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

Interactions of Soliton in weakly nonlocal nonlinear media

Solitary waves or solitons is a nonlinear phenomenon which has been studied intensively due to its application in solid-state matter such as Bose-Einstein condensates state,plasma physics, optical fibers and nematic liquid crystal. In particular, the study of nonlinear phenomena occurs in the structure of waves gained interest of scholars since their discovery by John Russell in 1844. The Nonlinear Schrödinger Equation (NLSE) is the theoretical framework for the investigation of nonlinear pulse propagation in optical fibers. Nonlocality can be found in an underlying transport mechanisms or long-range forces like electrostatic interactions in liquid crystals and many-body interactions with matter waves in Bose-Einstein condensate or plasma waves. The length of optical beam width and length of response function are used to classify nonlocality in optical materials. The nonlocality can be categorized as weak nonlocal if the width of the optical beam broader than the length of response function and if the width of the optical beam is narrower than the length of response function, it is considered as highly nonlocal. This work investigates the interactions of solitons in a weakly nonlocal Cubic NLSE with Gaussian external potential. The variational approximation (VA) method was employed to solve non integrable NLSE to ordinary differential equation (ODE). The soliton parameters and the computational program are used to simulate the propagation of the soliton width and its center-of-mass position. In the presence of Gaussian external potential, the soliton may be transmitted, reflected or trapped based on the critical velocity and potential strength. Direct numerical simulation of Cubic NLSE is programmed to verify the results of approximation method. Good agreement is achieved between the direct numerical solution and VA method results