815 research outputs found
Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms
By incorporating the zero-point energy contribution we derive simple and
accurate extensions of the usual Thomas-Fermi (TF) expressions for the
ground-state properties of trapped Bose-Einstein condensates that remain valid
for an arbitrary number of atoms in the mean-field regime. Specifically, we
obtain approximate analytical expressions for the ground-state properties of
spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct
analytical formulas in both the TF and the perturbative regimes, and remain
valid and accurate in between these two limiting cases. Mean-field quasi-1D and
-2D condensates appear as simple particular cases of our formulation. The
validity of our results is corroborated by an independent numerical computation
based on the 3D Gross-Pitaevskii equation.Comment: 5 pages, 3 figures. Final version published in Phys. Rev.
Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices
We study fundamental and compound gap solitons (GSs) of matter waves in
one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D)
weak-radial-confinement regime, which corresponds to realistic experimental
conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit
nontrivial radial structures. Associated with each 3D linear spectral band
exists a family of fundamental gap solitons that share a similar transverse
structure with the Bloch waves of the corresponding linear band. GSs with
embedded vorticity may exist \emph{inside} bands corresponding to other
values of . Stable GSs, both fundamental and compound ones (including vortex
solitons), are those which originate from the bands with lowest axial and
radial quantum numbers. These findings suggest a scenario for the experimental
generation of robust GSs in 3D settings.Comment: 5 pages, 5 figures; v2: matches published versio
Dynamical evolution of a doubly-quantized vortex imprinted in a Bose-Einstein Condensate
The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93},
160406 (2004)] on the decay of a doubly quantized vortex imprinted in Na condensates is analyzed by numerically solving the Gross-Pitaevskii
equation. Our results, which are in very good quantitative agreement with the
experiment, demonstrate that the vortex decay is mainly a consequence of
dynamical instability. Despite apparent contradictions, the local density
approach is consistent with the experimental results. The monotonic increase
observed in the vortex lifetimes is a consequence of the fact that, for large
condensates, the measured lifetimes incorporate the time it takes for the
initial perturbation to reach the central slice. When considered locally, the
splitting occurs approximately at the same time in every condensate, regardless
of its size.Comment: 5 pages, 4 figure
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