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Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice
By numerical simulation of the time-dependent Gross-Pitaevskii equation we
show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC)
vortex can be localized in a three-dimensional bichromatic quasi-periodic
optical-lattice (OL) potential generated by the superposition of two
standing-wave polarized laser beams with incommensurate wavelengths. This is a
generalization of the localization of a BEC in a one-dimensional bichromatic OL
as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We
demonstrate the stability of the localized state by considering its time
evolution in the form of a stable breathing oscillation in a slightly altered
potential for a large period of time. {Finally, we consider the localization of
a BEC in a random 1D potential in the form of several identical repulsive
spikes arbitrarily distributed in space
Pathway from condensation via fragmentation to fermionization of cold bosonic systems
For small scattering lengths, cold bosonic atoms form a condensate the
density profile of which is smooth. With increasing scattering length, the
density {\it gradually} acquires more and more oscillations. Finally, the
number of oscillations equals the number of bosons and the system becomes {\it
fermionized}. On this pathway from condensation to fermionization intriguing
phenomena occur, depending on the shape of the trap. These include macroscopic
fragmentation and
{\it coexistence} of condensed and fermionized parts that are separated in
space.Comment: 12 pages, 2 figure
Approximating Steady States in Equilibrium and Nonequilibrium Condensates
We obtain approximations for the time-independent Gross-Pitaevskii (GP) and
complex GP equation in two and three spatial dimensions by generalizing the
divergence-free WKB method. The results include an explicit expression of a
uniformly valid approximation for the condensate density of an ultracold Bose
gas confined in a harmonic trap that extends into the classically forbidden
region. This provides an accurate approximation of the condensate density that
includes healing effects at leading order that are missing in the widely
adopted Thomas-Fermi approximation. The results presented herein allow us to
formulate useful approximations to a range of experimental systems including
the equilibrium properties of a finite temperature Bose gas and the
steady-state properties of a 2D nonequilibrium condensate. Comparisons between
our asymptotic and numerical results for the conservative and
forced-dissipative forms of the GP equations as applied to these systems show
excellent agreement between the two sets of solutions thereby illustrating the
accuracy of these approximations.Comment: 5 pages, 1 figur
Landau dynamics of a grey soliton in a trapped condensate
It is shown that grey soliton dynamics in an one-dimensional trap can be
treated as Landau dynamics of a quasi-particle. A soliton of arbitrary
amplitude moves in the trapping potential without deformation of its density
profile as a particle of mass . The dynamics in the local density
approximation is shown to be consistent with the perturbation theory for dark
solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.Comment: REVTEX, 4 pages, submitte
Quantitative test of thermal field theory for Bose-Einstein condensates II
We have recently derived a gapless theory of the linear response of a
Bose-condensed gas to external perturbations at finite temperature and used it
to explain quantitatively the measurements of condensate excitations and decay
rates made at JILA [D. S. Jin et.al., Phys. Rev. Lett. 78, 764 (1997)]. The
theory describes the dynamic coupling between the condensate and non-condensate
via a full quasiparticle description of the time-dependent normal and anomalous
averages and includes all Beliaev and Landau processes. In this paper we
provide a full discussion of the numerical calculations and a detailed analysis
of the theoretical results in the context of the JILA experiment. We provide
unambiguous proof that the dipole modes are obtained accurately within our
calculations and present quantitative results for the relative phase of the
oscillations of the condensed and uncondensed atom clouds. One of the main
difficulties in the implementation of the theory is obtaining results which are
not sensitive to basis cutoff effects and we have therefore developed a novel
asymmetric summation method which solves this problem and dramatically improves
the numerical convergence. This new technique should make the implementation of
the theory and its possible future extensions feasible for a wide range of
condensate populations and trap geometries.Comment: 23 pages, 11 figures, revtex 4. Submitted to PRA. Sequel to: S. A.
Morgan et al, PRL, 91, 250403 (2003
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