一维周期性光学晶格中的带隙孤子

发布时间：2018-02-12 14:29

本文关键词： 超冷原子边界态非线性作用带隙孤子　出处：《燕山大学》2016年硕士论文　论文类型：学位论文

【摘要】：超冷原子(ultracold atoms)作为物理学中的热点内容已取得了很大进展。由于冷原子系统具有纯净而且可调性高的优点,冷原子系统为研究新领域提供了较为理想的平台。捕获和冷却技术的发展使得在光晶格中实现超冷原子的实验,而且用冷原子填充光学晶格已经成为一个替代性的途径去构建拓扑绝缘体。一维系统因为没有附加的对称性,通常被认为缺乏非平庸的拓扑相。但是在《一维超晶格中的边界态和拓扑相》中研究了一维准周期的光学晶格中捕获费米子的性质,并且这些系统显示非平庸的拓扑性质,这个重要的拓扑性质和周期性晶格中二维量子霍尔效应有相同的物理起源。那么,在一维玻色系统当中的性质又会是怎样的呢?是否存在边界态?论文研究工作如下:首先,介绍了冷原子的发展历程以及相关技术的研究现状和孤子的发现过程以及分类,并给出了本课题的研究内容。其次,介绍了一维费米系统的在周期性边界条件和开放性边界条件下系统的能谱,而且该系统在开放性边界条件下存在边界态。通过对比发现,一维费米系统可以映射到二维量子霍尔效应中。最后,研究一维玻色系统,在忽略粒子间相互作用情况下的边界态、带内态和系统的能带;接下来考虑粒子间相互作用,由于系统的非线性产生带隙孤子。我们研究了不同参数下孤子的类型、化学势和波函数。
[Abstract]:As a hot topic in physics, ultracold atoms has made great progress. Cold atomic system provides an ideal platform for the study of new fields. With the development of capture and cooling technology, the experiments of ultra-cold atoms are realized in optical lattice. And filling optical lattices with cold atoms has become an alternative way to build topological insulators. It is generally considered that there is a lack of non-mediocre topological phases. However, the properties of fermion trapping in one-dimensional quasi-periodic optical lattices are studied in boundary states and topological phases in one-dimensional superlattices, and these systems show non-mediocre topological properties. This important topological property has the same physical origin as the two-dimensional quantum Hall effect in periodic lattices. Is there a boundary state? The research work of this paper is as follows: firstly, the development of cold atoms, the research status of related technologies, the discovery process and classification of soliton are introduced, and the research contents of this topic are given. The energy spectra of one dimensional Fermi system under periodic boundary condition and open boundary condition are introduced. Moreover, the system has boundary state under open boundary condition. The one-dimensional Fermi system can be mapped to the two-dimensional quantum Hall effect. Finally, the boundary states, the in-band states and the energy bands of the system are studied in the one-dimensional boson system, and the interaction between the particles is considered. Due to the nonlinearity of the system, we study the types, chemical potential and wave functions of solitons with different parameters.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O734;O437

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