100 research outputs found
Delocalizing transition of multidimensional solitons in Bose-Einstein condensates
Critical behavior of solitonic waveforms of Bose-Einstein condensates in
optical lattices (OL) has been studied in the framework of continuous
mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo
abrupt delocalization as the strength of the OL is decreased below some
critical value. Similar delocalizing transition happens when the coefficient of
nonlinearity crosses the critical value. Contrarily, bright solitons in 1D OLs
retain their integrity over the whole range of parameter variations. The
interpretation of the phenomenon in terms of quantum bound states in the
effective potential is proposed.Comment: 12 pages, 19 figures, submitted to Phys. Rev.
Matter-wave solitons in radially periodic potentials
We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC)
with self-attraction or self-repulsion, trapped in an axially symmetric
optical-lattice potential periodic along the radius. Unlike previously studied
2D models with Bessel lattices, no localized states exist in the linear limit
of the present model, hence all localized states are truly nonlinear ones. We
consider the states trapped in the central potential well, and in remote
circular troughs. In both cases, a new species, in the form of \textit{radial
gap solitons}, are found in the repulsive model (the gap soliton trapped in a
circular trough may additionally support stable dark-soliton pairs). In remote
troughs, stable localized states may assume a ring-like shape, or shrink into
strongly localized solitons. The existence of stable annular states, both
azimuthally uniform and weakly modulated ones, is corroborated by simulations
of the corresponding Gross-Pitaevskii equation. Dynamics of strongly localized
solitons circulating in the troughs is also studied. While the solitons with
sufficiently small velocities are stable, fast solitons gradually decay, due to
the leakage of matter into the adjacent trough under the action of the
centrifugal force. Collisions between solitons are investigated too. Head-on
collisions of in-phase solitons lead to the collapse; -out of phase
solitons bounce many times, but eventually merge into a single soliton without
collapsing. The proposed setting may also be realized in terms of spatial
solitons in photonic-crystal fibers with a radial structure.Comment: 16 pages, 23 figure
Multidimensional semi-gap solitons in a periodic potential
The existence, stability and other dynamical properties of a new type of
multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional
(1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger
equation with the self-defocusing cubic nonlinearity are studied. The equation
describes propagation of light in a medium with normal group-velocity
dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its
spectrum does not support a true bandgap. Nevertheless, the variational
approximation (VA) and numerical computations reveal stable solutions that seem
as completely localized ones, an explanation to which is given. The solutions
are of the gap-soliton type in the transverse direction(s), in which the
periodic potential acts in combination with the diffraction and self-defocusing
nonlinearity. Simultaneously, in the longitudinal (temporal) direction these
are ordinary solitons, supported by the balance of the normal GVD and
defocusing nonlinearity. Stability of the solitons is predicted by the VA, and
corroborated by direct simulations.Comment: European Physical Joournal D, in pres
Multidimensional solitons in periodic potentials
The existence of stable solitons in two- and three-dimensional (2D and 3D)
media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation
with a periodic potential is demonstrated by means of the variational
approximation (VA) and in direct simulations. The potential stabilizes the
solitons against collapse. Direct physical realizations are a Bose-Einstein
condensate (BEC) trapped in an optical lattice, and a light beam in a bulk Kerr
medium of a photonic-crystal type. In the 2D case, the creation of the soliton
in a weak lattice potential is possible if the norm of the field (number of
atoms in BEC, or optical power in the Kerr medium) exceeds a threshold value
(which is smaller than the critical norm leading to collapse). Both
"single-cell" and "multi-cell" solitons are found, which occupy, respectively,
one or several cells of the periodic potential, depending on the soliton's
norm. Solitons of the former type and their stability are well predicted by VA.
Stable 2D vortex solitons are found too.Comment: 13 pages, 3 figures, Europhys. Lett., in pres
Matter wave soliton bouncer
Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic
mirror) under the effect of gravity has been studied by analytical and
numerical means. The analytical description is based on the variational
approach. Resonant oscillations of the soliton's center of mass and width,
induced by appropriate modulation of the atomic scattering length and the slope
of the linear potential are analyzed. In numerical experiments we observe the
Fermi type acceleration of the soliton when the vertical position of the
reflecting surface is periodically varied in time. Analytical predictions are
compared with the results of numerical simulations of the Gross-Pitaevskii
equation and qualitative agreement between them is found.Comment: 8 pages, 5 figure
Gap-Townes solitons and delocalizing transitions of multidimensional Bose-Einstein condensates in optical lattices
We show the existence of gap-Townes solitons for the multidimensional
Gross-Pitaeviskii equation with attractive interactions and in two- and
three-dimensional optical lattices. In absence of the periodic potential the
solution reduces to the known Townes solitons of the multi-dimensional
nonlinear Schr\"odinger equation, sharing with these the propriety of being
unstable against small norm (number of atoms) variations. We show that in the
presence of the optical lattice the solution separates stable localized
solutions (gap-solitons) from decaying ones, characterizing the delocalizing
transition occurring in the multidimensional case. The link between these
higher dimensional solutions and the ones of one dimensional nonlinear
Schr\"odinger equation with higher order nonlinearities is also discussed.Comment: 14 pages, 6 figure
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