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arXiv 1312.7486cond-mat.quant-gas
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冷原子系统中的人工规范场与自旋轨道耦合

Artificial Gauge Fields and Spin-Orbit Couplings in Cold Atom Systems

Junyi Zhang

摘要:

本文是法国高等师范学校M1学科书目研究项目的报告。本文回顾了冷原子系统中人工规范场和自旋轨道耦合的历史发展。我们从文学的源头来追溯这一思想发展的轨迹。为了教学的目的,我们试图仔细而清晰地给出例子,详细地验证各种近似和论点的有效性,并给出我们讨论的问题的清晰的物理和数学图像。本文第一部分介绍了Berry相位和Jaynes-Cummings模型的基本概念。第二部分综述了在冷原子系统中利用N-pod方案产生人工规范场的两种方案。第一种是基于缀饰原子图,提供了一种产生具有暗态的非阿贝尔规范场的方法。第二种是历史上较早实现的轮换制。非阿贝尔规范场必然导致自旋轨道耦合。本文综述了自旋轨道耦合的理论和实验研究进展。第四部分介绍了最近发展起来的光通量格的概念,它为冷原子系统中的强关联机制提供了可能。我们根据库珀的理论发展了一种几何解释。在附录中列出了一些有用的公式及其证明。

英文摘要:

This article is a report of Projet bibliographique of M1 at École Normale Supérieure. In this article we reviewed the historical developments in artificial gauge fields and spin-orbit couplings in cold atom systems. We resorted to origins of literatures to trace the ideas of the developments. For pedagogical purposes, we tried to work out examples carefully and clearly, to verified the validity of various approximations and arguments in detail, and to give clear physical and mathematical pictures of the problems that we discussed. The first part of this article introduced the fundamental concepts of Berry phase and Jaynes-Cummings model. The second part reviewed two schemes to generate artificial gauge fields with N-pod scheme in cold atom systems. The first one is based on dressed-atom picture which provide a method to generate non-Abelian gauge fields with dark states. The second one is about rotating scheme which is achieved earlier historically. Non-Abelian gauge field inevitably leads to spin-orbit coupling. We reviewed some developments in achieve spin-orbital coupling theoretically and experimentally. The fourth part was devoted to recently developed idea of optical flux lattice that provides a possibility to reach the strongly correlated regime in cold atom systems. We developed a geometrical interpretation based on Cooper's theory. Some useful formulae and their proofs were listed in the Appendix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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