低维Bose系统中孤子幅度的调控
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摘要
自从1999年人们在准一维(雪茄型)凝聚体中观察到暗孤子以来,有关玻色-爱因斯坦凝聚体(BECs)中的孤立子动力学性质的研究就成为凝聚态物理、低温物理等领域里的研究热点之一。BEC处于不同的外部势阱中会导致不同的非线性现象,如BEC局限在谐振外势阱中,粒子间为相互排斥作用会产生暗孤子,吸引作用下出现亮孤子;然而,当BEC处于双曲函数外势阱中,即使粒子间为相互排斥作用凝聚体中却形成亮孤子,吸引作用下却产生暗孤子。迄今为止,实验上已经可以利用Feshbach共振来调控凝聚体中粒子的散射长度,从而粒子之间的相互作用对BEC中孤立子动力学的影响也成为一个有趣的课题。本文基于平均场理论框架下描述BEC一系列物理性能的Gross-Pitaevskii方程,利用非线性微扰理论解析地研究了准一维、二维凝聚体中的孤立子行为,得到了一系列有意义的结果。全文结构如下:
第1章简要介绍了BEC的基本理论、国内外的研究动态和科研意义及本文的研究内容和方法。
由于实验上已利用Feshbach共振调控凝聚体中粒子的散射长度,从而控制粒子间的相互作用强度。因此,在第2章,我们解析地研究了粒子间的相互作用对准一维凝聚体中孤立子动力学的影响。结果表明,通过Feshbach共振使散射长度随时间增加时,凝聚体中的黑孤子会演化成稳定的灰孤子;当散射长度随时间减少时,凝聚体中的灰孤子将向黑孤子演化。同时我们基于现有的实验条件设计了一套具体的实验方案,实现黑孤子和灰孤子之间的稳定转化。
第3章,我们研究了准二维凝聚体中的非线性动力学性质。结果表明,当原子间为相互排斥作用时,凝聚体中首先会出现暗孤子;而这种暗孤子不稳定,会随时间演化成振幅较小的暗孤子环;形成的浅暗孤子环具有动力学稳定性。
最后是我们对本文研究工作的一个简要的总结和对以后的研究工作的展望。
Since the dark soliton in a quasi-one dimensional (cigar-shaped) condensate was observed in 1999, the study of dynamics properties of solitons in Bose Einstein condensates (BECs) has become one of the hot subjects in science region, such as condensate physics, low-temperature physics and so on. BEC trapped in different external potential will result in different nonlinear phenomena. For example, BEC trapped in external harmonic potential, there exists dark soliton in condensates with interatomic repulsive interaction, and there occurs bright soliton when interatomic interaction is attractive. If the condensate is trapped in hyperbolic functions potential, there exhibits dark soliton in condensates when interatomic interaction is attractive, and there appears bright soliton when interatomic interaction is repulsive. So far, it has been realized that controlling the scattering length of atoms in condensate via Feshbach resonance. Thereby it is an interesting subject that the effect of interatomic interaction on dynamics properties of solitons is considered in BEC. Based on the Gross-Pitaevskii equation which can describe a number of properties of BEC under the mean-field approximate, we have studied analytically the behaviors of soliton in quasi-one and quasi-two dimensional condensate in the thesis, by use of the nonlinear perturbation theory, and obtained series of significative result. The article is organized as follows:
In chapter 1, we introduce the basic theory, the general study situation, the scientific sense of BEC and the method and the content which we study in article.
It has been realized that the scattering length of atoms in condensate can be controlled by Feshbach resonance, consequently the interatomic interaction can also been controlled. So in chapter 2, we study analytically the effect of scattering length on the dynamics of soliton in quasi-one dimensional BEC. It is shown that, when the scattering length increased via Feshbach resonance, the black soliton transforms into the stable gray soliton in condensates; and when the scattering length decreased by Feshbach resonance, the gray soliton turns into the black soliton. Base on currently experimental conditions, we propose experimental protocols to realize the stable exchange between black and gray solitons.
In chapter 3, we study the nonlinear dynamics of a quasi-two dimensional condensate. It is found that, there is a dark soliton in condensate when the interatonic interaction is repulsive; the dark soliton is instability with the time, it evolves into ring dark soliton with a small amplitude; the shallow ring dark soliton will become dynamic stabilization.
Finally, we give a simple summary and prospect about solitons of BEC.
第1章简要介绍了BEC的基本理论、国内外的研究动态和科研意义及本文的研究内容和方法。
由于实验上已利用Feshbach共振调控凝聚体中粒子的散射长度,从而控制粒子间的相互作用强度。因此,在第2章,我们解析地研究了粒子间的相互作用对准一维凝聚体中孤立子动力学的影响。结果表明,通过Feshbach共振使散射长度随时间增加时,凝聚体中的黑孤子会演化成稳定的灰孤子;当散射长度随时间减少时,凝聚体中的灰孤子将向黑孤子演化。同时我们基于现有的实验条件设计了一套具体的实验方案,实现黑孤子和灰孤子之间的稳定转化。
第3章,我们研究了准二维凝聚体中的非线性动力学性质。结果表明,当原子间为相互排斥作用时,凝聚体中首先会出现暗孤子;而这种暗孤子不稳定,会随时间演化成振幅较小的暗孤子环;形成的浅暗孤子环具有动力学稳定性。
最后是我们对本文研究工作的一个简要的总结和对以后的研究工作的展望。
Since the dark soliton in a quasi-one dimensional (cigar-shaped) condensate was observed in 1999, the study of dynamics properties of solitons in Bose Einstein condensates (BECs) has become one of the hot subjects in science region, such as condensate physics, low-temperature physics and so on. BEC trapped in different external potential will result in different nonlinear phenomena. For example, BEC trapped in external harmonic potential, there exists dark soliton in condensates with interatomic repulsive interaction, and there occurs bright soliton when interatomic interaction is attractive. If the condensate is trapped in hyperbolic functions potential, there exhibits dark soliton in condensates when interatomic interaction is attractive, and there appears bright soliton when interatomic interaction is repulsive. So far, it has been realized that controlling the scattering length of atoms in condensate via Feshbach resonance. Thereby it is an interesting subject that the effect of interatomic interaction on dynamics properties of solitons is considered in BEC. Based on the Gross-Pitaevskii equation which can describe a number of properties of BEC under the mean-field approximate, we have studied analytically the behaviors of soliton in quasi-one and quasi-two dimensional condensate in the thesis, by use of the nonlinear perturbation theory, and obtained series of significative result. The article is organized as follows:
In chapter 1, we introduce the basic theory, the general study situation, the scientific sense of BEC and the method and the content which we study in article.
It has been realized that the scattering length of atoms in condensate can be controlled by Feshbach resonance, consequently the interatomic interaction can also been controlled. So in chapter 2, we study analytically the effect of scattering length on the dynamics of soliton in quasi-one dimensional BEC. It is shown that, when the scattering length increased via Feshbach resonance, the black soliton transforms into the stable gray soliton in condensates; and when the scattering length decreased by Feshbach resonance, the gray soliton turns into the black soliton. Base on currently experimental conditions, we propose experimental protocols to realize the stable exchange between black and gray solitons.
In chapter 3, we study the nonlinear dynamics of a quasi-two dimensional condensate. It is found that, there is a dark soliton in condensate when the interatonic interaction is repulsive; the dark soliton is instability with the time, it evolves into ring dark soliton with a small amplitude; the shallow ring dark soliton will become dynamic stabilization.
Finally, we give a simple summary and prospect about solitons of BEC.
引文
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