Bessel型光晶格中双组分玻色-爱因斯坦凝聚体的基态解

研究了平面Bessel型光晶格(BL)中双组分玻色-爱因斯坦凝聚(BECs)体系的基态解.从描述三维(3D)BECs体系的动力学方程Gross-Pitaevskii方程(GPE)出发,当垂直方向囚禁频率远大于平面上囚禁频率时,得到了描述2D-BECs体系的动力学方程.利用双组分BECs体系中原子之间相互作用与BL强度相互平衡的条件,得到了平面BL光晶格中2D-GPE的一组基态精确解,给出了基态的原子数分布,总原子数和能量与原子之间相互作用强度及BL势的关系.相对于单组分BEC体系,由于不同组分原子相互作用的存在,使得BL光晶格中双组分BECs基态具有更丰富的结构.当不存在不同组分原子之间的相互作用时,模型简化到单组分体系,并给出了相应的基态解,原子数分布和能量. 关键词： Bessel型光晶格 基态解 双组分玻色-爱因斯坦凝聚     

两组分BECs在光晶格中的隧穿动力学及其周期调制效应

研究了两组分玻色-爱因斯坦凝聚体(BECs)在一维光晶格中的隧穿动力学及周期调制效应.在两模近似下,运用数值分析的方法,讨论了两组分间相互作用对体系的隧穿动力学行为的影响.进一步讨论了两组分间相互作用在周期调制下系统的动力学特性,分析了随着调制振幅和频率的变化,系统发生隧穿、不稳定和自俘获的区域分布,发现在中低频调制下,系统的隧穿动力学发生了明显的改变.     

玻色-费米超流混合体系中的相互作用调制隧穿动力学

研究了玻色-费米超流混合体系中的相互作用调制隧穿动力学特性,其中玻色子位于对称双势阱中,费米子位于对称双势阱中心的简谐势阱中.采用双模近似方法得到描述双势阱玻色-爱因斯坦凝聚的动力学特性方程组,并将其与简谐势阱中分子玻色-爱因斯坦凝聚的Gross-Pitaevskii方程进行耦合.通过对不同参数下玻色-费米混合体系中的隧穿现象进行数值研究,发现简谐势阱中费米子与双势阱中玻色子的相互作用使双势阱玻色-爱因斯坦凝聚的隧穿动力学特性更加丰富.不但驱使双势阱中玻色-爱因斯坦凝聚从类约瑟夫森振荡转变为宏观量子自囚禁,而且宏观量子自囚禁表现为三种不同的形式:相位与时间呈负相关并随时间单调减小的自囚禁、相位随时间演化有界的自囚禁以及相位与时间呈正相关并随时间单调增大的自囚禁.     

三势阱玻色爱因斯坦凝聚体三体复合效应的数值研究

文章中着重研究在三势阱中的凝聚体所受到的非弹性碰撞相互作用,考虑有三体复合耗散和原子填充时三势阱中玻色-爱因斯坦凝聚体动力学性质,研究了三势阱中玻色-爱因斯坦凝聚体系的自囚禁与宏观量子遂穿问题,用数值分析和解析推导的方法,发现自俘获和宏观量子隧穿现,另外,在自俘获和宏观量子隧穿进程中发现了量子拍现象,并对这些现象给出合理的解释。     

冷原子物理中的一维少体问题

作为构成量子多体系统的基本单元,一维少体系统的研究不仅可以在理论上为多体系统的量子关联及动力学等性质提供更为基本的理解,也可以为实验上制备多体系统提供更加方便和功能更加全面的方法.本文回顾了冷原子物理中一维少体系统最新的实验和理论进展.首先介绍了少体实验中实现的谐振子势阱中确定原子数的精确制备,亚稳态势阱和双阱系统中原子的隧穿,以及强相互作用下等效自旋链的实验结果.然后深度解析了理论研究方面,特别是基于精确可解模型的一些重要结果,包括亚稳态势阱中相互作用原子的隧穿概率,以及相应实验上常见势阱的能谱分析、密度分布、隧穿动力学以及强相互作用极限下的有效自旋链模型等.     

三体相互作用下三势阱中玻色-爱因斯坦凝聚体的稳定性研究

着重研究受到非弹性碰撞相互作用,即考虑有三体复合耗散和原子填充时三势阱中玻色-爱因斯坦凝聚体的动力学性质.运用三模近似,得到三个耦合的GP方程,用数值的方法得到不同散射长度的数值结果,展示了玻色-爱因斯坦凝聚体在零相位和π相位时,会出现自俘获及量子隧穿现象,且定态解的稳定性与相位有关.     

噪声对双势阱玻色-爱因斯坦凝聚体系自俘获现象的影响

研究了对称双势阱玻色-爱因斯坦凝聚体系(BEC)存在均匀噪声或高斯噪声时的自俘获现象.结果发现噪声的存在破坏了自俘获现象的临界行为特征，使得原来约瑟夫森振荡和自俘获之间的临界点变成了一个过渡区域，而且噪声强度越大，这个过渡区域展得越宽.同时发现，对于确定的相互作用强度，当噪声强度增大到一定程度时，相平面会出现混乱，如果这时固定噪声强度增大相互作用强度，相平面中的轨道会重新出现.对纯量子系统加噪声后，自俘获同样不存在临界值，而是存在一个临界区域，且随噪声的增强临界区域会展宽.与平均场近似情况下不同的是，纯量子情况下噪声促进自俘获的产生，且噪声越强自俘获越明显. 关键词： 玻色-爱因斯坦凝聚 自俘获 双势阱 噪声     

量子相空间中对称受驱双势阱系统的量子隧穿动力过程

本文以纠缠轨线分子动力学方法研究对称受驱双势阱系统的量子隧穿动力学过程.驱动力的幅度和频率改变将对量子隧穿动力学过程产生巨大的影响,这为人们自主控制这一重要的过程提供理论基础.当体系的经典动力学呈现混沌状态时,它的量子动力学过程将发生显著的变化.在强驱动力作用下,双势阱系统的量子共振频率隧穿和非共振频率隧穿因为混沌行为的出现明显增强.通过对比相空间中具有相同初始态的纠缠轨线和经典轨线演化,我们给出量子隧穿过程清晰的物理图像.最后,我们讨论量子隧穿动力学过程中体系不确定度的演化和反映波包动力学过程的自关联函数演化.     

量子力学基本概念教学探讨

用一维无限深势阱中粒子的动态量子模型讨论了态叠加原理和时间与能量的不确定关系原理的意义,指出量子隧穿效应静态模型的疑难,建立了一个隧穿效应动态模型,并讨论了隧穿效应的微观机制.     

双组分玻色-爱因斯坦凝聚体中亚稳态存在条件及其寿命

本文对双势阱中凝聚的冷原子通过约瑟夫森结隧穿时所形成的亚稳态进行研究.通过介观自旋算符建立了体系的精确量子相位模型,利用对量子自旋的势场描述给出了在两阱中振荡的原子之间相位差为时,即亚稳态时所要满足的物理条件,并用瞬子方法计算了该亚稳态存在的寿命.     

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.     

Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates

We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length.     

Tunneling dynamics between two-component Bose–Einstein condensates

We present a mean-field model to study the tunneling dynamics between initially separated two-component Bose condensates in a time-dependent double-well potential. We solve the model in terms of a completely numerical procedure. In contrast to the usual Josephson effect between two coherently separated single-component condensates, we find that this system sustains a macroscopic quantum self-trapping even for sufficiently weak interatomic interactions and small initial population imbalance far below the critical value.     

Instabilities and vortex-lattice formation in rotating conventional and dipolar dilute-gas Bose-Einstein condensates

A theoretical study of vortex-lattice formation in atomic Bose-Einstein condensates confined by a rotating elliptical trap is presented. For the conventional case of purely s-wave interatomic interactions, this is done through a consideration of both hydrodynamic equations and time-dependent simulations of the Gross-Pitaevskii equation. We discriminate three distinct, experimentally testable regimes of instability: ripple, interbranch, and catastrophic. Additionally, we generalize the classical hydrodynamical approach to include long-range dipolar interactions, showing how the static solutions and their stability in the rotating frame are significantly altered. This enables us to examine the routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex-lattice formation.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schr(o)dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

Rabi flopping induces spatial demixing dynamics

We experimentally investigate the mixing and demixing dynamics of Bose-Einstein condensates in the presence of a linear coupling between two internal states. The observed amplitude reduction of the Rabi oscillations can be understood as a result of demixing dynamics of dressed states as experimentally confirmed by reconstructing the spatial profile of dressed state amplitudes. The observations are in quantitative agreement with numerical integration of coupled Gross-Pitaevskii equations without free parameters, which also reveals the criticality of the dynamics on the symmetry of the system. Our observations demonstrate new possibilities for changing effective atomic interactions and studying critical phenomena.     

Assessment of interspecies scattering lengths a12 from stability of two-component Bose-Einstein condensates

A stability method is used to assess possible values of interspecies scattering lengths a12 in two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. The technique, based on a recent stability analysis of solitonic excitations in two-component Bose-Einstein condensates, is applied to ninety combinations of atomic alkali pairs with given singlet and triplet intraspecies scattering lengths as input parameters. Results obtained for values of a12 are in a reasonable agreement with the few ones available in the literature and with those obtained from a Painlevé analysis of the coupled Gross-Pitaevskii equations.     

Vector rogue waves in binary mixtures of Bose-Einstein condensates

We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations of these coefficients that admit the existence of rogue waves.