1,754 research outputs found
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
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
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
Condensate fraction of cold gases in non-uniform external potential
Exact calculation of the condensate fraction in multi-dimensional
inhomogeneous interacting Bose systems which do not possess continuous
symmetries is a difficult computational problem. We have developed an iterative
procedure which allows to calculate the condensate fraction as well as the
corresponding eigenfunction of the one-body density matrix. We successfully
validate this procedure in diffusion Monte Carlo simulations of a Bose gas in
an optical lattice at zero temperature. We also discuss relation between
different criteria used for testing coherence in cold Bose systems, such as
fraction of particles that are superfluid, condensed or are in the
zero-momentum state.Comment: 4 pages, 2 figure
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
Localization of a Bose-Einstein condensate in a bichromatic optical lattice
By direct numerical simulation of the time-dependent Gross-Pitaevskii
equation we study different aspects of the localization of a non-interacting
ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic
quasi-periodic optical-lattice potential. Such a quasi-periodic potential, used
in a recent experiment on the localization of a BEC [Roati et al., Nature 453,
895 (2008)], can be formed by the superposition of two standing-wave polarized
laser beams with different wavelengths. We investigate the effect of the
variation of optical amplitudes and wavelengths on the localization of a
non-interacting BEC. We also simulate the non-linear dynamics when a
harmonically trapped BEC is suddenly released into a quasi-periodic potential,
{as done experimentally in a laser speckle potential [Billy et al., Nature 453,
891 (2008)]$ We finally study the destruction of the localization in an
interacting BEC due to the repulsion generated by a positive scattering length
between the bosonic atoms.Comment: 8 page
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