572 research outputs found
Quantum Correlations in Two-Particle Anderson Localization
We predict the quantum correlations between non-interacting particles
evolving simultaneously in a disordered medium. While the particle density
follows the single-particle dynamics and exhibits Anderson localization, the
two-particle correlation develops unique features that depend on the quantum
statistics of the particles and their initial separation. On short time scales,
the localization of one particle becomes dependent on whether the other
particle is localized or not. On long time scales, the localized particles show
oscillatory correlations within the localization length. These effects can be
observed in Anderson localization of non-classical light and ultra-cold atoms.Comment: 4 pages, 4 figures, comments welcom
Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices
We investigate the interaction between a light beam and a two-dimensional
photonic lattice that is photo-induced in a photorefractive crystal using
partially coherent light. We demonstrate that this interaction process is
associated with a host of new phenomena including lattice dislocation, lattice
deformation, and creation of structures akin to optical polarons. In addition,
two-dimensional discrete solitons are realized in such partially coherent
photonic lattices.Comment: 12 pages, 4 figures (revised). accepted by Phys. Rev. Let
Propagation and perfect transmission in three-waveguide axially varying couplers
We study a class of three-waveguide axially varying structures whose dynamics
are described by the su(3) algebra. Their analytic propagator can be found
based on the corresponding Lie group generators. In particular, we show that
the field propagator corresponding to three-waveguide structures that have
arbitrarily varying coupling coefficients and identical refractive indices is
associated with the orbital angular momentum algebra. The conditions necessary
to achieve perfect transmission from the first to the last waveguide element
are obtained and particular cases are elucidated analytically.Comment: 5 pages, 4 figure
Nonlinear Band Gap Transmission in Optical Waveguide Arrays
The effect of nonlinear transmission in coupled optical waveguide arrays is
theoretically investigated via numerical simulations on the corresponding model
equations. The realistic experimental setup is suggested injecting the beam in
a single boundary waveguide, linear refractive index of which () is larger
than one () of other identical waveguides in the array. Particularly, the
effect holds if , where is a linear coupling constant
between array waveguides, is a carrier wave frequency and is a
light velocity. Making numerical experiments in case of discrete nonlinear
Schr\"odinger equation it is shown that the energy transfers from the boundary
waveguide to the waveguide array above certain threshold intensity of the
injected beam. This effect is explained by means of the creation and
propagation of gap solitons in full analogy with the similar phenomenon of
nonlinear supratransmission [F. Geniet, J. Leon, PRL, {\bf 89}, 134102, (2002)]
in case of discrete sine-Gordon lattice.Comment: 4 pages, 6 figures. Phys. Rev. Lett. (in press
Ermakov-Lewis symmetry in photonic lattices
We present a class of waveguide arrays that is the classical analog of a
quantum harmonic oscillator where the mass and frequency depend on the
propagation distance. In these photonic lattices refractive indices and second
neighbor couplings define the mass and frequency of the analog quantum
oscillator, while first neighbor couplings are a free parameter to adjust the
model. The quantum model conserves the Ermakov-Lewis invariant, thus the
photonic crystal also posses this symmetry.Comment: 8 pages, 3 figure
Landau-Zener Tunnelling in Waveguide Arrays
Landau-Zener tunnelling is discussed in connection with optical waveguide
arrays. Light injected in a specific band of the Bloch spectrum in the
propagation constant can be transmitted to another band, changing its physical
properties. This is achieved using two waveguide arrays with different
refractive indices, which amounts to consider a Schr\"odinger equation in a
periodic potential with a step. The step causes wave "acceleration" and thus
induces Landau-Zener tunnelling. The region of physical parameters where this
phenomenon can occur is analytically determined and a realistic experimental
setup is suggested. Its application could allow the realization of light
filters.Comment: 4 pages, 6 figure
Breather Statics and Dynamics in Klein--Gordon Chains with a Bend
In this communication, we examine a nonlinear model with an impurity
emulating a bend. We justify the geometric interpretation of the model and
connect it with earlier work on models including geometric effects. We focus on
both the bifurcation and stability analysis of the modes that emerge as a
function of the strength of the bend angle, but we also examine dynamical
effects including the scattering of mobile localized modes (discrete breathers)
off of such a geometric structure. The potential outcomes of such numerical
experiments (including transmission, trapping within the bend as well as
reflection) are highlighted and qualitatively explained. Such models are of
interest both theoretically in understanding the interplay of breathers with
curvature, but also practically in simple models of photonic crystals or of
bent chains of DNA.Comment: 14 pages, 16 figure
Bistable light detectors with nonlinear waveguide arrays
Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides
is studied and shown to be a means to conceive light detectors that switch
under excitation by a weak signal. The detector is obtained by coupling two
single 1D waveguide to an array of coupled waveguides with adjusted indices and
coupling. The process is understood by analytical description in the
conservative and continuous case and illustrated by numerical simulations of
the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published
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