13 research outputs found
Dragging two-dimensional discrete solitons by moving linear defects
We study the mobility of small-amplitude solitons attached to moving defects
which drag the solitons across a two-dimensional (2D) discrete
nonlinear-Schr\"{o}dinger (DNLS) lattice. Findings are compared to the
situation when a free small-amplitude 2D discrete soliton is kicked in the
uniform lattice. In agreement with previously known results, after a period of
transient motion the free soliton transforms into a localized mode pinned by
the Peierls-Nabarro potential, irrespective of the initial velocity. However,
the soliton attached to the moving defect can be dragged over an indefinitely
long distance (including routes with abrupt turns and circular trajectories)
virtually without losses, provided that the dragging velocity is smaller than a
certain critical value. Collisions between solitons dragged by two defects in
opposite directions are studied too. If the velocity is small enough, the
collision leads to a spontaneous symmetry breaking, featuring fusion of two
solitons into a single one, which remains attached to either of the two
defects
Driving defect modes of Bose-Einstein condensates in optical lattices
We present an approximate analytical theory and direct numerical computation
of defect modes of a Bose-Einstein condensate loaded in an optical lattice and
subject to an additional localized (defect) potential. Some of the modes are
found to be remarkably stable and can be driven along the lattice by means of a
defect moving following a step-like function defined by the period of Josephson
oscillations and the macroscopic stability of the atoms.Comment: 4 pages, 5 figure
Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity
We study defect modes of a Bose-Einstein condensate in an optical lattice
with a localized defect within the framework of the one-dimensional
Gross-Pitaevskii equation. It is shown that for a significant range of
parameters the defect modes can be accurately described by an expansion over
Wannier functions, whose envelope is governed by the coupled nonlinear
Schr\"{o}dinger equation with a delta-impurity. The stability of the defect
modes is verified by direct numerical simulations of the underlying
Gross-Pitaevskii equation with a periodic plus defect potentials. We also
discuss possibilities of driving defect modes through the lattice and suggest
ideas for their experimental generation.Comment: 14 pages, 9 Figures, 1 Tabl
Dissipation-induced coherent structures in Bose-Einstein condensates
We discuss how to engineer the phase and amplitude of a complex order
parameter using localized dissipative perturbations. Our results are applied to
generate and control various types of atomic nonlinear matter waves (solitons)
by means of localized dissipative defects.Comment: 4pages, 7 figure
Symmetric and asymmetric localized modes in linear lattices with an embedded pair of -nonlinear sites
We construct families of symmetric, antisymmetric, and asymmetric solitary
modes in one-dimensional bichromatic lattices with the
second-harmonic-generating () nonlinearity concentrated at a pair
of sites placed at distance . The lattice can be built as an array of
optical waveguides. Solutions are obtained in an implicit analytical form,
which is made explicit in the case of adjacent nonlinear sites, . The
stability is analyzed through the computation of eigenvalues for small
perturbations, and verified by direct simulations. In the cascading limit,
which corresponds to large mismatch , the system becomes tantamount to the
recently studied single-component lattice with two embedded sites carrying the
cubic nonlinearity. The modes undergo qualitative changes with the variation of
. In particular, at , the symmetry-breaking bifurcation (SBB),
which creates asymmetric states from symmetric ones, is supercritical and
subcritical for small and large values of , respectively, while the
bifurcation is always supercritical at . In the experiment, the
corresponding change of the phase transition between the second and first kinds
may be implemented by varying the mismatch, via the wavelength of the input
beam. The existence threshold (minimum total power) for the symmetric modes
vanishes exactly at , which suggests a possibility to create the solitary
mode using low-power beams. The stability of solution families also changes
with