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arXiv:1503.07195 · Physical Review A

Dynamics of Hubbard-band quasiparticles in disordered optical lattices

V. W. Scarola, Brian DeMarco

Published Nov 30, 2015• 7 citations
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Abstract

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.

DOI
10.1103/physreva.92.053628

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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.
Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass 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 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 non-zero temperature. In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system. The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution.
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.
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.
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 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.