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Journal of Physics Conference Series

Anti-continuum approach on nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattice

M H Badarudin, M. S. A. Hadi, Bakhram Umarov

Published Mar 1, 2017• 1 citation
Publisher

Abstract

This paper aims to analyze the stability of nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattice by anti-continuum approach. It is relatively convenient to employ the anti-continuum method for solving discrete nonlinear Schrödinger equation. This method has shown the ability to produce similar result of analysis of the system stability as produced by other methods. The dynamical stability of the system has been investigated within certain permissible range of parameters.

DOI
10.1088/1742-6596/819/1/012021

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From the discrete nonlinear Schrödinger equation and the linear stability analysis, the modulational instability (MI) of dipolar Bose–Einstein Condensates (BECs) in an optical lattice is studied. The MI relation of the dipolar BECs in the optical lattice with the on-site interaction and the inter-site interaction is obtained. The results show that there is a great influence of inter-site interaction on MI of dipolar BEC in the optical lattice. This gives us some useful information for manipulating dipolar BECs in practice.
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.
We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.