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 ($n_0$) is larger than one ($n$) of other identical waveguides in the array. Particularly, the effect holds if $\omega(n_0-n)/c>2Q$, where $Q$ is a linear coupling constant between array waveguides, $\omega$ is a carrier wave frequency and $c$ 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

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

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

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