Theoretical Studies of Rotating Trapped Atomic Gases

这一提议描述了对超冷原子云的旋转特性的理论研究。在他以前的工作的基础上，研究者将探索几个主题，有以下四个目标。他将计算在磁场存在下自旋为1的玻色子的快速旋转气体中形成的拓扑结构。他将确定在光学晶格节点上旋转小簇原子的动力学。他将提出一个实用的方案，以创造与中性原子相耦合的场，就像电磁场与带电粒子相耦合一样。(4)他将研究旋转云之间的干涉，并证明干涉实验可以区分凝聚和强相关的旋转状态。这些项目的动机是对这些酶的基本物理性质的兴趣[主题(1),(2)和(4)]，以及希望产生实验协议来创建和测量物质的奇异状态[主题(2),(3)和(4)]。主题(1)讨论旋转原子云的基本基态性质。主题(2)允许研究孤立系统中能量和熵转移的基本问题，同时可能提供产生量子霍尔效应类似物的实验途径。主题(3)旨在为探索涡旋物理、量子霍尔效应、涡旋晶格的钉住以及晶格与量子霍尔效应之间的相互作用提供一个有价值的工具。课题(4)研究了凝聚态和相关态的基本相干特性，并提供了区分凝聚态和相关态的实验策略。研究者将使用一系列与之前项目相关的分析和计算技术。这些包括最低朗道水平微积分，场论，变分方法，数值精确对角化和数值蒙特卡罗。

This proposal describes a theoretical study of the rotational properties of clouds of ultracold atoms.Building on his previous work, the investigator will explore several topical subjects, with the fol-lowing four objectives. (1) He will calculate the topological structures which will form in a rapidlyrotating gases of spin-1 bosons in the presence of magnetic fields. (2) He will determine the kinet-ics of spinning up small clusters of atoms at the nodes of an optical lattice. (3) He will producea practical scheme for creating fields which couple to neutral atoms in the same way that theelectromagnetic fields couple to charged particle. (4) He will study interference between rotatingclouds and demonstrate that an interference experiment can distinguishing condensed and stronglycorrelated rotating states.These projects are motivated by both interest in fundamental physical properties of these coldgases [topics (1), (2), and (4)] and by a desire to produce experimental protocols to create andmeasure exotic states of matter [topics (2), (3), and (4)]. Topic (1) addresses the basic groundstate properties of clouds of rotating atoms. Topic (2) allows the study of fundamental questions ofenergy and entropy transfer in isolated systems, while possibly providing an experimental pathwayto producing analogs of quantum Hall effects. Topic (3) is aimed at producing a valuable tool forexploring vortex physics, quantum Hall effects, the pinning of vortex lattices, and the interplaybetween lattices and quantum Hall effects. Topic (4) studies the basic coherence properties of bothcondensed and correlated states, and provides an experimental strategy for distinguishing thesestates.The investigator will use an array of analytic and computational techniques, related to thoseused in previous projects. These include lowest-Landau-level calculus, field theory, variationalmethods, numerical exact diagonalization, and numerical Monte-Carlo.