准二维玻色-爱因斯坦凝聚和原子激光器 Alternative Title Quasi-2D Bose-Einstein Condensation and Atom Laser 杨宏伟 Thesis Advisor 汪志诚 2004-05-12 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 博士 Keyword 玻色-爱因斯坦凝聚 原子激光器 Abstract 在这篇论文中，准二维束缚势玻色 - 爱因斯坦凝聚体的一些性质和原子激光器被讨论研究。在第二章中，我们通过解 Gross-Pitaevskii（GP）能量泛函解析地得到了准二维玻色凝聚体的相互作用常数，可以看出它不但与 s- 波散射长度有关还与紧束缚方向上的特征长度有关，同时，得到了准二维 GP 方程。对于正负两种不同的散射长度，准二维 GP 方程的定态波函数的形状被分别画出，而且在图中还给出了不同原子数时定态波函数形状的变化情况。并且，通过数值模拟我们计算了不同原子数的能量和化学势。同时，我们用变分的方法研究了负散射长度准二维束缚玻色气体的塌缩现象。一种变分的方法被用于计算准二维束缚玻色凝聚体的激发谱，两个基态激发模式被找到，它们的振动频率被计算得到。在第三章中，原子激光器的定义被给出，它的组成要素被详细地描述。我们研究了一个简单的原子激光器模型。这个模型是一个被引入增益和衰减项后的GP方程，注意，在这个模型中我们没有考虑输出耦合。用这个模型解析地讨论了激光模式的阈值和稳态性问题。我们讨论了被用于描述各种原子激光器模型的 rate 方程，平均场（GP）方程和量子主方程之间的优缺点。 Other Abstract In this dissertation, several properties of quasi-2D trapped Bose-Einstein condensate and atom lasers are studied and discussed. In Chapter 2, we obtain analytically the interaction constant of quasi-2D trapped Bose condensate, which is function of not only s-wave scattering length but also characteristic length in tight confinement direction, by solving Goss-Pitaevskii (GP) energy functional, and get quasi-2D GP equation. The shapes of the stable wave functions of quasi-2D GP equation for positive and negative scattering lengths are respectively plotted for different atom number. Corresponding energy and chemical potential are also worked out by numerical method. Moreover, we use variational method to study collapse of quasi-2D trapped Bose gas with negative scattering length. A variational method is used to calculate the excitation spectrum of quasi-2D trapped Bose condensate and two collective excitation mode are found, and their oscillation frequencies obtained. In Chapter 3, A atom laser is defined, and its elements are detailedly described. We investigate a simple atom laser model by introducing phenomenologically gain and loss terms in the GP equation, noting that we don't consider output coupling in this model, and discuss analytically threshold and stability of lasering mode. We discuss advantages and defects among the rate equation, the mean-field (GP) equation and quantum master equation, which are respectively used to describe all kinds of atom laser models. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/229000 Collection 物理科学与技术学院 Recommended CitationGB/T 7714 杨宏伟. 准二维玻色-爱因斯坦凝聚和原子激光器[D]. 兰州. 兰州大学,2004.
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