100 research outputs found
Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein
condensates (BEC), with low-dimensional (1D) conservative plus dissipative
nonlinear optical lattices are investigated. In the case of focusing media
(with attractive atomic systems) the collapse of the wave packet is arrested by
the dissipative periodic nonlinearity. The adiabatic variation of the
background scattering length leads to metastable matter-wave solitons.
When the atom feeding mechanism is used, a dissipative soliton can exist in
focusing 2D media with 1D periodic nonlinearity. In the defocusing media
(repulsive BEC case) with harmonic trap in one dimension and one dimensional
nonlinear optical lattice in other direction, the stable soliton can exist.
This prediction of variational approach is confirmed by the full numerical
simulation of 2D Gross-Pitaevskii equation.Comment: 9 pages, 8 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.
Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices
The modulational instability and discrete matter wave solitons in dipolar
BEC, loaded into a deep optical lattice, are investigated analytically and
numerically. The process of modulational instability of nonlinear plane matter
waves in a dipolar nonlinear lattice is studied and the regions of instability
are established. The existence and stability of bulk discrete solitons are
analyzed analytically and confirmed by numerical simulations. In a marked
contrast with the usual DNLS behavior (no dipolar interactions), we found a
region where the two fundamental modes are simultaneously unstable allowing
enhanced mobility across the lattice for large norm values. To study the
existence and properties of surface discrete solitons, an analysis of the dimer
configuration is performed. The properties of symmetric and antisymmetric modes
including the stability diagrams and bifurcations are investigated in closed
form. For the case of a bulk medium, properties of fundamental on-site and
inter-site localized modes are analyzed. On-site and inter-site surface
localized modes are studied finding that they do not exist when nonlocal
interactions predominate with respect to local ones.Comment: 12 pages, 13 figure
Stable two-dimensional dispersion-managed soliton
The existence of a dispersion-managed soliton in two-dimensional nonlinear
Schr\"odinger equation with periodically varying dispersion has been explored.
The averaged equations for the soliton width and chirp are obtained which
successfully describe the long time evolution of the soliton. The slow dynamics
of the soliton around the fixed points for the width and chirp are investigated
and the corresponding frequencies are calculated. Analytical predictions are
confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein
condensate in optical lattice is discussed. The existence of a
dispersion-managed matter-wave soliton in such system is shown.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.
Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
We consider, by means of the variational approximation (VA) and direct
numerical simulations of the Gross-Pitaevskii (GP) equation, the dynamics of 2D
and 3D condensates with a scattering length containing constant and
harmonically varying parts, which can be achieved with an ac magnetic field
tuned to the Feshbach resonance. For a rapid time modulation, we develop an
approach based on the direct averaging of the GP equation,without using the VA.
In the 2D case, both VA and direct simulations, as well as the averaging
method, reveal the existence of stable self-confined condensates without an
external trap, in agreement with qualitatively similar results recently
reported for spatial solitons in nonlinear optics. In the 3D case, the VA again
predicts the existence of a stable self-confined condensate without a trap. In
this case, direct simulations demonstrate that the stability is limited in
time, eventually switching into collapse, even though the constant part of the
scattering length is positive (but not too large). Thus a spatially uniform ac
magnetic field, resonantly tuned to control the scattering length, may play the
role of an effective trap confining the condensate, and sometimes causing its
collapse.Comment: 7 figure
Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC)
periodically modulated by a laser beam is presented. We show, both
theoretically and numerically, that modulational instability/stability is the
mechanism by which wavefunctions of soliton type can be generated in cigar
shaped BEC subject to a 1D optical lattice. The theory explains why bright
solitons can exist in BEC with positive scattering length and why condensate
with negative scattering length can be stable and give rise to dark solitary
pulses.Comment: Submitted, 4 pages, 3 figures. Revised versio
Solitons in Tonks-Girardeau gas with dipolar interactions
The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas
with dipole-dipole (DD) interactions is reported. The governing equation is
taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the
nonlocal cubic term accounting for the DD attraction. In different regions of
the parameter space (the dipole moment and atom number), matter-wave solitons
feature flat-top or compacton-like shapes. For the flat-top states, the NLSE
with the local cubic-quintic (CQ) nonlinearity is shown to be a good
approximation. Specific dynamical effects are studied assuming that the
strength of the DD interactions is ramped up or drops to zero. Generation of
dark-soliton pairs in the gas shrinking under the action of the intensifying DD
attraction is observed. Dark solitons exhibit the particle-like collision
behavior. Peculiarities of dipole solitons in the TG gas are highlighted by
comparison with the NLSE including the local CQ terms. Collisions between the
solitons are studied too. In many cases, the collisions result in merger of the
solitons into a breather, due to strong attraction between them.Comment: 15 pages, 8 figures, accepted by J. Phys. B: At. Mol. Opt. Phy
The Efimov's effect for a model of a three particle discrete Shr\"odinger operator
In the paper we study existance of infinitly many egenvalues for a model of a
three particle discrete Shr\"odinger operator.Comment: Russia
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