540 research outputs found
Transmission of matter wave solitons through nonlinear traps and barriers
The transmissions of matter wave solitons through linear and nonlinear
inhomogeneities induced by the spatial variations of the trap and the
scattering length in Bose-Einstein condensates are investigated. New phenomena,
such as the enhanced transmission of a soliton through a linear trap by a
modulation of the scattering length, are exhibited. The theory is based on the
perturbed Inverse Scattering Transform for solitons, and we show that radiation
effects are important. Numerical simulations of the Gross-Pitaevskii equation
confirm the theoretical predictions.Comment: 6 pages, 4 figure
Symmetry breaking, coupling management, and localized modes in dual-core discrete nonlinear-Schr\"{o}dinger lattices
We introduce a system of two linearly coupled discrete nonlinear
Schr\"{o}dinger equations (DNLSEs), with the coupling constant subject to a
rapid temporal modulation. The model can be realized in bimodal Bose-Einstein
condensates (BEC). Using an averaging procedure based on the multiscale method,
we derive a system of averaged (autonomous) equations, which take the form of
coupled DNLSEs with additional nonlinear coupling terms of the four-wave-mixing
type. We identify stability regions for fundamental onsite discrete symmetric
solitons (single-site modes with equal norms in both components), as well as
for two-site in-phase and twisted modes, the in-phase ones being completely
unstable. The symmetry-breaking bifurcation, which destabilizes the fundamental
symmetric solitons and gives rise to their asymmetric counterparts, is
investigated too. It is demonstrated that the averaged equations provide a good
approximation in all the cases. In particular, the symmetry-breaking
bifurcation, which is of the pitchfork type in the framework of the averaged
equations, corresponds to a Hopf bifurcation in terms of the original system.Comment: 6 pages, 3 figure
Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management
The existence of compactons in the discrete nonlinear Schr\"odinger equation
in the presence of fast periodic time modulations of the nonlinearity is
demonstrated. In the averaged DNLS equation the resulting effective inter-well
tunneling depends on modulation parameters {\it and} on the field amplitude.
This introduces nonlinear dispersion in the system and can lead to a
prototypical realization of single- or multi-site stable discrete compactons in
nonlinear optical waveguide and BEC arrays. These structures can dynamically
arise out of Gaussian or compactly supported initial data.Comment: 4 pages, 4 figure
Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate
We use the time-dependent mean-field Gross-Pitaevskii equation to study the
formation of a dynamically-stabilized dissipation-managed bright soliton in a
quasi-one-dimensional Bose-Einstein condensate (BEC). Because of three-body
recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a
BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a
perturbation procedure that an alimentation of atoms from an external source to
the BEC may compensate for the dissipation loss and lead to a
dynamically-stabilized soliton. The result of the analytical perturbation
method is in excellent agreement with mean-field numerics. It seems possible to
obtain such a dynamically-stabilized BEC soliton without dissipation in
laboratory.Comment: 5 pages, 3 figure
Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures
Generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated
traps is investigated. The generation of waves is achieved by periodically
changing a parameter of the system in time. Two types of modulations of
parameters are considered, first a variation of the fermion-bosons scattering
length, and secondly the boson-boson scattering length. We predict the
properties of the generated Faraday patterns and study the parameter regions
where they can be excited.Comment: Final published versio
Adiabatic Compression of Soliton Matter Waves
The evolution of atomic solitary waves in Bose-Einstein condensate (BEC)
under adiabatic changes of the atomic scattering length is investigated. The
variations of amplitude, width, and velocity of soliton are found for both
spatial and time adiabatic variations. The possibility to use these variations
to compress solitons up to very high local matter densities is shown both in
absence and in presence of a parabolic confining potential.Comment: to appear in J.Phys.
Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity
The dynamics of a metastable attractive Bose-Einstein condensate trapped by a
system of laser beams is analyzed in the presence of small fluctuations of the
laser intensity. It is shown that the condensate will eventually collapse. The
expected collapse time is inversely proportional to the integrated covariance
of the time autocorrelation function of the laser intensity and it decays
logarithmically with the number of atoms. Numerical simulations of the
stochastic 3D Gross-Pitaevskii equation confirms analytical predictions for
small and moderate values of mean field interaction.Comment: 13 pages, 7 eps figure
Painlev\'{e} test of coupled Gross-Pitaevskii equations
Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried
out with the result that the coupled equations pass the P-test only if a
special relation containing system parameters (masses, scattering lengths) is
satisfied. Computer algebra is applied to evaluate j=4 compatibility condition
for admissible external potentials. Appearance of an arbitrary real potential
embedded in the external potentials is shown to be the consequence of the
coupling. Connection with recent experiments related to stability of
two-component Bose-Einstein condensates of Rb atoms is discussed.Comment: 13 pages, no figure
What is the right theory for Anderson localization of light?
Anderson localization of light is traditionally described in analogy to
electrons in a random potential. Within this description the disorder strength
-- and hence the localization characteristics -- depends strongly on the
wavelength of the incident light. In an alternative description in analogy to
sound waves in a material with spatially fluctuating elastic moduli this is not
the case. Here, we report on an experimentum crucis in order to investigate the
validity of the two conflicting theories using transverse-localized optical
devices. We do not find any dependence of the observed localization radii on
the light wavelength. We conclude that the modulus-type description is the
correct one and not the potential-type one. We corroborate this by showing that
in the derivation of the traditional, potential-type theory a term in the wave
equation has been tacititly neglected. In our new modulus-type theory the wave
equation is exact. We check the consistency of the new theory with our data
using a field-theoretical approach (nonlinear sigma model)
Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap
In this work, we study parametric resonances in an elongated cigar-shaped BEC
in a combined harmonic trap and a time dependent optical lattice by using
numerical and analytical techniques. We show that there exists a relative
competition between the harmonic trap which tries to spatially localize the BEC
and the time varying optical lattice which tries to delocalize the BEC. This
competition gives rise to parametric resonances (collapse and revival of the
oscillations of the BEC width). Parametric resonances disappear when one of the
competing factors i.e strength of harmonic trap or the strength of optical
lattice dominates. Parametric instabilities (exponential growth of Bogoliubov
modes) arise for large variations in the strength of the optical lattice.Comment: 9 pages, 20 figure
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