RUI: Topology, Gauge Fields and Phase Coherence in the Transport Dynamics of Ultracold Atoms

受限的超冷原子提供了独特的能力，可以创建设计师系统，可以定制以提供直接访问量子力学特性，否则可能会被掩盖。 一类重要的性质是拓扑性质，因为它们主要由定义参数的抽象空间的结构来定义。 由于拓扑学是对任何结构（无论是真实的还是抽象的）的最一般性描述，因此这些特征可以用来发现看似无关的现象之间的联系，从而为所有这些现象提供强有力的见解。本研究的目的是分析几个这样的现象，一些新提出的，一些众所周知的，但不太了解，比较从拓扑的角度来看。该方法将把它们转换为广义输运问题，跟踪系统及其参数如何随时间演变，然后将其与冷原子的动力学实验联系起来。 这项研究将涉及在创造与变化的局部相位相关的规范场的背景下，相位的内在量子特性，以及与量子系统相关的相干效应。 无论是在非线性或经典物理极限的存在下，拓扑性质的生存是一个必不可少的基本物理问题，将被检查的所有机制研究。这项研究的结果有可能在创造新的材料和设备，利用新的可用的拓扑和相位特性，以及，因为这些问题中的许多都与物理学的所有领域相关。 研究的某些方面具有改进传感器和陀螺仪的技术应用潜力，并且在新兴的原子电子学领域，电子学的原子模拟。这项研究的一个高度优先事项是让公立大学的多名本科生参与，这些大学有许多第一代和有风险的学生，他们往往没有机会参加科学研究。 目标是继续并扩大先前赠款的成功，以吸引和引导这些国内学生进入科学和技术职业。

Confined ultracold atoms provide the unique capability to create designer systems that can be tailored to provide direct access to quantum mechanical properties that may be otherwise obscured. An important class of such properties is topological in nature in the sense that they are primarily defined by the structure of the abstract space of their defining parameters. Since topology is the most general description of any structure, real or abstract, such features can be used to find connections among phenomena that may seem unrelated, and thereby provide powerful insights into them all. The goal of this research is to analyze several such phenomena, some newly proposed here and some well-known but not well-understood, comparatively from a topological perspective. The method will be to recast them as generalized transport problems, tracking how the system and its parameters evolve in time, which will then be related to dynamical experiments with cold atoms. The study will involve the intrinsic quantum characteristic of phase in the context of creating gauge fields associated with varying local phase, and coherence effects associated with quantum systems. Whether the topological properties survive the loss of phase coherence in the presence of nonlinearity or in taking the classical physics limit is an essential fundamental physics question that will be examined for all mechanisms studied.The outcome of this study has potential for applications in creating novel materials and devices that take advantage of the newly available topological and phase properties, as well as, for significantly broadening our understanding of fundamental physics, since many of these issues have relevance across all areas of physics. Some aspects of the research have technological applications potential for improved sensors and gyroscopes, and in the emerging field of atomtronics, the atomic analog of electronics. A high priority of the research will be to engage multiple undergraduate students at a public university attended by many first generation and at-risk students who often do not get the opportunity to participate in scientific research. The goal is to continue and expand on the success of a prior grant to attract and channel such domestic students into careers in science and technology.