Realizing Exotic Quantum States with Cold Atoms

简单的规则可能导致复杂的行为。 这条格言在量子力学中尤其正确，量子力学是描述原子等微观物体的理论。 理论物理学的工具将被用来确定这种奇异的行为如何出现在超冷原子气体中。 虽然这些研究可能会在量子计算、计量学或材料科学等领域产生新的应用，但这一系列项目的直接目标是测试量子系统中涌现物理学的基本概念。有三条相互脱节的研究路线。首先，当原子被限制在紧密的管道中时，它们的行为与在三维空间中自由运动的原子不同。我们将研究这种奇异的一维状态和更传统的三维物理之间的交叉。其次，最近在电子系统中发现了一种奇异状态。 这些材料被称为“拓扑绝缘体”，具有绝缘体，但具有导电表面模式。 此外，表面模式以非常规的方式表现。 这些系统的冷原子类似物将被研究。最后，我们将研究含磁性杂质电子系统的冷原子类似物。 含有磁性杂质的金属显示出许多重要的现象，其中一些尚未完全理解。 该项目的目标是建立一个用于测试各种理论想法的受控系统。该项目有三个研究方向，将促进对冷原子和多体物理的理解。 这些选择与最近的实验和理论发展相吻合。 第一个研究方向将涉及超流部分极化费米气体中一维和三维之间的维度交叉。 1D系统显示FFLO状态的波动版本。 有希望的是，真正的远程FFLO秩序可以稳定的中间约束。 PI将使用非齐次Bogoliubov-de-Gennes方程研究该交叉。 第二个研究方向将涉及人工原子Chern绝缘体中的晶格缺陷。 有一个潜在的transformitive猜想，这种缺陷有关的分数量子霍尔效应。 这些物理现象的大部分可以通过单粒子薛定谔方程的数值研究来揭示。 即使这个猜想是不正确的，这项研究也会告诉我们这些缺陷，这些缺陷在固态系统中很重要。 第三个研究项目将涉及在冷原子中观察近藤物理的尝试。通过在冷原子中研究这个问题，我们的目标是更直接地了解这种奇异的物理学。 绿色功能技术将用于后一个项目。

Simple rules can lead to complicated behavior. This maxim is particularly true in quantum mechanics, the theory describing microscopic objects such as atoms. Tools of theoretical physics will be used to determine how such exotic behavior emerges in ultracold atomic gases. While these studies may potentially lead to novel applications in areas such as quantum computing, metrology, or materials science, the direct goal of this set of projects is to test fundamental concepts about emergent physics in quantum systems. There are three disconnected lines of research. First, when atoms are confined to tight tubes they behave differently than atoms which are free to move in three dimensions. The cross-over between this exotic one-dimensional state and more conventional three-dimensional physics will be studied. Second, an exotic state was recently discovered in electronic systems. Dubbed "topological insulators," these materials have insulating bulks, but conducting surface modes. Moreover the surface modes behave in unconventional ways. The cold atom analogs of these systems will be studied. Finally, the cold atom analogs of electron systems with magnetic impurities will be studied. Metals with magnetic impurities display a number of important phenomena, some of which are not completely understood. The goal is to produce a controlled system for testing various theoretical ideas.This project has three research directions which will advance understanding of cold atoms, and many-body physics. These are chosen to dovetail with recent experimental and theoretical development. The first research direction will involve the dimensional crossover between 1D and 3D in a superfluid partially polarized Fermi gas. The 1D system displays a fluctuating version of the FFLO state. There is hope that true long-range FFLO order can be stabilized for intermediate confinement. The PI will use the inhomogeneous Bogoliubov-de-Gennes equations to study this crossover. The second research direction will involve lattice defects in an artificial atomic Chern insulator. There is a potentially transformitive conjecture that such defects are related to the fractional quantum Hall effect. Much of this physics can be revealed by numerical studies of the single-particle Schrodinger equation. Even if the conjecture is incorrect, the study will teach us about these defects, which are important in solid state systems. The third research project will involve attempts to see Kondo physics in cold atoms. By studying this problem in cold atoms, the goal is to obtain a more direct insight into this exotic physics. Greens function techniques will be used for this latter project.