Comment: 11 pages, Revte
Bose-Einstein condensation in shallow traps
In this paper we study the properties of Bose-Einstein condensates in shallow
traps. We discuss the case of a Gaussian potential, but many of our results
apply also to the traps having a small quadratic anharmonicity. We show the
errors introduced when a Gaussian potential is approximated with a parabolic
potential, these errors can be quite large for realistic optical trap parameter
values. We study the behavior of the condensate fraction as a function of trap
depth and temperature and calculate the chemical potential of the condensate in
a Gaussian trap. Finally we calculate the frequencies of the collective
excitations in shallow spherically symmetric and 1D traps.Comment: 6 pages, 4 figure
Hydrodynamic excitations of Bose condensates in anisotropic traps
The collective excitations of Bose condensates in anisotropic axially
symmetric harmonic traps are investigated in the hydrodynamic and Thomas-Fermi
limit. We identify an additional conserved quantity, besides the axial angular
momentum and the total energy, and separate the wave equation in elliptic
coordinates. The solution is reduced to the algebraic problem of diagonalizing
finite dimensional matrices. The classical quasi-particle dynamics in the local
density approximation for energies of the order of the chemical potential is
shown to be chaotic.Comment: 4 pages revtex including 1 table, and 1 figure in postscrip
Damping of low-energy excitations of a trapped Bose condensate at finite temperatures
We present the theory of damping of low-energy excitations of a trapped Bose
condensate at finite temperatures, where the damping is provided by the
interaction of these excitations with the thermal excitations. We emphasize the
key role of stochastization in the behavior of the thermal excitations for
damping in non-spherical traps. The damping rates of the lowest excitations,
following from our theory, are in fair agreement with the data of recent JILA
and MIT experiments. The damping of quasiclassical excitations is determined by
the condensate boundary region, and the result for the damping rate is
drastically different from that in a spatially homogeneous gas.Comment: 10 pages RevTeX, correction of the misprints and addition of the
sentence clarifying the result for quasiclassical excitationscorrection of
the misprints and addition of the sentence clarifying the result for
quasiclassical excitation
On the stability of standing matter waves in a trap
We discuss excited Bose-condensed states and find the criterion of dynamical
stability of a kink-wise state, i.e., a standing matter wave with one nodal
plane perpendicular to the axis of a cylindrical trap. The dynamical stability
requires a strong radial confinement corresponding to the radial frequency
larger than the mean-field interparticle interaction. We address the question
of thermodynamic instability related to the presence of excitations with
negative energy.Comment: 4 pages, 3 figure
Dielectric formalism and damping of collective modes in trapped Bose-Einstein condensed gases
We present the general dielectric formalism for Bose-Einstein condensed
systems in external potential at finite temperatures. On the basis of a model
arising within this framework as a first approximation in an intermediate
temperature region for large condensate we calculate the damping of low-energy
excitations in the collisionless regime.Comment: 4 pages, no figures, RevTe
Classical quasi-particle dynamics in trapped Bose condensates
The dynamics of quasi-particles in repulsive Bose condensates in a harmonic
trap is studied in the classical limit. In isotropic traps the classical motion
is integrable and separable in spherical coordinates. In anisotropic traps the
classical dynamics is found, in general, to be nonintegrable. For
quasi-particle energies E much smaller than thechemical potential, besides the
conserved quasi-particle energy, we identify two additional nearly conserved
phase-space functions. These render the dynamics inside the condensate
(collective dynamics) integrable asymptotically for E/chemical potential very
small. However, there coexists at the same energy a dynamics confined to the
surface of the condensate, which is governed by a classical Hartree-Fock
Hamiltonian. We find that also this dynamics becomes integrable for E/chemical
potential very small, because of the appearance of an adiabatic invariant. For
E/chemical potential of order 1 a large portion of the phase-space supports
chaotic motion, both, for the Bogoliubov Hamiltonian and its Hartree-Fock
approximant. To exemplify this we exhibit Poincar\'e surface of sections for
harmonic traps with the cylindrical symmetry and anisotropy found in TOP traps.
For E/chemical potential very large the dynamics is again governed by the
Hartree-Fock Hamiltonian. In the case with cylindrical symmetry it becomes
quasi-integrable because the remaining small chaotic components in phase space
are tightly confined by tori.Comment: 13 pages Latex, 6 eps.gz-figure
Dynamics of Bose condensed gases in highly deformed traps
We provide a unified investigation of normal modes and sound propagation at
zero temperature in Bose condensed gases confined in highly asymmetric harmonic
traps and interacting with repulsive forces. By using hydrodynamic theory for
superfluids we obtain explicit analytic results for the dispersion law of the
low energy discretized modes for both cigar and disk shaped geometries,
including the regime of large quantum numbers where discrete modes can be
identified with phonons. The correspondence with sound propagation in
cylindrical traps and the one-dimensional nature of cigar type configurations
are explicitly discussed.Comment: 12 pages Revtex, no figure
Bose-Einstein condensation in quasi2D trapped gases
We discuss BEC in (quasi)2D trapped gases and find that well below the
transition temperature the equilibrium state is a true condensate,
whereas at intermediate temperatures one has a quasicondensate
(condensate with fluctuating phase). The mean-field interaction in a quasi2D
gas is sensitive to the frequency of the (tight) confinement in the
"frozen" direction, and one can switch the sign of the interaction by changing
. Variation of can also reduce the rates of inelastic
processes, which opens prospects for tunable BEC in trapped quasi2D gases.Comment: 4 revtex pages, 1 figure, text is revised, figure improve
Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate
A hydrodynamic description is used to study the normal modes of a vortex in a
zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the
circulating superfluid velocity far from the vortex core provides a small
perturbation that splits the originally degenerate normal modes of a
vortex-free condensate. The relative frequency shifts are small in all cases
considered (they vanish for the lowest dipole mode with |m|=1), suggesting that
the vortex is stable. The Bogoliubov equations serve to verify the existence of
helical waves, similar to those of a vortex line in an unbounded weakly
interacting Bose gas. In the large-condensate (small-core) limit, the
condensate wave function reduces to that of a straight vortex in an unbounded
condensate; the corresponding Bogoliubov equations have no bound-state
solutions that are uniform along the symmetry axis and decay exponentially far
from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We
have altered the material in Secs. 3B and 4 in connection with the normal
modes that have |m|=1. Our present treatment satisfies the condition that the
fundamental dipole mode of a condensate with (or without) a vortex should
have the bare frequency $\omega_\perp