132 research outputs found
Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction
The dynamics of a nonconservative Gross-Pitaevskii equation for trapped
atomic systems with attractive two-body interaction is numerically
investigated, considering wide variations of the nonconservative parameters,
related to atomic feeding and dissipation. We study the possible limitations of
the mean field description for an atomic condensate with attractive two-body
interaction, by defining the parameter regions where stable or unstable
formation can be found. The present study is useful and timely considering the
possibility of large variations of attractive two-body scattering lengths,
which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review
Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction
We determine the quantitative effect, in the maximum number of particles and
other static observables, due to small anharmonic terms added to the confining
potential of an atomic condensed system with negative two-body interaction. As
an example of how a cubic or quartic anharmonic term can affect the maximum
number of particles, we consider the trap parameters and the results given by
Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)]. However, this study can be
easily transferred to other trap geometries to estimate anharmonic effects.Comment: Total of 5 pages, 3 figures and 1 table. To appear in Phys. Rev.
Instability of a Bose-Einstein Condensate with Attractive Interaction
We study the stability of a Bose-Einstein condensate of harmonically trapped
atoms with negative scattering length, specifically lithium 7. Our method is to
solve the time-dependent nonlinear Schrodinger equation numerically. For an
isolated condensate, with no gain or loss, we find that the system is stable
(apart from quantum tunneling) if the particle number N is less than a critical
number N_c. For N > N_c, the system collapses to high-density clumps in a
region near the center of the trap. The time for the onset of collapse is on
the order of 1 trap period. Within numerical uncertainty, the results are
consistent with the formation of a "black hole" of infinite density
fluctuations, as predicted by Ueda and Huang. We obtain numerically N_c
approximately 1251. We then include gain-loss mechanisms, i.e., the gain of
atoms from a surrounding "thermal cloud", and the loss due to two- and
three-body collisions. The number N now oscillates in a steady state, with a
period of about 145 trap periods. We obtain N_c approximately 1260 as the
maximum value in the oscillations.Comment: Email correspondence to [email protected] ; 18 pages and 9 EPS
figures, using REVTeX and BoxedEPS macro
Mean-field analysis of collapsing and exploding Bose-Einstein condensates
The dynamics of collapsing and exploding trapped Bose-Einstein condensat es
caused by a sudden switch of interactions from repulsive to attractive a re
studied by numerically integrating the Gross-Pitaevskii equation with atomic
loss for an axially symmetric trap. We investigate the decay rate of
condensates and the phenomena of bursts and jets of atoms, and compare our
results with those of the experiments performed by E. A. Donley {\it et al.}
[Nature {\bf 412}, 295 (2001)]. Our study suggests that the condensate decay
and the burst production is due to local intermittent implosions in the
condensate, and that atomic clouds of bursts and jets are coherent. We also
predict nonlinear pattern formation caused by the density instability of
attractive condensates.Comment: 7 pages, 8 figures, axi-symmetric results are adde
Mean-field description of collapsing and exploding Bose-Einstein condensates
We perform numerical simulation based on the time-dependent mean-field
Gross-Pitaevskii equation to understand some aspects of a recent experiment by
Donley et al. on the dynamics of collapsing and exploding Bose-Einstein
condensates of Rb atoms. They manipulated the atomic interaction by an
external magnetic field via a Feshbach resonance, thus changing the repulsive
condensate into an attractive one and vice versa. In the actual experiment they
changed suddenly the scattering length of atomic interaction from positive to a
large negative value on a pre-formed condensate in an axially symmetric trap.
Consequently, the condensate collapses and ejects atoms via explosion. We find
that the present mean-field analysis can explain some aspects of the dynamics
of the collapsing and exploding Bose-Einstein condensates.Comment: 9 Latex pages, 10 ps and eps files, version accepted in Physical
Review A, minor changes mad
Ground state and elementary excitations of single and binary Bose-Einstein condensates of trapped dipolar gases
We analyze the ground-state properties and the excitation spectrum of
Bose-Einstein condensates of trapped dipolar particles. First, we consider the
case of a single-component polarized dipolar gas. For this case we discuss the
influence of the trapping geometry on the stability of the condensate as well
as the effects of the dipole-dipole interaction on the excitation spectrum. We
discuss also the ground state and excitations of a gas composed of two
antiparallel dipolar components.Comment: 12 pages, 9 eps figures, final versio
Bose-Einstein condensates in atomic gases: simple theoretical results
These notes present simple theoretical approaches to study Bose-Einstein
condensation in trapped atomic gases and their comparison to recent
experimental results : - the ideal Bose gas model - Fermi pseudopotential to
model the atomic interaction potential - finite temperature Hartree-Fock
approximation - Gross-Pitaevskii equation for the condensate wavefunction -
what we learn from a linearization of the Gross-Pitaevskii equation -
Bogoliubov approach and thermodynamical stability - phase coherence properties
of Bose-Einstein condensates - symmetry breaking description of condensatesComment: 146 pages, 17 figures, Lecture Notes of Les Houches Summer School
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