59 research outputs found
Instantons and radial excitations in attractive Bose-Einstein condensates
Imaginary- and real-time versions of an equation for the condensate density
are presented which describe dynamics and decay of any spherical Bose-Einstein
condensate (BEC) within the mean field appraoch. We obtain quantized energies
of collective finite amplitude radial oscillations and exact numerical
instanton solutions which describe quantum tunneling from both the metastable
and radially excited states of the BEC of 7Li atoms. The mass parameter for the
radial motion is found different from the gaussian value assumed hitherto, but
the effect of this difference on decay exponents is small. The collective
breathing states form slightly compressed harmonic spectrum, n=4 state lying
lower than the second Bogolyubov (small amplitude) mode. The decay of these
states, if excited, may simulate a shorter than true lifetime of the metastable
state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure
Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation
In the present work, we improve a numerical method, developed to solve the
Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used
in the equation, which permits to evaluate the wave-function normalization
after the numerical solution. We have a two point boundary value problem, where
the second point is taken at infinity. The differential equation is solved
using the shooting method and Runge-Kutta integration method, requiring that
the asymptotic constants, for the function and its derivative, are equal for
large distances. In order to obtain fast convergence, the secant method is
used.Comment: 2 figure
Order Parameter at the Boundary of a Trapped Bose Gas
Through a suitable expansion of the Gross-Pitaevskii equation near the
classical turning point, we obtain an explicit solution for the order parameter
at the boundary of a trapped Bose gas interacting with repulsive forces. The
kinetic energy of the system, in terms of the classical radius and of the
harmonic oscillator length , follows the law , approaching, for large , the
results obtained by solving numerically the Gross-Pitaevskii equation. The
occurrence of a Josephson-type current in the presence of a double trap
potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also
available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm
Bosons in anisotropic traps: ground state and vortices
We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic
trap, modeled by an anisotropic harmonic potential. We evaluate the wave
function and the energy of the Bose Einstein condensate as a function of the
particle number, both for positive and negative scattering length. The results
for the transverse and vertical size of the cloud of atoms, as well as for the
kinetic and potential energy per particle, are compared with the predictions of
approximated models. We also compare the aspect ratio of the velocity
distribution with first experimental estimates available for Rb. Vortex
states are considered and the critical angular velocity for production of
vortices is calculated. We show that the presence of vortices significantly
increases the stability of the condensate in the case of attractive
interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at
http://anubis.science.unitn.it/~dalfovo/papers/papers.htm
Evolution of a Bose-condensed gas under variations of the confining potential
We discuss the dynamic properties of a trapped Bose-condensed gas under
variations of the confining field and find analytical scaling solutions for the
evolving coherent state (condensate). We further discuss the characteristic
features and the depletion of this coherent state.Comment: 4 pages, no postscript figure
Stability of Bose condensed atomic Li-7
We study the stability of a Bose condensate of atomic Li in a (harmonic
oscillator) magnetic trap at non-zero temperatures. In analogy to the stability
criterion for a neutron star, we conjecture that the gas becomes unstable if
the free energy as a function of the central density of the cloud has a local
extremum which conserves the number of particles. Moreover, we show that the
number of condensate particles at the point of instability decreases with
increasing temperature, and that for the temperature interval considered, the
normal part of the gas is stable against density fluctuations at this point.Comment: Submitted for publication in Physical Review
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
Barrier effects on the collective excitations of split Bose-Einstein condensates
We investigate the collective excitations of a single-species Bose gas at T=0
in a harmonic trap where the confinement undergoes some splitting along one
spatial direction. We mostly consider onedimensional potentials consisting of
two harmonic wells separated a distance 2 z_0, since they essentially contain
all the barrier effects that one may visualize in the 3D situation. We find,
within a hydrodynamic approximation, that regardless the dimensionality of the
system, pairs of levels in the excitation spectrum, corresponding to
neighbouring even and odd excitations, merge together as one increases the
barrier height up to the current value of the chemical potential. The
excitation spectra computed in the hydrodynamical or Thomas-Fermi limit are
compared with the results of exactly solving the time-dependent
Gross-Pitaevskii equation. We analyze as well the characteristics of the
spatial pattern of excitations of threedimensional boson systems according to
the amount of splitting of the condensate.Comment: RevTeX, 12 pages, 13 ps figure
Weak force detection using a double Bose-Einstein condensate
A Bose-Einstein condensate may be used to make precise measurements of weak
forces, utilizing the macroscopic occupation of a single quantum state. We
present a scheme which uses a condensate in a double well potential to do this.
The required initial state of the condensate is discussed, and the limitations
on the sensitivity due to atom collisions and external coupling are analyzed.Comment: 12 pages, 2 figures, Eq.(41) has been correcte
Condensate fraction and critical temperature of a trapped interacting Bose gas
By using a mean field approach, based on the Popov approximation, we
calculate the temperature dependence of the condensate fraction of an
interacting Bose gas confined in an anisotropic harmonic trap. For systems
interacting with repulsive forces we find a significant decrease of the
condensate fraction and of the critical temperature with respect to the
predictions of the non-interacting model. These effects go in the opposite
direction compared to the case of a homogeneous gas. An analytic result for the
shift of the critical temperature holding to first order in the scattering
length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at
http://anubis.science.unitn.it/~oss/bec/BEC.htm
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