126 research outputs found
Discrete localized modes supported by an inhomogeneous defocusing nonlinearity
We report that infinite and semi-infinite lattices with spatially
inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength
increases rapidly enough toward the lattice periphery, support stable
unstaggered (UnST) discrete bright solitons, which do not exist in lattices
with the spatially uniform SDF nonlinearity. The UnST solitons coexist with
stable staggered (ST) localized modes, which are always possible under the
defocusing onsite nonlinearity. The results are obtained in a numerical form,
and also by means of variational approximation (VA). In the semi-infinite
(truncated) system, some solutions for the UnST surface solitons are produced
in an exact form. On the contrary to surface discrete solitons in uniform
truncated lattices, the threshold value of the norm vanishes for the UnST
solitons in the present system. Stability regions for the novel UnST solitons
are identified. The same results imply the existence of ST discrete solitons in
lattices with the spatially growing self-focusing nonlinearity, where such
solitons cannot exist either if the nonlinearity is homogeneous. In addition, a
lattice with the uniform onsite SDF nonlinearity and exponentially decaying
inter-site coupling is introduced and briefly considered too. Via a similar
mechanism, it may also support UnST discrete solitons, under the action of the
SDF nonlinearity. The results may be realized in arrayed optical waveguides and
collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical
lattices. A generalization for a two-dimensional system is briefly considered
too.Comment: 14 pages, 7 figures, accepted for publication in PR
Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices
Spatially periodic modulation of the intersite coupling in two-dimensional
(2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps
in it. This work aims to build stable localized modes in the new bandgaps.
Numerical analysis shows that single-peak and composite two- and four-peak
discrete static solitons and breathers emerge as such modes in certain
parameter areas inside the mini-gaps of the 2D superlattice induced by the
periodic modulation of the intersite coupling along both directions.The
single-peak solitons and four-peak discrete solitons are stable in a part of
their existence domain, while unstable stationary states (in particular,
two-soliton complexes) may readily transform into robust localized breathers.Comment: Chaos, in pres
Nonlinear symmetry breaking of Aharonov-Bohm cages
We study the influence of mean field cubic nonlinearity on Aharonov-Bohm
caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak
nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear
breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a
sharp transition in the dynamics and enables stronger wavepacket spreading.
This transition is distinct from other flatband networks, where continuous
spreading is induced by effective nonlinear hopping or resonances with
delocalized modes, and is in contrast to the quantum limit, where two-particle
hopping enables arbitrarily large spreading. This nonlinear symmetry breaking
transition is readily observable in femtosecond laser-written waveguide arrays.Comment: 6 pages, 5 figure
High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
We study normal modes propagating on top of the stable uniform background in
arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep
optical lattice. Both the on-site mean-field dynamics of the droplets and their
displacement due to the repulsive dipole-dipole interactions (DDIs) are taken
into account. Dispersion relations for two modes, \textit{viz}., high- and low-
frequency counterparts of optical and acoustic phonon modes in condensed
matter, are derived analytically and verified by direct simulations, for both
cases of the repulsive and attractive contact interactions. The (counterpart of
the) optical-phonon branch does not exist without the DDIs. These results are
relevant in the connection to emerging experimental techniques enabling
real-time imaging of the condensate dynamics and direct experimental
measurement of phonon dispersion relations in BECs.Comment: Physical Review A, in pres
Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions
The stability and collapse of fundamental unstaggered bright solitons in the
discrete Schrodinger equation with the nonpolynomial on-site nonlinearity,
which models a nearly one-dimensional Bose-Einstein condensate trapped in a
deep optical lattice, are studied in the presence of the long-range
dipole-dipole (DD) interactions. The cases of both attractive and repulsive
contact and DD interaction are considered. The results are summarized in the
form of stability/collapse diagrams in the parametric space of the model, which
demonstrate that the the attractive DD interactions stabilize the solitons and
help to prevent the collapse. Mobility of the discrete solitons is briefly
considered too.Comment: 6 figure
Influence of different disorder types on Aharonov-Bohm caging in the diamond chain
The linear diamond chain with fine-tuned effective magnetic flux has a
completely flat energy spectrum and compactly-localized eigenmodes, forming an
Aharonov-Bohm cage. We study numerically how this localization is affected by
different types of disorder (static and time-evolving) relevant to recent
realizations of Aharonov-Bohm cages in periodically-modulated optical waveguide
arrays. We demonstrate robustness of localization under static and
periodically-evolving disorder, while in contrast non-quenched (time-dependent)
disorder leads to wavepacket spreading and delocalization.Comment: 13 figure
Discrete solitons in an array of quantum dots
We develop a theory for the interaction of classical light fields with an a
chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into
account the local-field effects. The QD chain is modeled by a one-dimensional
(1D) periodic array of two-level quantum particles with tunnel coupling between
adjacent ones. The local-field effect is taken into regard as QD depolarization
in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is
described by a system of two discrete nonlinear Schr\"{o}dinger (DNLS)
equations for local amplitudes of the probabilities of the ground and first
excited states. The two equations are coupled by a cross-phase-modulation cubic
terms, produced by the local-field action, and by linear terms too. In
comparison with previously studied DNLS systems, an essentially new feature is
a phase shift between the intersite-hopping constants in the two equations. By
means of numerical solutions, we demonstrate that, in this QD chain, Rabi
oscillations (RO) self-trap into stable bright\textit{\ Rabi solitons} or
\textit{Rabi breathers}. Mobility of the solitons is considered too. The
related behavior of observable quantities, such as energy, inversion, and
electric-current density, is given a physical interpretation. The results apply
to a realistic region of physical parameters.Comment: 12 pages, 10 figures, Phys. Rev. B, in pres
Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates
We investigate effects of dipole-dipole (DD) interactions on
immiscibility-miscibility transitions (IMTs) in two-component Bose-Einstein
condensates (BECs) trapped in the harmonic-oscillator (HO) potential, with the
components linearly coupled by a resonant electromagnetic field (accordingly,
the components represent two different spin states of the same atom). The
problem is studied by means of direct numerical simulations. Different mutual
orientations of the dipolar moments in the two components are considered. It is
shown that, in the binary BEC formed by dipoles with the same orientation and
equal magnitudes, the IMT cannot be induced by the DD interaction alone, being
possible only in the presence of the linear coupling between the components,
while the miscibility threshold is affected by the DD interactions. However, in
the binary condensate with the two dipolar components polarized in opposite
directions, the IMT can be induced \emph{without} any linear coupling. Further,
we demonstrate that those miscible and immiscible localized states, formed in
the presence of the DD interactions, which are unstable evolve into robust
breathers, which tend to keep the original miscibility or immiscibility,
respectively. An exception is the case of a very strong DD attraction, when
narrow stationary modes are destroyed by the instability. The binary BEC
composed of co-polarized dipoles with different magnitudes are briefly
considered too.Comment: 10 figure
Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates
We introduce a discrete model for binary spin-orbit-coupled (SOC)
Bose-Einstein condensates (BEC) trapped in a deep one-dimensional optical
lattice. Two different types of the couplings are considered, with spatial
derivatives acting inside each species, or between the species. The discrete
system with inter-site couplings dominated by the SOC, while the usual hopping
is negligible, \textit{emulates} condensates composed of extremely heavy atoms,
as well as those with opposite signs of the effective atomic masses in the two
components.\ Stable localized composite states of miscible and immiscible types
are constructed. The effect of the SOC on the immiscibility-miscibility
transition in the localized complexes, which emulates the phase transition
between insulating and conducting states in semiconductors, is studied.Comment: Journal of Physics B , in pres
Stable optical vortices in nonlinear multicore fibers
The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF
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