720 research outputs found
Creating solitons by means of spin-orbit coupling
This mini-review collects theoretical results predicting the creation of
matter-wave solitons by the pseudo-spinor system of Gross-Pitaevskii equations
(GPEs) with the self-attractive cubic nonlinearity and linear
first-order-derivative terms accounting for the spin-orbit coupling (SOC). In
one dimension (1D), the so predicted bright solitons are similar to their
well-known counterparts supported by the GPE in the absence of SOC. Completely
novel results were recently obtained for 2D and 3D systems: SOC suppresses the
collapse instability of the multidimensional GPE, creating fully stable 2D
ground-state solitons and metastable 3D ones of two types: semi-vortices (SVs),
with vorticities m = 1 in one spin component and m = 0 in the other, and mixed
modes (MMs), with m = 0 and m = (+/-)1 present in both components. With the
Galilean invariance broken by SOC, moving solitons exist up to a certain
critical velocity, suffering delocalization above it. The newest result
predicts stable 2D "quantum droplets" of the MM type in the presence of the
Lee-Huang-Yang corrections to the GPE system, induced by quantum fluctuations
around the mean-field states, in the case when the inter-component attraction
dominates over the self-repulsion in each component.Comment: a slightly shortened version will be published as an invited
mini-review (perspective) in EP
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
Two-component gap solitons with linear interconversion
We consider one-dimensional solitons in a binary Bose-Einstein condensate
with linear coupling between the components, trapped in an optical-lattice
potential. The inter-species and intra-species interactions may be both
repulsive or attractive. Main effects considered here are spontaneous breaking
of the symmetry between components in symmetric and antisymmetric solitons, and
spatial splitting between the components. These effects are studied by means of
a variational approximation and numerical simulations.Comment: 4 pages, 9 figure
Generation of \c{hi}2 solitons from the Airy wave through the parametric instability
Spontaneous creation of solitons in quadratic media by the downconversion,
i.e., parametric instability against the generation of fundamental-frequency
excitations, from the truncated Airy-wave (AW) mode in the second-harmonic
component is studied. Parameter regions are identified for the generation of
one, two, and three solitons, with additional small-amplitude "jets". Shares of
the total power carried by individual solitons are found. Also considered are
soliton patterns generated by the downconversion from a pair of AWs bending in
opposite directions.Comment: 4 pages, 6 figures, Optics Letters, in pres
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