Many-Body Physics of Fermions in One Dimension

我们日常使用的电子设备主要是由电子--携带电流的负电荷粒子--在材料中独立运动的材料组成的，就像其他电子不存在一样。然而，在某些材料中，电子的行为是集体的，而不是单独的，这种集体行为通常会产生奇异的和技术上有用的电或磁性能(例如，超导--没有电阻的电流流动)。为了促进新型电子设备的发展，人们对发展对外来材料中可能出现的集体现象的基本理解非常感兴趣。特别令人感兴趣的是一维(1D)系统，其中电子只允许沿一个空间维度运动。在一维中，集体行为是规则，而不是例外--电子之间任意弱的相互作用总是应该引起集体现象。与高维系统中的典型行为形成鲜明对比的是，在高维系统中，每个独立的电子都携带一个电荷和一个被称为自旋的固有角动量，而一维系统中的自旋和电荷的传输是解耦的。值得注意的是，自旋和电荷是通过以不同速度传播的波在一维中传输的。在碳纳米管和量子线等系统中已经观察到了这方面的间接证据。这个实验研究项目的目标是直接观察一维超冷原子气体中的自旋电荷分离和相关现象。通过激光形成的波导，原子被限制在一维空间中，如果原子的质量密度被理解为扮演电子电荷密度的角色，那么原子就可以精确地模拟电子的行为。研究原子而不是电子系统的优势在于，密度、温度和相互作用强度等参数是广泛可调的。此外，该原子系统允许实时直观地显示自旋密度波和质量密度波的传播。因此，原子系统可以进行系统的研究，旨在阐明有限的温度、有限的系统大小和强相互作用在一维电子系统中所起的作用。这些研究将有助于基于碳纳米管和量子线的“自旋电子器件”的发展。限制在二维光学晶格中的超冷费米子原子将被用来系统地探索一维相互作用费米系统的奇异性质，验证对其行为的长期预测，并测试自旋电荷分离在高温和强相互作用下持续的程度。在真实空间中直接观测自旋-电荷分离将通过两种方法完成。首先，将激发系统的低阶简正模，包括自旋-偶极模、密度-偶极模和密度-四极模，并测量它们的振荡频率作为相互作用强度的函数。自旋-电荷分离将表现为密度-偶极和密度-四极模频率对相互作用强度的相对不敏感性，而自旋-偶极模的频率随着相互作用的增加而显着降低。或者，可以通过局部地将少量原子从自旋态之一射出，从而向系统中注入空穴来观察真实空间中的自旋-电荷分离。注入的空穴随后将分解为自旋和电荷激发，它们的传播速度取决于相互作用的强度。相互作用的一维费米系统的第二个显著特征--它们的关联函数呈现非普遍的幂定律衰减--也将通过沿一维管膨胀后云的动量分布中的量子噪声关联来观察到。

The electronic devices we use on a daily basis are primarily constructed from materials in which electrons - the negatively charged particles which carry electric current - move around independently inside the material as though the other electrons are not present. However, certain materials exist in which the electrons behave collectively rather than individually and this collective behavior typically gives rise to exotic and technologically useful electrical or magnetic properties (e.g. superconductivity - the flow of electric current without resistance). To foster the development of new types of electronic devices, there is significant interest in developing a fundamental understanding of the collective phenomena that can emerge in exotic materials. Of particular interest are one-dimensional (1D) systems where the motion of electrons is only allowed along one spatial dimension. In 1D, collective behavior is the rule rather than the exception - arbitrarily weak interactions between the electrons should always give rise to collective phenomena. In stark contrast to the typical behavior seen in higher-dimensional systems where independent electrons each carry an electric charge together with an intrinsic angular momentum known as spin, the transport of spin and charge in 1D is decoupled. Remarkably, spin and charge are transported in 1D by waves which propagate at different speeds. Indirect evidence for this has been observed in systems such as carbon nano-tubes and quantum wires. The goal of this experimental research project is to directly observe spin charge separation and related phenomena in a 1D gas of ultracold atoms. The atoms are confined to 1D by a waveguide formed from laser light and precisely imitate the behavior of electrons if the mass density of atoms is understood to play the role of the charge density of electrons. The advantage of studying the atomic rather than electronic system is that parameters such as the density, temperature, and interaction strengths are widely tunable. Furthermore, the atomic system allows for a direct visualization of the propagation of spin- and mass-density waves in real time. Thus, atomic systems are amenable to systematic studies which aim to elucidate the role that finite temperature, finite system size, and strong interactions play in 1D electronic systems. Such studies will aid the development of "spintronic" devices based on carbon nanotubes and quantum wires.Ultracold fermionic atoms confined in a two-dimensional optical lattice will be used to systematically explore the exotic properties of 1D interacting Fermi systems, verify longstanding predictions for their behavior, and test the extent to which spin-charge separation persists at high temperature and with strong interactions. The direct observation of spin-charge separation in real space will be accomplished by two methods. First, low-lying normal modes of the system including spin-dipole, density-dipole and density-quadrupole modes will be excited and their oscillation frequencies measured as a function of interaction strength. Spin-charge separation will manifest itself as a relative insensitivity of the density-dipole and density-quadrupole mode frequencies on interaction strength in contrast to a significant reduction in frequency of the spin-dipole mode with increasing interactions. Alternatively, spin-charge separation in real space can be observed by locally ejecting a small number of atoms from one of the spin states and thereby injecting holes into the system. The injected holes will subsequently break into spin and charge excitations which propagate at different velocities depending on the interaction strength. A second hallmark feature of interacting 1D Fermi systems - that their correlation functions exhibit non-universal power law decay - will also be observed through quantum noise correlations in the momentum distribution of clouds following expansion along the 1D tubes.