161 research outputs found
Dynamics of a BEC bright soliton in an expulsive potential
We theoretically investigate the dynamics of a matter-wave soliton created in
a harmonic potential, which is attractive in the transverse direction but
expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC)
bright soliton made of Li atoms has been observed in a recent experiment
(Science {\bf 296}, 1290 (2002)). We show that the non-polynomial Schr\"odinger
equation, an effective one-dimensional equation we derived from the
three-dimensional Gross-Pitaevskii equation, is able to reproduce the main
experimental features of this BEC soliton in an expulsive potential.Comment: 5 pages, 4 figures (2 of them with colors
The fate of phonons in freely expanding Bose-Einstein condensates
Phonon-like excitations can be imprinted into a trapped Bose-Einstein
condensate of cold atoms using light scattering. If the condensate is suddenly
let to freely expand, the initial phonons lose their collective character by
transferring their energy and momentum to the motion of individual atoms. The
basic mechanisms of this evaporation process are investigated by using the
Gross-Pitaevskii theory and dynamically rescaled Bogoliubov equations.
Different regimes of evaporation are shown to occur depending on the phonon
wavelength. Distinctive signatures of the evaporated phonons are visible in the
density distribution of the expanded gas, thus providing a new type of
spectroscopy of Bogoliubov excitations.Comment: 13 pages, 16 figure
Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate
We study the interaction between low-lying transverse collective oscillations
and thermal excitations of an elongated Bose-Einstein condensate by means of
perturbation theory. We consider a cylindrically trapped condensate and
calculate the transverse elementary excitations at zero temperature by solving
the linearized Gross-Pitaevskii equations in two dimensions. We use them to
calculate the matrix elements between thermal excited states coupled with the
quasi-2D collective modes. The Landau damping of transverse collective modes is
investigated as a function of temperature. At low temperatures, the damping
rate due to the Landau decay mechanism is in agreement with the experimental
data for the decay of the transverse quadrupole mode, but it is too small to
explain the slow experimental decay of the transverse breathing mode. The
reason for this discrepancy is discussed.Comment: 6 pages, LaTeX, 1 figur
Transition from 3D to 1D in Bose Gases at Zero Temperature
We investigate the effects of dimensional reduction in Bose gases induced by
a strong harmonic confinement in the transverse cylindric radial direction. By
using a generalized Lieb-Liniger theory, based on a variational treatment of
the transverse width of the Bose gas, we analyze the transition from a 3D
Bose-Einstein condensate to the 1D Tonks-Girardeau gas. The sound velocity and
the frequency of the lowest compressional mode give a clear signature of the
regime involved. We study also the case of negative scattering length deriving
the phase diagram of the Bose gas (uniform, single soliton, multi soliton and
collapsed) in toroidal confinement.Comment: 5 pages, 5 figures, to be published in Phys. Rev.
Dynamics of Collapse of a Confined Bose Gas
Rigorous results on the nonlinear dynamics of a dilute Bose gas with a
negative scattering length in an harmonic magnetic trap are presented and
sufficient conditions for the collapse of the system are formulated. By using
the virial theorem for the Gross-Pitaevskii equations in an external field we
analyze the temporal evolution of the mean square radius of the gas cloud. In
the 2D case the quantity undergoes harmonic oscillation with frequency It implies that for a negative value of energy of the system, the gas cloud
will collapse after a finite time interval. For positive energy the cloud
collapses if the initial conditions correspond to a large enough amplitude of
oscillations. Stable oscillations with a small amplitude are possible. In the
3D case the system also collapsed after a finite time for a state with negative
energy. A stringent condition for the collapse is also derived.Comment: 10 pages, REVTEX, 2 figures (available upon request
Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps
Interaction between collective monopole oscillations of a trapped
Bose-Einstein condensate and thermal excitations is investigated by means of
perturbation theory. We assume spherical symmetry to calculate the matrix
elements by solving the linearized Gross-Pitaevskii equations. We use them to
study the resonances of the condensate induced by temperature when an external
perturbation of the trapping frequency is applied and to calculate the Landau
damping of the oscillations.Comment: revtex, 9 pages, 5 figure
Landau damping in dilute Bose gases
Landau damping in weakly interacting Bose gases is investigated by means of
perturbation theory. Our approach points out the crucial role played by
Bose-Einstein condensation and yields an explicit expression for the decay rate
of elementary excitations in both uniform and non uniform gases. Systematic
results are derived for the phonon width in homogeneous gases interacting with
repulsive forces. Special attention is given to the low and high temperature
regimes.Comment: 11 pages, latex, 1 figure available upon request. The paper accepted
for publication in Phys. Lett.
Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
A method is proposed for a self-consistent evaluation of the coupling
constant in the Gross-Pitaevskii equation without involving a pseudopotential
replacement. A renormalization of the coupling constant occurs due to medium
effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is
shown that a simplified version of the Hartree-Fock-Bogoliubov approximation
leads to a variational problem for both the condensate and a two-body wave
function describing the behaviour of a pair of bosons in the Bose-Einstein
condensate. The resulting coupled equations are free of unphysical divergences.
Particular cases of this scheme that admit analytical estimations are
considered and compared to the literature. In addition to the well-known cases
of low-dimensional trapping, cross-over regimes can be studied. The values of
the kinetic, interaction, external, and release energies in low dimensions are
also evaluated and contributions due to short-range correlations are found to
be substantial.Comment: 15 pages, ReVTEX, no 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
Solitary Wave Interactions In Dispersive Equations Using Manton's Approach
We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150},
397 (1979)] to compute solitary wave interactions in translationally invariant,
dispersive equations that support such localized solutions. The approach is
illustrated using as examples solitons in the Korteweg-de Vries equation,
standing waves in the nonlinear Schr{\"o}dinger equation and kinks as well as
breathers of the sine-Gordon equation.Comment: 5 pages, 4 figures, slightly modified version to appear in Phys. Rev.
- …