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Transport and disorder-induced localization of ultracold Fermi gases

William McGehee

Published Jul 14, 2015• 0 citations
OpenAlex

Abstract

We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.

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We experimentally study localization and dynamics of ultracold fermions in speckle and optical lattice potentials to explore Anderson localization, many-body localization, and relaxation dynamics in strongly correlated systems. Anderson localization is probed by releasing non-interacting, spin-polarized gases into three dimensional, anisotropic disordered potentials produced from optical speckle. A fraction of the atoms are localized by the disorder, and a mobility edge is found separating localized from extended states. The length scale of the speckle is varied, and the localized state is found to scale linearly with the geometric mean of the speckle autocorrelation length. We realize the Fermi Hubbard model by loading atoms in a cubic optical lattice. Non-equilibrium momentum distributions are created via Raman transitions, and the excitation relaxation rate is measured in the lattice. Transport experiments were performed in a disordered optical lattice to explore the disordered Hubbard model. These experiments reveal localization in the presence of strong interactions and an interaction driven metal-to-insulator transition. The localized state is found to be insensitive to a doubling in the temperature of the gas and is consistent with predictions of many-body localization.
We observe the emergence of a disorder-induced insulating state in a strongly interacting atomic Fermi gas trapped in an optical lattice. This closed quantum system, free of a thermal reservoir, realizes the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. We observe disorder-induced localization of a metallic state through measurements of mass transport. By varying the lattice potential depth, we detect interaction-driven delocalization of the disordered insulating state. We also measure localization that persists as the temperature of the gas is raised. These behaviors are consistent with many-body localization, which is a novel paradigm for understanding localization in interacting quantum systems at nonzero temperature.
Ultracold fermionic atoms in a disordered optical lattice can realize the disordered Fermi-Hubbard model, allowing investigations of the nature of strongly-correlated fermions in a minimal setting. This thesis describes two such studies. In the first, we observe the momentum relaxation of strongly-correlated fermions in the absence of disorder. We find a violation of the weak-scattering prediction for the scaling with temperature, which is analogous to the linear-in-temperature scaling of resistivity in substances called ``bad metals.'' In the second, we probe a disordered and strongly-correlated system using quenches of the interaction strength that take it far from equilibrium. We find that the relaxation of double occupancies following the quenches has distinct dynamical regimes controlled by the interplay of interactions and disorder. We present a minimal picture of the relaxation process that illustrates the origin of these regimes, which are related to the Mott--metal--Anderson transitions of the ground state at half-filling.
We observe the emergence of a disorder-induced insulating state in a strongly interacting atomic Fermi gas trapped in an optical lattice. This closed quantum system free of a thermal reservoir realizes the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. In measurements of disorder-induced localization obtained via mass transport, we detect interaction-driven delocalization and localization that persists as the temperature of the gas is raised. These behaviors are consistent with many-body localization, which is a novel paradigm for understanding localization in interacting quantum systems at non-zero temperature.
We report on the impact of variable-scale disorder on 3D Anderson localization of a noninteracting ultracold atomic gas. A spin-polarized gas of fermionic atoms is localized by allowing it to expand in an optical speckle potential. Using a sudden quench of the localized density distribution, we verify that the density profile is representative of the underlying single-particle localized states. The geometric mean of the disordering potential correlation lengths is varied by a factor of 4 via adjusting the aperture of the speckle focusing lens. We observe that the root-mean-square size of the localized gas increases approximately linearly with the speckle correlation length, in qualitative agreement with the scaling predicted by weak scattering theory.
This thesis describes the construction of an experimental apparatus to study disorder physics using ultracold fermionic atomic gases. We use this apparatus to realize 3D Ander-son localization for the first time for quantum matter waves. We provide the first measure-ment of how the mobility edge—a hallmark of 3-dimensionality—and of localization lengths depend on the disorder strength. In a second experimental study, we add an optical lattice to the disorder potential to realize the disordered Fermi-Hubbard model, which is a minimal model for strongly correlated electronic solids. The interplay of interactions and disorder is investigated. We find an Anderson-like disorder-driven metal-to-insulator transition as well as disorder-induced breaking of the Mott gap in the strongly interacting regime. ii To my Parents and to Sveta iii Acknowledgements I first want to thank Brian, who taught me the important notion that experimental physics lives in the intersection space between equations and reality, and that both will gladly turn around and bite off your finger if you are not careful. In this dangerous situation, it is the necessity that one becomes a better scientist, and it is also the hope that one becomes a better human being. I would like to thank my family and friends, and I would like to point out that, for many of us, graduate school is a rather self-centered experience in which we are only left to worry about ourselves while we do what we love among people whom we appreciate. Yet those who inspire and sustain us are left out of the author lists and honorable mentions. In summary, graduate school is a wonderful place and a privilege, and I am grateful that the fundamental laws of the universe have so conspired that I’ve had the chance to be here.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.