arXiv subjects

Ramaz Khomeriki

Publications and source records attributed to Ramaz Khomeriki.

At least 37 records · Page 2Linked to original sources

arXiv2011

Realization of Discrete Quantum Billiard in 2D Optical Lattices

We propose the method for optical visualization of Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive index than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over direction of propagation for both ordered and disordered cases, exploring sensitivity of the averaged picture with respect to the beam injection position. For our finite systems the resulting patterns reminiscent the ones set in billiards and therefore we introduce a definition of discrete quantum billiard discussing the possible relevance to its well established continuous counterpart.

cond-mat.dis-nn↗

arXiv2011

Two interacting particles in a random potential

We study the scaling of the localization length of two interacting particles in a one-dimensional random lattice with the single particle localization length. We obtain several regimes, among them one interesting weak Fock space disorder regime. In this regime we derive a weak logarithmic scaling law. Numerical data support the absence of any strong enhancement of the two particle localization length.

cond-mat.dis-nn↗

arXiv2010

Nonlinear Landau-Zener Tunnelling in Coupled Waveguide Arrays

The possibility of direct observation of Nonlinear Landau-Zener tunnelling effect with a device consisting of two waveguide arrays connected with a tilted reduced refractive index barrier is discussed. Numerical simulations on this realistic setup are interpreted via simplified double well system and different asymmetric tunnelling scenarios were predicted just varying injected beam intensity.

physics.optics↗

arXiv2010

Interaction induced fractional Bloch and tunneling oscillations

We study the dynamics of few interacting bosons in a one-dimensional lattice with dc bias. In the absence of interactions the system displays single particle Bloch oscillations. For strong interaction the Bloch oscillation regime reemerges with fractional Bloch periods which are inversely proportional to the number of bosons clustered into a bound state. The interaction strength is affecting the oscillation amplitude. Excellent agreement is found between numerical data and a composite particle dynamics approach. For specific values of the interaction strength a particle will tunnel from the interacting cloud to a well defined distant lattice location.

cond-mat.other↗

arXiv2009

Trapping of Nonlinear Gravitational Waves by Two-Fluid Systems

We show that the coupled two-fluid gravitating system (e.g. stiff matter and 'vacuum energy') could trap nonlinear gravitational waves (e.g. Einstein-Rosen waves). The gravitational wave amplitude varies harmonically in time transferring the energy coherently to the stiff matter wave, and then the process goes to the backward direction. This process mimics the behaviour of trapped electromagnetic waves in two-level media. We have defined the limits for the frequency of this energy transfer oscillations.

gr-qc↗

arXiv2009

Spatial solitons rays in periodic optical lattices

The light ray of a spatial soliton in an optical film whose refractive index is smoothly modulated (wavelength much larger than the typical soliton width) in both spatial directions is shown to possess chaotic regimes for which the propagation is erratic. This is interpreted as a parametric driven pendulum, obtained by a new perturbative approach of the Maxwell equation. These findings are then demonstrated to compare well to the eikonal law of light ray propagation (nonlinearity compensates diffraction).

nlin.PS↗

arXiv2009

Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wave length gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories.

cond-mat.other↗

arXiv2009

Delocalization and spreading in a nonlinear Stark ladder

We study the evolution of a wave packet in a nonlinear Schrödinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. With increasing strength of nonlinearity we observe: (I) localization as a transient, with subsequent subdiffusion (weak mode-mode interactions); (II) immediate subdiffusion (strong mode-mode interactions); (III) single site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For single mode excitations and weak nonlinearities stability intervals are predicted and observed upon variation of the dc bias strength, which affect the short and long time dynamics.

cond-mat.stat-mech↗

arXiv2008

Tristability in the pendula chain

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.

nlin.PS↗

arXiv2008

Self-Chaotization in Coupled Optical Waveguides

We consider theoretically two coupled optical waveguides with a varying barrier height along the waveguides direction. The barrier could be constructed by the elongated island with a reduced refractive index (which acts as a potential barrier), such that in the middle region it splits a waveguide into two weakly coupled parts. It is predicted by numerical simulations and analytical consideration that the presence of some imperfection of the system parameters can cause splitting of injected laser beam and one will observe two intensity maximums at the output, while for small imperfections the input and output beam intensity distributions will be the same. The switching between two regimes could be achieved changing spectral width of the beam or refractive index of the island. This nontrivial effect is explained by possibility of transitions between the different eigenstates of the system in the region of large potential barrier heights. The mentioned effect could be used for all-optical readdressing and filtering purposes.

physics.optics↗

arXiv2008

Stochastic Resonance in the Fermi-Pasta-Ulam Chain

We consider a damped $β$-Fermi-Pasta-Ulam chain, driven at one boundary subjected to stochastic noise. It is shown that, for a fixed driving amplitude and frequency, increasing the noise intensity, the system's energy resonantly responds to the modulating frequency of the forcing signal. Multiple peaks appear in the signal to noise ratio, signalling the phenomenon of stochastic resonance. The presence of multiple peaks is explained by the existence of many stable and metastable states that are found when solving this boundary value problem for a semi-continuum approximation of the model. Stochastic resonance is shown to be generated by transitions between these states.

nlin.PS↗

arXiv2007

Nonlinear Dynamics in Double Square Well Potential

Considering the coherent nonlinear dynamics in double square well potential we find the example of coexistence of Josephson oscillations with a self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is illustrated and confirmed by numerical simulations. This property allows to make suggestions on possible experiments using Bose-Einstein condensates in engineered optical lattices or weakly coupled optical waveguide arrays.

nlin.PS↗

arXiv2007

Driving light pulses with light in two-level media

A two-level medium, described by the Maxwell-Bloch (MB) system, is engraved by establishing a standing cavity wave with a linearly polarized electromagnetic field that drives the medium on both ends. A light pulse, polarized along the other direction, then scatters the medium and couples to the cavity standing wave by means of the population inversion density variations. We demonstrate that control of the applied amplitudes of the grating field allows to stop the light pulse and to make it move backward (eventually to drive it freely). A simplified limit model of the MB system with variable boundary driving is obtained as a discrete nonlinear Schroedinger equation with tunable external potential. It reproduces qualitatively the dynamics of the driven light pulse.

physics.optics↗

arXiv2006

Long-Range Effects in Layered Spin Structures

We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with short-range and mean-field interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of long-range interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of long-range interactions crucially affect the behavior of the system.

cond-mat.stat-mech↗

arXiv2006

Driven Macroscopic Quantum Tunneling of Ultracold Atoms in Engineered Optical Lattices

Coherent macroscopic tunneling of a Bose-Einstein condensate between two parts of an optical lattice separated by an energy barrier is theoretically investigated. We show that by a pulsewise change of the barrier height, it is possible to switch between tunneling regime and a self-trapped state of the condensate. This property of the system is explained by effectively reducing the dynamics to the nonlinear problem of a particle moving in a double square well potential. The analysis is made for both attractive and repulsive interatomic forces, and it highlights the experimental relevance of our findings.

cond-mat.mes-hall↗

arXiv2006

Coexistence of Josephson oscillations and novel self-trapping regime in optical waveguide arrays

Considering the coherent nonlinear dynamics between two weakly linked optical waveguide arrays, we find the first example of coexistence of Josephson oscillations with a novel self-trapping regime. This macroscopic bistability is explained by proving analytically the simultaneous existence of symmetric, antisymmetric and asymmetric stationary solutions of the associated Gross-Pitaevskii equation. The effect is, moreover, illustrated and confirmed by numerical simulations. This property allows to conceive an optical switch based on the variation of the refractive index of the linking central waveguide.

nlin.PS↗

arXiv2005

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.

physics.optics↗

arXiv2005

Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.

nlin.PS↗