84 research outputs found
Control of wavepacket spreading in nonlinear finite disordered lattices
In the absence of nonlinearity all normal modes (NMs) of a chain with
disorder are spatially localized (Anderson localization). We study the action
of nonlinearity, whose strength is ramped linearly in time. It leads to a
spreading of a wavepacket due to interaction with and population of distant
NMs. Eventually the nonlinearity induced frequency shifts take over, and the
wavepacket becomes selftrapped. On finite chains a critical ramping speed is
obtained, which separates delocalized final states from localized ones. The
critical value depends on the strength of disorder and is largest when the
localization length matches the system size.Comment: 7 pages, 4 figures, submitted to PR
A simple method to construct Flat Band lattices
We develop a simple and general method to construct arbitrary Flat Band
lattices. We identify the basic ingredients behind zero-dispersion bands and
develop a method to construct extended lattices based on a consecutive
repetition of a given mini-array. The number of degenerated localized states is
defined by the number of connected mini-arrays times the number of modes
preserving the symmetry at a given connector site. In this way, we create one
or more (depending on the lattice geometry) complete degenerated Flat Bands for
quasi-one and two-dimensional systems. We probe our method by studying several
examples, and discuss the effect of additional interactions like anisotropy or
nonlinearity. At the end, we test our method by studying numerically a ribbon
lattice using a continuous description.Comment: 11 pages, 11 figure
Fano blockade by a Bose-Einstein condensate in an optical lattice
We study the transport of atoms across a localized Bose-Einstein condensate
in a one-dimensional optical lattice. For atoms scattering off the condensate
we predict total reflection as well as full transmission for certain parameter
values on the basis of an exactly solvable model. The findings of analytical
and numerical calculations are interpreted by a tunable Fano-like resonance and
may lead to interesting applications for blocking and filtering atom beams.Comment: 4 pages, 4 figures (fig4 was resized for arXiv
Mobility of high-power solitons in saturable nonlinear photonic lattices
We theoretically study the properties of one-dimensional nonlinear saturable
photonic lattices exhibiting multiple mobility windows for stationary
solutions. The effective energy barrier decreases to a minimum in those power
regions where a new intermediate stationary solution appears. As an
application, we investigate the dynamics of high-power gaussian-like beams
finding several regions where the light transport is enhanced.Comment: 3 pages, 3 figures, to be published in Optics Letter
Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity
We investigate mobility regimes for localized modes in the discrete nonlinear
Schr\"{o}dinger (DNLS) equation with the cubic-quintic onsite terms. Using the
variational approximation (VA), the largest soliton's total power admitting
progressive motion of kicked discrete solitons is predicted, by comparing the
effective kinetic energy with the respective Peierls-Nabarro (PN) potential
barrier. The prediction is novel for the DNLS model with the cubic-only
nonlinearity too, demonstrating a reasonable agreement with numerical findings.
Small self-focusing quintic term quickly suppresses the mobility. In the case
of the competition between the cubic self-focusing and quintic self-defocusing
terms, we identify parameter regions where odd and even fundamental modes
exchange their stability, involving intermediate asymmetric modes. In this
case, stable solitons can be set in motion by kicking, so as to let them pass
the PN barrier. Unstable solitons spontaneously start oscillatory or
progressive motion, if they are located, respectively, below or above a
mobility threshold. Collisions between moving discrete solitons, at the
competing nonlinearities frame, are studied too.Comment: 12 pages, 15 figure
Strong asymmetry for surface modes in nonlinear lattices with long-range coupling
We analyze the formation of localized surface modes on a nonlinear cubic
waveguide array in the presence of exponentially-decreasing long-range
interactions. We find that the long-range coupling induces a strong asymmetry
between the focusing and defocusing cases for the topology of the surface modes
and also for the minimum power needed to generate them. In particular, for the
defocusing case, there is an upper power threshold for exciting staggered
modes, which depends strongly on the long-range coupling strength. The power
threshold for dynamical excitation of surface modes increase (decrease) with
the strength of long-range coupling for the focusing (defocusing) cases. These
effects seem to be generic for discrete lattices with long-range interactions.Comment: 4 pages, 5 figures, submitted for publicatio
Quantum localized states in photonic flat-band lattices
The localization of light in flat-band lattices has been recently proposed
and experimentally demonstrated in several configurations, assuming a classical
description of light. Here, we study the problem of light localization in the
quantum regime. We focus on quasi one-dimensional and two-dimensional lattices
which exhibit a perfect flat-band inside their linear spectrum. Localized
quantum states are constructed as eigenstates of the interaction Hamiltonian
with a vanishing eigenvalue and a well defined total photon number. These are
superpositions of Fock states with probability amplitudes given by positive as
well as negative square roots of multinomial coefficients. The classical
picture can be recovered by considering poissonian superpositions of localized
quantum states with different total photon number. We also study the
separability properties of flat band quantum states and apply them to the
transmission of information via multi-core fibers, where these states allow for
the total passive suppression of photon crosstalk and exhibit robustness
against photon losses. At the end, we propose a novel on-chip setup for the
experimental preparation of localized quantum states of light for any number of
photons.Comment: 12 pages, 5 figure
Compactification tuning for nonlinear localized modes in sawtooth lattices
We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise noncompact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yields further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.The research has been performed with support from the Swedish Research Council within the Swedish Research Links program, 348-2013-6752. U.N. appreciates the Spanish government projects FIS 2011-25167 and FPDI-2013-18422 as well as the Aragon project (Grupo FENOL). R.A.V. acknowledges support from Programa ICM grant RC130001, Programa de Financiamiento Basal de CONICYT (FB0824/2008), and FONDECYT Grant No. 1151444.Peer Reviewe
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