Many-Body Physics of Fermions in One Dimension

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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.