Solitons mobility in a dipolar Bose-Einstein condensate in an optical lattice

The present work is devoted to the theoretical investigation of the dynamics of Bose –Einstein condensates (BEC) in optical lattice with the long range magnetic dipole-dipole interaction between atoms. The system is described by a nonlocal nonlinear Schrodinger equation (NLSE). We consider the case when the lattice depth is sufficiently large (tight binding approximation). In this case nonlocal NLSE can be reduced to discrete NLSE equation. We show that discrete NLSE equation for some range of parameters can be reduced further to integrable Ablowitz-Ladik equation which supports moving solitons. Taking the one-soliton solution of Ablowitz-Ladik equation as an initial condition we have performed detailed numerical study of a soliton dynamics in both nonlocal NLSE and discrete NLSE. The conditions of existence and stability of moving solitons in dipolar BEC in an optical lattice are numerically revealed. Also the applicability limits for the tight binding approximation for the experimentally achievable range of parameters are investigated

Study of localized solutions of the nonlinear discrete model for dipolar Bose-Einstein condensate in an optical lattice by the homoclinic orbit method

It is well known that the dynamics of the Bose Einstein condensate (BEC) trapped in an optical lattice can be described in tight-binding approximation by the discrete Nonlinear Schrödinger Equation (DNLSE) [1,2]. This model opens the way to study different aspects of the BEC dynamics in an optical lattice, such as discrete solitons and nonlinear localized modes and their stability and dynamics, modulational instability, superfluid-insulator transition, etc

Modulational instability in salerno model

We investigate the properties of modulational instability in the Salerno equation in quasione dimension in Bose-Einstein condensate (BEC). We analyze the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC

Introduction to nonlinear discrete systems: theory and modelling

An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate droplets. In basic physical courses, usually the linear properties of discrete systems are studied. In this paper we propose a pedagogical introduction to the theory of nonlinear distributed systems. The main ideas and methods are illustrated using a universal model for different physical applications, the discrete nonlinear Schrödinger (DNLS) equation. We consider solutions of the DNLS equation and analyse their linear stability. The notions of nonlinear plane waves, modulational instability, discrete solitons and the anti-continuum limit are introduced and thoroughly discussed. A Mathematica program is provided for better comprehension of results and further exploration. Also, a few problems, extending the topic of the paper, for independent solution are given

Vibration spectrum of a two-soliton molecule in dipolar Bose–Einstein condensates

We study the vibration of soliton molecules in dipolar Bose–Einstein condensates by variational approach and numerical simulations of the nonlocal Gross–Pitaevskii equation. We employ the periodic variation of the strength of dipolar atomic interactions to excite oscillations of solitons near their equilibrium positions. When the parametric perturbation is sufficiently strong the molecule breaks up into individual solitons, like the dissociation of ordinary molecules. The waveform of the molecule and resonance frequency, predicted by the developed model, are confirmed by numerical simulations of the governing equation

Atomic coupler with two-mode squeezed vacuum state

We investigate the entanglement transfer from the two-mode squeezed state (TMS) to the atomic system by studying the dependence of the negativity on the coupling between the modes of the waveguides. This study is very important since the entanglement is an important feature which has no classical counterpart and it is the main resource of quantum information processing. We use a linear coupler which is composed of two waveguides placed close enough to allow exchanging energy between them via evanescent waves. Each waveguide includes a localized atom

Interaction of a spatial soliton on an interface between two nonlinear media

Spatial solitons are the solutions of nonlinear partial differential equations describing the propagation of optical beams in Kerr type nonlinear medium. This paper studies the scattering of a spatial solitons of the Cubic-Quintic Nonlinear Schrödinger Equation (C-Q NLSE) on an interface between two nonlinear media. The scattering process will be investigated by variational approximation method and by direct numerical solution of C-Q NLSE. This variational approximation method has been used to analyse the dynamic of the width and center of mass position of a soliton during the scattering process. Meanwhile, a direct numerical simulation of C-Q NLSE is run to check the accuracy of the approximation by using the same range of parameters and initial condition. The results for direct numerical simulation of CQNLSE for soliton parameters are quite similar with the variational equation. The studies showed that soliton can be reflected by or transmitted through the interface, also the nonlinear surface wave can be formed depending on the parameters of interface and initial soliton