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（携带电流的带负电荷的粒子）在材料内部独立运动的材料构成的，就好像其他电子不存在一样。然而，某些材料中存在电子的集体行为而不是单独行为，这种集体行为通常会产生奇异的和技术上有用的电或磁特性（例如超导性-无电阻电流的流动）。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。特别感兴趣的是一维（1D）系统，其中电子只允许沿着一个空间维度运动。在一维中，集体行为是规律而不是例外——电子之间的任意弱相互作用总是会引起集体现象。与在高维系统中看到的典型行为形成鲜明对比的是，在高维系统中，独立的电子每个都携带一个电荷和一个被称为自旋的固有角动量，在一维中，自旋和电荷的输运是去耦的。值得注意的是，自旋和电荷是通过以不同速度传播的波以一维方式传输的。这方面的间接证据已经在碳纳米管和量子线等系统中观察到。本实验研究项目的目的是直接观察一维超冷原子气体中的自旋电荷分离及相关现象。如果原子的质量密度被理解为扮演电子电荷密度的角色，那么由激光形成的波导将原子限制在一维范围内，并精确地模仿电子的行为。研究原子系统而不是电子系统的优点是，密度、温度和相互作用强度等参数是可广泛调节的。此外，原子系统允许对自旋波和质量密度波的实时传播进行直接可视化。因此，原子系统适合于旨在阐明有限温度、有限系统尺寸和强相互作用在一维电子系统中所起作用的系统研究。这样的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原子将用于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的持续程度。实际空间中自旋-电荷分离的直接观测将通过两种方法实现。首先，激发系统的低洼正态模式，包括自旋偶极子、密度偶极子和密度四极子模式，并测量其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-偶极子和密度-四极子模式频率对相互作用强度的相对不敏感，相反，自旋-偶极子模式的频率随着相互作用的增加而显著降低。另一种方法是，在实际空间中，通过局部地从其中一种自旋状态中喷出少量原子，从而向系统中注入空穴，可以观察到自旋-电荷分离。注入的空穴随后将分裂成自旋和电荷激发，它们以不同的速度传播，这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标志特征——它们的相关函数表现出非普遍的幂律衰减——也将通过云的动量分布中的量子噪声相关性观察到，这些动量分布是沿着一维管膨胀的。

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.