旋量玻色爱因斯坦凝聚体动力学的解析研究

项目名称： 旋量玻色爱因斯坦凝聚体动力学的解析研究

项目编号： No.11475073

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 赵敦

作者单位： 兰州大学

项目金额： 75万元

中文摘要： 玻色-爱因斯坦凝聚体（BEC）是研究量子宏观现象和量子操控的重要平台,物质波动力学是BEC领域实验和理论研究的重要内容。旋量BEC由于原子的自旋自由度被释放而展现了许多与磁性相关的新特性,在实验中已观察到丰富的新现象，如自旋构型, 量子磁化,二次塞曼效应等。与单分量的情形相比，旋量BEC的动力学方程更难求解，解析结果很少。本项目主要致力于旋量BEC的动力学性质和物质波孤子管理及其稳定性的解析研究，从多分量Gross-Pitaevskii平均场方程出发，发展各种解析方法，集中探讨旋量BEC的自旋构型和量子磁化性质，以及塞曼效应和原子间s-波散射长度对动力学的影响，对旋量BEC的物质波动力学性质及管理进行细致刻画，并与实验结果进行比较，期望对进一步的实验提出建议。本项目研究成果将有助于深入理解旋量BEC的动力学特性。

中文关键词： 玻色-爱因斯坦凝聚；平均场理论；Gross-Pitaevskii方程；孤子管理；精确解

英文摘要： Bose-Einstein condensate(BEC) provides an important platform to explore various macroscopic quantum effects and quantum manipulation. The studies on the dynamics of the matter-waves are important issues both in experiments and theories. Due to the liberation of the spin degree of freedom, spinor BEC displays abundant new features related to magnetism, many new phenomena have been observed in experiments, such as spin configurations, quantum magnetization, and quadratic Zeeman effect, etc. Comparing with the scalar BEC,it is quite difficult to solve the partial differential equations for spinor BEC, and little analytical results are known. This project focus on the analytical study on spinor BEC，mainly for the matter-wave dynamics, its management and stability. Starting with the multi-component Gross-Pitaevskii mean-field equations, we will develop various analytical methods to deal with the dynamics. We will chiefly focus on exploring various spin configurations and quantum magnetization, and how the quadratic Zeeman effect and the s-wave scattering lengths affect the dynamics. We will give detailed description to the dynamical behaviour and its management of the spinor BEC, and give some comparison with the results in experiments. We also expect to give some suggestions to further experiments. This project will be helpful for deep understanding to the dynamical features of the spinor BEC.

英文关键词： Bose-Einstein condensates;mean field theory;Gross-Pitaevskii equation;soliton management;exact solution