旋量玻色—爱因斯坦凝聚体中的拓扑激发研究

发布时间：2018-09-19 20:22

【摘要】：玻色-爱因斯坦凝聚体(BEC)的实现迅速推动了超冷原子、冷分子物理的快速发展。BEC所具有的独特宏观量子相干特性和人工可调控性,不仅使之成为了测试量子多体物理的基础性实验平台,而且也为凝聚态计算和非线性科学等,提供了万能的模拟平台。近些年,随着新技术、新方法在实验中的应用,探索BEC中新颖的、具有拓扑性质的量子态已成为国际研究的热点问题。我们在本文中将主要讨论旋量玻色-爱因斯坦凝聚体中的拓扑激发,主要包括旋量BEC的平均场理论、旋量序参量流形的对称性分类、拓扑激发的基本理论以及对旋量BEC中拓扑激发的数值研究。第一章主要阐述BEC的相关理论基础。首先对玻色-爱因斯坦凝聚研究的历史发展进行了回顾。然后简短地介绍了理想玻色-爱因斯坦凝聚和相互作用玻色-爱因斯坦凝聚的基本理论。最后介绍了两体散射理论,探讨了散射长度的物理意义,并介绍了常用的调控散射长度的方法 Feshbach共振。在第二章中,首先介绍了具有相互作用的旋量BEC的二次量子化理论,分别计算了自旋1、自旋2和自旋3时的旋量BEC的哈密顿量。然后运用平均场理论,得到了自旋1和自旋2旋量BEC满足的Gross-Pitaevskii方程,探讨了自旋1和自旋2的一致性系统各种可能的基态,并给出了在某些特定参数下的相图。第三章首先利用群论和微分流形的知识引入了BEC的序参量流形的概念,然后介绍了利用对称性寻找基态的方法,并利用该方法分别对自旋1和自旋2系统可能的基态进行分类。最后简单介绍了拓扑分类的同伦论,利用同伦论分析了各种旋量序参量流形中可能存在的拓扑激发类型,并特别讨论了涡旋和Skyrmion两类拓扑激发。第四章首先探讨了两分量旋转BEC中自旋轨道耦合对体系的影响,发现自旋轨道耦合会诱发双曲型Skyrmion的产生,在相互作用的不同区域,自旋轨道耦合对Skyrmion的影响各不相同。然后讨论了自旋1的三分量旋转BEC,发现自旋轨道耦合会诱发半skyrmion与三涡旋结构。最后讨论了面内四极磁场的旋转BEC,发现面内四极磁场和旋转双重作用可导致中央Mermin-Ho涡旋的产生,并在自旋结构中出现双曲型meron和半skyrmion两种拓扑结构。
[Abstract]:The realization of Bose-Einstein condensate (BEC) has rapidly promoted the rapid development of ultra-cold atoms and cold molecular physics. Bec has unique macroscopic quantum coherence properties and artificial controllability. It not only makes it a basic experimental platform for testing quantum multi-body physics, but also provides a universal simulation platform for condensed matter calculation and nonlinear science. In recent years, with the application of new techniques and methods in experiments, the exploration of novel and topological quantum states in BEC has become a hot topic in international research. In this paper, we will mainly discuss the topological excitation in spinor Bose-Einstein condensates, including the mean field theory of spinor BEC, the symmetry classification of spinor order parametric manifolds. The basic theory of topological excitation and numerical study of topological excitation in spinor BEC. The first chapter mainly elaborates the related theory foundation of BEC. Firstly, the history of Bose-Einstein condensation is reviewed. Then the basic theories of ideal Bose-Einstein condensate and interacting Bose-Einstein condensate are briefly introduced. Finally, the theory of two-body scattering is introduced, the physical meaning of scattering length is discussed, and the common method of controlling scattering length is introduced, which is called Feshbach resonance. In chapter 2, the second quantization theory of spinor BEC with interaction is introduced, and the Hamiltonian of spinor BEC with spin 1, spin 2 and spin 3 is calculated, respectively. Then, by using the mean field theory, the Gross-Pitaevskii equations of spin 1 and spin 2 spinor BEC are obtained. The possible ground states of the consistent system of spin 1 and spin 2 are discussed, and the phase diagrams under certain parameters are given. In chapter 3, the concept of BEC's ordered parametric manifold is introduced by using the knowledge of group theory and differential manifold, and then the method of finding ground state by symmetry is introduced, and the possible ground states of spin 1 and spin 2 systems are classified by this method, respectively. Finally, the homotopy theory of topological classification is briefly introduced. By using the homotopy theory, the possible types of topological excitations in various spinor ordered parametric manifolds are analyzed, and two kinds of topological excitations, vortex and Skyrmion, are discussed in particular. In chapter 4, the effects of spin-orbit coupling on the system in two-component rotating BEC are discussed. It is found that spin-orbit coupling can induce hyperbolic Skyrmion. In different regions of interaction, the influence of spin-orbit coupling on Skyrmion is different. Then the three-component rotational BEC, of spin 1 is discussed and it is found that the spin-orbit coupling induces semi-skyrmion and three-vortex structures. Finally, it is discussed that the rotating BEC, of in-plane quadrupole magnetic field can lead to the generation of central Mermin-Ho vortex by the interaction of in-plane quadrupole magnetic field and rotation, and there are two topologies of hyperbolic meron and semi-skyrmion in the spin structure.
【学位授予单位】：中国科学院大学(中国科学院物理研究所)
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O469

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