低维玻色气为何不发生玻色-爱因斯坦凝聚

本文详细讨论了玻色—爱因斯坦凝聚现象,指出了态密度对玻色气体凝聚的影响,并从数学和物理上解释了低维玻色气不产生玻—爱凝聚的原因.     

复合势中的玻色一爱因斯坦凝聚孤子的操控

提出了一种处理在光晶格势和抛物势共同作用下的玻色-爱因斯坦凝聚孤子动力学的拓展变分法．利用拓展变分方法给出了玻色．爱因斯坦凝聚孤子的解析处理,并和基于分步傅立叶变换的直接数值方法进行比较,发现这种拓展变分方法能够充分揭示上述外势场中的玻色．爱因斯坦凝聚孤子的动力学行为．同时,给出了能支持多稳定晶格囚禁玻色一爱因斯坦凝聚孤子的多晶格稳定势槽,并通过调控光晶格势实现了玻色一爱因斯坦凝聚孤子从某一稳定晶格势槽为初始位置到任意位置的操控．这为玻色一爱因斯坦凝聚的实验和应用研究提供了一定的理论依据．     

反抛物势与双光晶格势中的三维玻色-爱因斯坦凝聚涡旋孤子

提出了一种处理囚禁于反抛物势和双光晶格复合势中玻色-爱因斯坦凝聚涡旋孤子动力学的能量密度泛函和直接数值仿真相结合的方法.利用静态Gross-Pitaevskii方程和柱对称玻色-爱因斯坦凝聚涡旋孤子试探波函数,给出了玻色-爱因斯坦凝聚静态涡旋孤子能量密度泛函的解析式,再运用数值模拟含时Gross-Pi-taevskii方程的方法,得到了稳定演化的涡旋孤子;并且通过调控双光晶格势,实现了玻色-爱因斯坦凝聚涡旋孤子从某一晶格势槽为初始位置到任意位置的操控,为玻色-爱因斯坦凝聚的实验和应用研究提供了一定的理论依据.值得指出的是,双涡旋孤子的稳定演化与操控是最重要的发现.     

再论玻色—爱因斯坦凝聚的相变特征

本文较详细地讨论了玻色－爱因斯坦凝聚现象．从等温相交和等容相交角度，解释了玻色—爱因斯坦凝聚的相交特征．     

随机边界条件下玻色-爱因斯坦凝聚的临界温度

研究了d维空间随机箱中玻色气体的凝聚问题，在箱子的线度L满足均匀分布和高斯分布两种情况下，分别求出了系统发生玻色-爱因斯坦凝聚的临界温度Tc，并将Tc与固定箱子中玻色气体发生玻色-爱因斯坦凝聚的临界温度Tc^R作了比较，发现Tc小于或等于Tc^R，其具体的关系取决于L所满足的分布函数．同样研究了被限制在频率随机改变的谐振子势阱中的玻色气体的凝聚问题，发现Tc与Tc^R的关系与上面的结论类似．     

浅谈玻色—爱因斯坦凝聚

阐述玻色—爱因斯坦凝聚的概念，形成的条件，物理性质及其远景     

随机边界条件下玻色一爱因斯坦凝聚的临界温度

研究了d维空间随机箱中玻色气体的凝聚问题,在箱子的线度L满足均匀分布和高斯分布两种情况下,分别求出了系统发生玻色一爱因斯坦凝聚的临界温度Tc,并将Tc与固定箱子中玻色气体发生玻色一爱因斯坦凝聚的临界温度TRc作了比较,发现Tc小于或等于TRc,其具体的关系取决于L所满足的分布函数.同样研究了被限制在频率随机改变的谐振子势阱中的玻色气体的凝聚问题,发现Tc与TRc的关系与上面的结论类似.     

外势场中粒子的态密度和坡色—爱因斯担凝聚

以简单的幂函数势为在外势场中的粒子态密度，以及理想玻色气体实现玻色－爱因斯坦凝聚的条件和性质。     

浅谈玻色—爱因斯坦凝聚

阐述玻色-爱因斯坦凝聚的概念，形成的条件，物理性质及其远景。     

二维囚禁广义玻色气体的玻色-爱因斯坦凝聚

应用广义玻色-爱因斯坦分布函数研究在幂函数外势中二维广义玻色气体的玻色-爱因斯坦凝聚(BEC),导出二维广义玻色气体的临界温度、基态粒子占据率和热容量等物理量的解析表达式,讨论了非广延参数q对玻色系统热统计性质的影响.     

Bose-Einstein 凝聚态中的一维Gross-Pitaevskii方程的包络周期解和孤立波解

非线性Schrdinger方程的精确解对于理解Bose-Einstein凝聚态动力学演化有重要的作用。应用Jacobi椭圆函数展开法, 求得描述Bose-Einstein凝聚态的一维Gross-Pitaevskii方程的包络周期解。在极限情况下, 包络周期解可导出包络孤立波解。     

一类带无界势的非线性Schrdinger方程的整体解

对于描述玻色-爱因斯坦凝聚的带无界势的非线性Schrdinger方程,证明了解整体存在的充分条件,并且该条件与方程的基态解密切相关.     

一类带无界势的非线性Schroedinger方程的整体解

对于描述玻色-爱因斯坦凝聚的带无界势的非线性Schroedinger方程，证明了解整体存在的充分条件，并且该条件与方程的基态解密切相关。     

Dynamics of collapsing and exploding Bose-Einstein condensates.

When atoms in a gas are cooled to extremely low temperatures, they will-under the appropriate conditions-condense into a single quantum-mechanical state known as a Bose-Einstein condensate. In such systems, quantum-mechanical behaviour is evident on a macroscopic scale. Here we explore the dynamics of how a Bose-Einstein condensate collapses and subsequently explodes when the balance of forces governing its size and shape is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the interatomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally applied magnetic field yields detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wavefunction and oscillating remnant condensates that survive the collapse. All these processes have curious dependences on time, on the strength of the interaction and on the number of condensate atoms. Although the system would seem to be simple and well characterized, our measurements reveal many phenomena that challenge theoretical models.     

Coherent zero-state and pi-state in an exciton-polariton condensate array

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.     

一维光晶格中玻色-爱因斯坦凝聚的粒子数分布

对捕陷在三维轴对称谐振势阱叠加一维光晶格的组合势中的玻色凝聚气体,基于平均场Gross-Pitae-vskii方程理论,并运用G-P能量泛函和变分方法,得出了非线性薛定谔方程的一维形式,运用数值计算的方法,研究了组合势中子凝聚体的粒子数分布与光晶格深度之间的关系,同时分析了磁势阱对子凝聚体粒子数分布的影响。     

Nonlinear and quantum atom optics

Coherent matter waves in the form of Bose-Einstein condensates have led to the development of nonlinear and quantum atom optics - the de Broglie wave analogues of nonlinear and quantum optics with light. In nonlinear atom optics, four-wave mixing of matter waves and mixing of combinations of light and matter waves have been observed; such progress culminated in the demonstration of phase-coherent matter-wave amplification. Solitons represent another active area in nonlinear atom optics: these non-dispersing propagating modes of the equation that governs Bose-Einstein condensates have been created experimentally, and observed subsequently to break up into vortices. Quantum atom optics is concerned with the statistical properties and correlations of matter-wave fields. A first step in this area is the measurement of reduced number fluctuations in a Bose-Einstein condensate partitioned into a series of optical potential wells.     

Bose-Einstein condensation on a microelectronic chip

Although Bose-Einstein condensates of ultracold atoms have been experimentally realizable for several years, their formation and manipulation still impose considerable technical challenges. An all-optical technique that enables faster production of Bose-Einstein condensates was recently reported. Here we demonstrate that the formation of a condensate can be greatly simplified using a microscopic magnetic trap on a chip. We achieve Bose-Einstein condensation inside the single vapour cell of a magneto-optical trap in as little as 700 ms-more than a factor of ten faster than typical experiments, and a factor of three faster than the all-optical technique. A coherent matter wave is emitted normal to the chip surface when the trapped atoms are released into free fall; alternatively, we couple the condensate into an 'atomic conveyor belt', which is used to transport the condensed cloud non-destructively over a macroscopic distance parallel to the chip surface. The possibility of manipulating laser-like coherent matter waves with such an integrated atom-optical system holds promise for applications in interferometry, holography, microscopy, atom lithography and quantum information processing.     

磁场光学网格中的双极玻色子的单孤波激发

研究磁场中光学网格的Bose-Einstein冷凝的非线性动力学.给出了出现在不同参数区域的不同类型的单孤波激发.     

玻色-爱因斯坦凝聚中的色散关系

超流性是玻色-爱因斯坦凝聚宏观量子效应的重要体现,分别用运动方程法和哈密顿量对角化方法,通过傅里叶变换导出了玻色-爱因斯坦凝聚超流体的色散关系,并给出了凝聚体中声子速度的表达式.结果表明,在长波极限下,色散关系与波数近似成线性关系.