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arXiv:1305.6072 · Physical Review Letters

Disorder-Induced Localization in a Strongly Correlated Atomic Hubbard Gas

Stanimir Kondov, William McGehee, Wenchao Xu, Brian DeMarco

Published Feb 26, 2015• 277 citations
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Abstract

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.

DOI
10.1103/physrevlett.114.083002

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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.
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 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.
Quantum degenerate gases trapped in optical lattices are ideal test beds for fundamental physics because these systems are tunable, well characterized, and isolated from the environment. Controlled disorder can be introduced to explore suppression of quantum diffusion in the absence of conventional dephasing mechanisms such as phonons, which are unavoidable in experiments on electronic solids. Recent experiments use transport of degenerate Fermi gases in optical lattices [S. S. Kondov et al., Phys. Rev. Lett. 114, 083002 (2015)] to probe extreme regimes. These experiments find evidence for an intriguing insulating phase where quantum diffusion is completely suppressed by strong disorder. Quantitative interpretation of these experiments remains an open problem that requires inclusion of nonzero entropy, strong interaction, and trapping in an Anderson-Hubbard model. We argue that the suppression of transport can be thought of as localization of Hubbard-band quasiparticles. We construct a theory of dynamics of Hubbard-band quasiparticles tailored to trapped optical lattice experiments. We compare the theory directly with center-of-mass transport experiments of Kondov et al. with no fitting parameters. The close agreement between theory and experiments shows that the suppression of transport is only partly due to finite-entropy effects. We argue that the complete suppression of transport is consistent with short-time, finite-size precursors of Anderson localization of Hubbard-band quasiparticles. The combination of our theoretical framework and optical lattice experiments offers an important platform for studying localization in isolated many-body quantum systems.
Quantum degenerate gases trapped in optical lattices are ideal test beds for fundamental physics because these systems are tunable, well characterized, and isolated from the environment. Controlled disorder can be introduced to explore suppression of quantum diffusion in the absence of conventional dephasing mechanisms such as phonons, which are unavoidable in experiments on electronic solids. Recent experiments use transport of degenerate Fermi gases in optical lattices [S. S. Kondov et al., Phys. Rev. Lett. 114, 083002 (2015)] to probe extreme regimes. These experiments find evidence for an intriguing insulating phase where quantum diffusion is completely suppressed by strong disorder. Quantitative interpretation of these experiments remains an open problem that requires inclusion of nonzero entropy, strong interaction, and trapping in an Anderson-Hubbard model. We argue that the suppression of transport can be thought of as localization of Hubbard-band quasiparticles. We construct a theory of dynamics of Hubbard-band quasiparticles tailored to trapped optical lattice experiments. We compare the theory directly with center-of-mass transport experiments of Kondov et al. with no fitting parameters. The close agreement between theory and experiments shows that the suppression of transport is only partly due to finite-entropy effects. We argue that the complete suppression of transport is consistent with short-time, finite-size precursors of Anderson localization of Hubbard-band quasiparticles. The combination of our theoretical framework and optical lattice experiments offers an important platform for studying localization in isolated many-body quantum systems.
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.
Observations of center-of-mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center-of-mass motion even with insulating states in the center. We identify short- and long-time-scale mechanisms for edge-state transport in insulating phases. We also argue that the center-of-mass velocity can aid in identifying a Bose-glass phase. Our zero-temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center-of-mass dynamics expected at nonzero temperature.