Long lived matter waves Bloch oscillations and dynamical localization by time dependent nonlinearity management

We introduce a new method to achieve long lived Bloch oscillations and dynamical localization of matter wave gap solitons in optical lattices. The method is based on time dependent modulations of the nonlinearity which can be experimentally implemented by means of the Feshbach resonance technique. In particular, we show that the width of the wave packet is preserved if time modulations of the nonlinearity are taken proportional to the curvature of the linear band spectrum which for most typical experimental settings are well approximated by harmonic time modulations of proper frequencies

Investigation of the spectra of coupled polaritons on the periodically modulated metallic layer and the narrow regions of anomalous transparency

The paper deals with the theoretical investigation of plane, normally incident electromagnetic wave transmission through the flat metal film whose dielectric constant has small periodical sinusoidal modulation in one dimension parallel to the projection of the electric field onto the film surface. The dependencies of the film transmittancy on the parameters of the problem (frequency, modulation depth and absorption) are examined. It is shown that the film transmittancy increases considerably when the conditions for resonance interaction of an incident electromagnetic wave with surface plasmon polaritons (SPPs) are met. It is found that for small but finite absorption there are two frequencies in the vicinity of which the transmittancy can achieve the values of the order of unity due to resonances on symmetric and antisymmetric (relative to the mean plane) SPP modes. It is shown that for each value of absorption there exists a certain optimal modulation depth, which maximizes the resonance transparency.Comment: 18 pages, 8 figures, proceeding of conference "Plasmonics: metallic nanostructures and their optical properties", SPIE's 48-th Annual Meeting, 3-8 August, 2003, San Diego, US

A finitely presented orderable group with insoluble word problem

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.Comment: 17 page

Dynamical localization of gap-solitons by time periodic forces

The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic modulation of the nonlinearity in space to eliminate nonexistence regions of gap-solitons in reciprocal space. We show that when this condition is achieved, the observation of dynamical localization in true nonlinear regime becomes possible. The results apply to all systems described by the periodic nonlinear Schr\"odinger equation, including Bose-Einstein condensates of ultracold atoms trapped in optical lattices and arrays of waveguides or photonic crystals in nonlinear optics.Comment: accepted for Europhysics Letter

Light scattering by a medium with a spatially modulated optical conductivity: the case of graphene

We describe light scattering from a graphene sheet having a modulated optical conductivity. We show that such modulation enables the excitation of surface plasmon-polaritons by an electromagnetic wave impinging at normal incidence. The resulting surface plasmon-polaritons are responsible for a substantial increase of electromagnetic radiation absorption by the graphene sheet. The origin of the modulation can be due either to a periodic strain field or to adatoms (or absorbed molecules) with a modulated adsorption profile.Comment: http://iopscience.iop.org/0953-8984/24/24/24530

Localized modes in arrays of boson-fermion mixtures

It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and periodic nonlinearity. In such system there exist localized modes having peculiar properties. In particular, for some regions of parameters there exists a lower bound for a number of atoms necessary for creation of a mode, while for other domains small amplitude gap solitons are not available in vicinity of either of the gap edges. We found that the lowest branch of the symmetric solution may either exist only for a restricted range of energies in a gap or does not exist, unlike in pure bosonic condensates. The simplest bifurcations of the modes are shown and stability of the modes is verified numerically

PT-symmetric coupler with a coupling defect : soliton interaction with exceptional point

We study the interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. This defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of antisymmetric solitons are more complex, showing domains of successive broadening of the beam and of the beam splitting in two outward propagating solitons, in addition to the single breather generation and blowup. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough, the only observable outcome of the soliton-defect interaction is the generation of the breather.The work was supported by the Program of Introducing Talents of Discipline to Universities under Grant No. B12024. Y. V. B. and V. V. K. were supported by FCT (Portugal) grants PEst-C/FIS/UI0607/2013, PEst-OE/FIS/UI0618/2011, PTDC/FIS-OPT/1918/2012. C. H. and G. X. H. were supported by the NSF-China grants 11105052 and 11174080

Surface modes and breathers in finite arrays of nonlinear waveguides

We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one-- and two--dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.Comment: Accepted for publication in Physical Review