252 research outputs found
Guiding-center solitons in rotating potentials
We demonstrate that rotating quasi-one-dimensional potentials, periodic or
parabolic, support solitons in settings where they are otherwise impossible.
Ground-state and vortex solitons are found in defocusing media, if the rotation
frequency exceeds a critical value. The revolving periodic potentials exhibit
the strongest stabilization capacity at a finite optimum value of their
strength, while the rotating parabolic trap features a very sharp transition to
stability with the increase of rotation frequency.Comment: 16 pages, 6 figures, to appear in Physical Review
Bright solitons from defocusing nonlinearities
We report that defocusing cubic media with spatially inhomogeneous
nonlinearity, whose strength increases rapidly enough toward the periphery, can
support stable bright localized modes. Such nonlinearity landscapes give rise
to a variety of stable solitons in all three dimensions, including 1D
fundamental and multihump states, 2D vortex solitons with arbitrarily high
topological charges, and fundamental solitons in 3D. Solitons maintain their
coherence in the state of motion, oscillating in the nonlinear potential as
robust quasi-particles and colliding elastically. In addition to numerically
found soliton families, particular solutions are found in an exact analytical
form, and accurate approximations are developed for the entire families,
including moving solitons.Comment: 13 pages, 6 figures, to appear in Physical Review
Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media
We demonstrate the existence of stable three-dimensional spatiotemporal
solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental
(nonspinning) STSs forming one-parameter families are stable if their
propagation constant exceeds a certain critical value, that is inversely
proportional to the range of nonlocality of nonlinear response. All spinning
three-dimensional STSs are found to be unstable.Comment: 14 pages, 6 figures, accepted to PRE, Rapid Communication
Stable spatiotemporal solitons in Bessel optical lattices
We investigate the existence and stability of three-dimensional (3D) solitons
supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the
lattice strength exceeds a threshold value, we show numerically, and using the
variational approximation, that the solitons are stable within one or two
intervals of values of their norm. In the latter case, the Hamiltonian-vs.-norm
diagram has a "swallowtail" shape, with three cuspidal points. The model
applies to Bose-Einstein condensates (BECs) and to optical media with saturable
nonlinearity, suggesting new ways of making stable 3D BEC solitons and "light
bullets" of an arbitrary size.Comment: 9 pages, 4 figures, Phys. Rev. Lett., in pres
Twisted toroidal vortex-solitons in inhomogeneous media with repulsive nonlinearity
Toroidal modes in the form of so-called Hopfions, with two independent
winding numbers, a hidden one (twist, s), which characterizes a circular vortex
thread embedded into a three-dimensional soliton, and the vorticity around the
vertical axis m, appear in many fields, including the field theory,
ferromagnetics, and semi- and superconductors. Such topological states are
normally generated in multi-component systems, or as trapped quasi-linear modes
in toroidal potentials. We uncover that stable solitons with this structure can
be created, without any linear potential, in the single-component setting with
the strength of repulsive nonlinearity growing fast enough from the center to
the periphery, for both steep and smooth modulation profiles. Toroidal modes
with s=1 and vorticity m=0,1,2 are produced. They are stable for m<=1, and do
not exist for s>1. An approximate analytical solution is obtained for the
twisted ring with s=1, m=0. Under the application of an external torque, it
rotates like a solid ring. The setting can be implemented in BEC, by means of
the Feshbach resonance controlled by inhomogene-ous magnetic fields.Comment: 12 pages, 5 figures, to appear in Physical Review Letter
Stable two-dimensional soliton complexes in Bose-Einstein condensates with helicoidal spin-orbit coupling
We show that attractive two-dimensional spinor Bose-Einstein condensates with
helicoidal spatially periodic spin-orbit coupling (SOC) support a rich variety
of stable fundamental solitons and bound soliton complexes. Such states exist
with chemical potentials belonging to the semi-infinite gap in the band
spectrum created by the periodically modulated SOC. All these states exist
above a certain threshold value of the norm. The chemical potential of
fundamental solitons attains the bottom of the lowest band, whose locus is a
ring in the space of Bloch momenta, and the radius of the ring is a
non-monotonous function of the SOC strength. The chemical potential of soliton
complexes does not attain the band edge. The complexes are bound states of
several out-of-phase fundamental solitons whose centers are placed at local
maxima of the SOC-modulation phase. In this sense, the impact of the helicoidal
SOC landscape on the solitons is similar to that of a periodic two-dimensional
potential. In particular, it can compensate repulsive forces between
out-of-phase solitons, making their bound states stable. Extended stability
domains are found for complexes built of two and four solitons (dipoles and
quadrupoles, respectively). They are typically stable below a critical value of
the chemical potential.Comment: minor corrections, published version, 2020 New J. Phys. 22 10301
Double symmetry breaking of solitons in one-dimensional virtual photonic crystals
We demonstrate that spatial solitons undergo two consecutive spontaneous
symmetry breakings (SSBs), with the increase of the total power, in nonlinear
photonic crystals (PhCs) built as arrays of alternating linear and nonlinear
stripes, in the case when maxima of the effective refractive index coincide
with minima of the self-focusing coefficient, and vice versa, i.e.,the
corresponding linear and nonlinear periodic potentials are in competition. This
setting may be induced, as a virtual PhC, by means of the EIT
(electromagnetically-induced-transparency) technique, in a uniform optical
medium. It may also be realized as a Bose-Einstein condensate (BEC) subject to
the action of combined periodic optical potential and periodically modulated
Feshbach resonance. The first SSB happens at the center of a linear stripe,
pushing a broad low-power soliton into an adjacent nonlinear stripe and
gradually suppressing side peaks in the soliton's shape. Then, the soliton
restores its symmetry, being pinned to the midpoint of the nonlinear stripe.
The second SSB occurs at higher powers, pushing the narrow soliton off the
center of the nonlinear channel,while the soliton keeps its internal symmetry.
The results are obtained by means of numerical and analytical methods. They may
be employed to control switching of light beams by means of the varying power.Comment: 8 pages, 5 figures, Phys. Rev. A, in pres
Nonlinear Scattering of a Bose-Einstein Condensate on a Rectangular Barrier
We consider the nonlinear scattering and transmission of an atom laser, or
Bose-Einstein condensate (BEC) on a finite rectangular potential barrier. The
nonlinearity inherent in this problem leads to several new physical features
beyond the well-known picture from single-particle quantum mechanics. We find
numerical evidence for a denumerably infinite string of bifurcations in the
transmission resonances as a function of nonlinearity and chemical potential,
when the potential barrier is wide compared to the wavelength of oscillations
in the condensate. Near the bifurcations, we observe extended regions of
near-perfect resonance, in which the barrier is effectively invisible to the
BEC. Unlike in the linear case, it is mainly the barrier width, not the height,
that controls the transmission behavior. We show that the potential barrier can
be used to create and localize a dark soliton or dark soliton train from a
phonon-like standing wave.Comment: 15 pages, 15 figures, new version includes clarification of
definition of transmission coefficient in general nonlinear vs. linear cas
Asymmetric Wave Propagation Through Nonlinear PT-symmetric Oligomers
In the present paper, we consider nonlinear PT-symmetric dimers and trimers
(more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice.
We examine the stationary states of such chains in the form of plane waves, and
analytically compute their reflection and transmission coefficients through the
nonlinear PT symmetric oligomer, as well as the corresponding rectification
factors which clearly illustrate the asymmetry between left and right
propagation in such systems. We examine not only the existence but also the
dynamical stability of the plane wave states and interestingly find them to be
generically unstable. Lastly, we generalize our numerical considerations to the
more physically relevant case of Gaussian initial wavepackets and confirm that
the asymmetry in the transmission properties persists in the case of such
wavepackets, as well
Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials
We construct families of ordinary and gap solitons (GSs), including solitary
vortices, in the two-dimensional (2D) system based on the
nonlinear-Schr\"Aodinger/Gross-Pitaevskii equation with the 2D or quasi-1D
(Q1D) periodic linear potential, combined with the periodic modulation of the
cubic nonlinearity (also in the 2D or Q1D form), which is, generally,
incommensurate with the linear potential, thus forming a \nonlinear
quasicrystal". Stable vortices are built as complexes of four peaks with the
separation between them equal to the double period of the linear potential. The
system may be realized in photonic crystals or Bose-Einstein condensates
(BECs). The variational approximation (VA) is applied to ordinary solitons
(residing in the semi-infinite gap), and numerical methods are used to
construct solitons of all the types. Stability regions are identified for
soliton families in all the versions of the model.Comment: 8 pages, 11 figures. Accepted for a Special issue on Photonics of
Physica Script
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