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Chinese Physics Letters

Controlled Manipulation with a Bose–Einstein Condensates N -Soliton Train under the Influence of Harmonic and Tilted Periodic Potentials

Feng-De Zong, Zhang Jie-Fang

Published Jul 1, 2008• 6 citations
Publisher

Abstract

A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.

DOI
10.1088/0256-307x/25/7/011

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A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.
In this paper, a perturbed complex Toda chain has been employed to describe the adiabatic interactions in an N-soliton train of the Gross-Pitaevskii equation. Perturbations induced by weak quadratic and periodic external potentials are analytically and numerically studied. It is found that the perturbed complex Toda chain adequately models the N-soliton train dynamics for both types of potentials. As an application of the developed theory, we consider the dynamics of a train of matter-wave solitons confined in a quadratic trap and optical lattice, as well as tilted periodic potentials. In the last case, we demonstrate that there exist critical values of the strength of the linear or periodic potential for which one or more localized states can be extracted from a soliton train. In addition, some interesting results in the experiments and applications of the Bose-Einstein condensates are also obtained.
N-soliton 火车在一个应用联合外部潜力套住描述 Bose 爱因斯坦冷凝物(BEC ) 的动力学的使不安的复杂 Toda 链(PCTC ) 的一个模型由弱泛音和倾斜的周期的部件组成首先被开发。用发达理论， BEC N-soliton 火车动力学被显示被 4N 很好接近联合非线性的微分方程，它在从振幅，速度， centre-of-mass 位置，和阶段的相互影响产生的系统描述基本相互作用。简化分析理论允许为描绘 BEC N-soliton 火车行为的一个有效、方便的方法。它进一步给为的潜力或更局部性的状态罐头的力量的批评价值从一列 soliton 火车被提取并且证明 BEC N-soliton 火车能由简单地操作潜力的力量从一个格子地点有选择地搬到另外一个。
A perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within an N-soliton train of the nonlinear Schrödinger equation. Perturbations induced by weak quadratic and periodic external potentials are studied by both analytical and numerical means. It is found that the perturbed CTC adequately models the N-soliton train dynamics for both types of potentials. As an application of the developed theory, we consider the dynamics of a train of matter-wave solitons confined to a parabolic trap and optical lattice, as well as tilted periodic potentials. In the last case, we demonstrate that there exist critical values of the strength of the linear potential for which one or more localized states can be extracted from a soliton train. An analytical expression for these critical strengths for expulsion is also derived.
A variational method is developed to describe the dynamics of a Bose-Einstein condensate (BEC) trapped in an applied external potential consisting of both a harmonic and periodic component. Using this variational method, the BEC dynamics is shown to be well approximated by four coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude (width), chirp, center position, and center frequency. The simplified analytic theory allows for an efficient and convenient method for characterizing the experimental BEC behavior when localized condensates are generated. It further gives the critical strength ratio of harmonic to periodic potential necessary to support multiple stable lattice sites for the condensate and demonstrates that there can be an underlying chaotic behavior in the condensate system.
An extended variational method for describing the dynamics of a Bose-Einstein condensate （BEC） chirped soliton in the presence of periodic and harmonic potentials is developed. It is shown that the BEC chirped soliton dynamics can be deduced via the extended variational method to a set of four coupled nonlinear differential equations. This deduced set of equations agrees remarkably well with full numerical simulations and highlights the dominant physical interactions in the system, namely amplitude, width, chirp, center-position, and center-frequency dynamics. The extended analytic theory provides a useful, accurate, and greatly simplified description of the governing BEC chirped soliton dynamics. It further gives the critical strength ratio of periodic to harmonic potential necessary to support multiple stable lattice sites for the BEC chirped soliton and demonstrates that the BEC chirped soliton can move selectively from one lattice site to another by simply manipulating the potentials. In addition, some interesting results for the experiments and applications of the BEC are also obtained.
An extended variation method for describing the dynamical evolution of Bose-Einstein condensate solitons in the presence of optic-lattice and harmonic potentials was developed.This method agreed well with full numerical simulations and highlighted the dominant physical interactions in the system,namely,amplitude,width,chirp,center-position,and center-frequency dynamics.It further presented the critical strength ratio of optic-lattice to harmonic potential necessary to support multiple stable lattice sites for the Bose-Einstein condensate solitons and demonstrated that the Bose-Einstein condensate solitons could move selectively from one stable lattice site location to arbitrary final position by simply manipulating the optic-lattice potential.In addition,some interesting results for the experiments and applications of the Bose-Einstein condensates were also obtained.