176 research outputs found
Dark-Bright Solitons in Inhomogeneous Bose-Einstein Condensates
We investigate dark-bright vector solitary wave solutions to the coupled
non-linear Schr\"odinger equations which describe an inhomogeneous two-species
Bose-Einstein condensate. While these structures are well known in non-linear
fiber optics, we show that spatial inhomogeneity strongly affects their motion,
stability, and interaction, and that current technology suffices for their
creation and control in ultracold trapped gases. The effects of controllably
different interparticle scattering lengths, and stability against
three-dimensional deformations, are also examined.Comment: 5 pages, 5 figure
Collapse of triaxial bright solitons in atomic Bose-Einstein condensates
We study triaxial bright solitons made of attractive Bose-condensed atoms
characterized by the absence of confinement in the longitudinal axial direction
but trapped by an anisotropic harmonic potential in the transverse plane. By
numerically solving the three-dimensional Gross-Pitaevskii equation we
investigate the effect of the transverse trap anisotropy on the critical
interaction strength above which there is the collapse of the condensate. The
comparison with previous predictions [Phys. Rev. A {\bf 66}, 043619 (2002)]
shows significant differences for large anisotropies.Comment: Accepted for the publication in Phys. Lett.
Many-body solitons in a one-dimensional condensate of hard core bosons
A mapping theorem leading to exact many-body dynamics of impenetrable bosons
in one dimension reveals dark and gray soliton-like structures in a toroidal
trap which is phase-imprinted. On long time scales revivals appear that are
beyond the usual mean-field theory
Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
Solitons are among the most distinguishing fundamental excitations in a wide
range of non-linear systems such as water in narrow channels, high speed
optical communication, molecular biology and astrophysics. Stabilized by a
balance between spreading and focusing, solitons are wavepackets, which share
some exceptional generic features like form-stability and particle-like
properties. Ultra-cold quantum gases represent very pure and well-controlled
non-linear systems, therefore offering unique possibilities to study soliton
dynamics. Here we report on the first observation of long-lived dark and
dark-bright solitons with lifetimes of up to several seconds as well as their
dynamics in highly stable optically trapped Rb Bose-Einstein
condensates. In particular, our detailed studies of dark and dark-bright
soliton oscillations reveal the particle-like nature of these collective
excitations for the first time. In addition, we discuss the collision between
these two types of solitary excitations in Bose-Einstein condensates.Comment: 9 pages, 4 figure
Nonlinear atom optics and bright gap soliton generation in finite optical lattices
We theoretically investigate the transmission dynamics of coherent matter
wave pulses across finite optical lattices in both the linear and the nonlinear
regimes. The shape and the intensity of the transmitted pulse are found to
strongly depend on the parameters of the incident pulse, in particular its
velocity and density: a clear physical picture for the main features observed
in the numerical simulations is given in terms of the atomic band dispersion in
the periodic potential of the optical lattice. Signatures of nonlinear effects
due the atom-atom interaction are discussed in detail, such as atom optical
limiting and atom optical bistability. For positive scattering lengths, matter
waves propagating close to the top of the valence band are shown to be subject
to modulational instability. A new scheme for the experimental generation of
narrow bright gap solitons from a wide Bose-Einstein condensate is proposed:
the modulational instability is seeded in a controlled way starting from the
strongly modulated density profile of a standing matter wave and the solitonic
nature of the generated pulses is checked from their shape and their
collisional properties
Simple method for excitation of a Bose-Einstein condensate
An appropriate, time-dependent modification of the trapping potential may be
sufficient to create effectively collective excitations in a cold atom
Bose-Einstein condensate. The proposed method is complementary to earlier
suggestions and should allow the creation of both dark solitons and vortices.Comment: 8 pages, 7 figures, version accepted for publication in Phys. Rev.
A method for collective excitation of Bose-Einstein condensate
It is shown that by an appropriate modification of the trapping potential one
may create collective excitation in cold atom Bose-Einstein condensate. The
proposed method is complementary to earlier suggestions. It seems to be
feasible experimentally --- it requires only a proper change in time of the
potential in atomic traps, as realized in laboratories already.Comment: 4 pages, 4 figures; major revision, several references added,
interacting particles case adde
Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate
The stability properties and perturbation-induced dynamics of the full set of
stationary states of the nonlinear Schroedinger equation are investigated
numerically in two physical contexts: periodic solutions on a ring and
confinement by a harmonic potential. Our comprehensive studies emphasize
physical interpretations useful to experimentalists. Perturbation by stochastic
white noise, phase engineering, and higher order nonlinearity are considered.
We treat both attractive and repulsive nonlinearity and illustrate the
soliton-train nature of the stationary states.Comment: 9 pages, 11 figure
Stability of dark solitons in a Bose-Einstein condensate trapped in an optical lattice
We investigate the stability of dark solitons (DSs) in an effectively
one-dimensional Bose-Einstein condensate in the presence of the magnetic
parabolic trap and an optical lattice (OL). The analysis is based on both the
full Gross-Pitaevskii equation and its tight-binding approximation counterpart
(discrete nonlinear Schr{\"o}dinger equation). We find that DSs are subject to
weak instabilities with an onset of instability mainly governed by the period
and amplitude of the OL. The instability, if present, sets in at large times
and it is characterized by quasi-periodic oscillations of the DS about the
minimum of the parabolic trap.Comment: Typo fixed in Eq. (1): cos^2 -> sin^
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
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