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arXiv:2311.07505 · Physical Review Research

Characterizing localization effects in an ultracold disordered Fermi gas by diffusion analysis

Sian Barbosa, Maximilian Kiefer-Emmanouilidis, Felix Lang, Jennifer Koch, Artur Widera

Published Jul 8, 2024• 7 citations
arXivHTMLPDF

Abstract

Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all particles are localized for finite-strength disorder, and the system can become partially diffusive. Unraveling the intricate signatures of localization from such observed diffusion is a longstanding problem. Here, we experimentally study a degenerate, spin-polarized Fermi gas in a disorder potential formed by an optical speckle pattern. We record the diffusion through the disordered potential upon release from an external confining potential. We compare different methods to analyze the resulting density distributions, including a new approach to capture particle dynamics by evaluating absorption-image statistics. Using standard observables, such as diffusion exponent and coefficient, localized fraction, or localization length, we find that some show signatures for a transition to localization above a critical disorder strength, while others show a smooth crossover to a modified diffusion regime. In laterally displaced disorder, we spatially resolve different transport regimes simultaneously, which allows us to extract the subdiffusion exponent expected for weak localization. Our work emphasizes that the transition toward localization can be investigated by closely analyzing the system's diffusion, offering ways of revealing localization effects beyond the signature of exponentially decaying density distribution. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033039

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Disorder can fundamentally modify the transport properties of a system. A striking example is Anderson localization, suppressing transport due to destructive interference of propagation paths. In inhomogeneous many-body systems, not all particles are localized for finite-strength disorder, and the system can become partially diffusive. Unraveling the intricate signatures of localization from such observed diffusion is a longstanding problem. Here, we experimentally study a degenerate, spin-polarized Fermi gas in a disorder potential formed by an optical speckle pattern. We record the diffusion through the disordered potential upon release from an external confining potential. We compare different methods to analyze the resulting density distributions, including a new approach to capture particle dynamics by evaluating absorption-image statistics. Using standard observables, such as diffusion exponent and coefficient, localized fraction, or localization length, we find that some show signatures for a transition to localization above a critical disorder strength, while others show a smooth crossover to a modified diffusion regime. In laterally displaced disorder, we spatially resolve different transport regimes simultaneously, which allows us to extract the subdiffusion exponent expected for weak localization. Our work emphasizes that the transition toward localization can be investigated by closely analyzing the system's diffusion, offering ways of revealing localization effects beyond the signature of exponentially decaying density distribution. Published by the American Physical Society 2024
We study Anderson localization in two-dimensional, disordered, spin-orbit systems belonging to the symplectic symmetry class using momentum-space signatures such as the coherent backscattering antipeak and the coherent forward-scattering peak. Significantly, these momentum-space features are readily accessible in ultracold atom experiments through absorption imaging after time-of-flight expansion. Here, the critical exponent and mobility edge of the metal-insulator transition are successfully obtained through a finite-time analysis of the coherent backscattering width. An anomalous residual diffusion, unique to two dimensions, is identified at the transition point where the system changes from a metal to an insulator. A spin localization phenomenon is also observed in the deep localized regime. Published by the American Physical Society 2024
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.
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential. A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component. We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy. These measurements provide a benchmark for more sophisticated theories of AL.
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this paradigm may break down in complex systems, where quantum interference and memory effects render the particle propagation anomalous, often fostering localization. Here we report on the observation of such anomalous dynamics in a minimal setting: an ultracold mass-imbalanced mixture of two fermionic gases in three dimensions. We release light impurities into a gas of heavier atoms and follow their evolution across different collisional regimes. Under strong interspecies interactions, by lowering the temperature we unveil a crossover from normal diffusion to subdiffusion. Simultaneously, a localized fraction of the light gas emerges, displaying no discernible dynamics over hundreds of collisions. Our findings, incompatible with the conventional Fermi-liquid picture, are instead captured by a model of an atom propagating through a (quasi-)static disordered landscape of point-like scatterers. These results highlight the key role of quantum interference in our mixture, which emerges as a versatile platform for exploring disorder-free localization phenomena.
Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles to travel between source and drain reservoirs. This channel can be populated with columnar (repulsive) optical potential spikes of square cross section with arbitrary pattern. These spikes constitute impurities, the scattering centers for the otherwise free propagation of the particles. This geometry does not allow for classical potential trapping which can be hard to exclude in other experimental setups. Here we add further theoretical evidence for Anderson localization in this system by comparing the transport processes within a regular and a random pattern of impurities. It is demonstrated that the transport within randomly distributed impurities is suppressed and the corresponding localization length becomes shorter than the channel length. However, if an equal density of impurities are distributed in a regular manner, the transport is only modestly disturbed. This observation corroborates the conclusions of the experimental observation: the localization is indeed attributed to the disorder. Beyond analyzing the density distribution and the localization length, we also calculate a quantum ``impedance'' exhibiting qualitatively different behavior for regular and random impurity patterns.
The development of atom cooling and trapping techniques and the ability to load optical lattices or disordered potentials with Bose-Einstein condensates or degenerate Fermi gases has opened a whole field of research around the strong localization of matter waves. In this theoretical work we study the coherent transport of matter waves evolving in disordered optical potentials (speckle). The influence of correlated disorder is first studied numerically in the framework of the Anderson model. Subsequently, a self-consistent diagrammatic calculation allows us to determine analytically the basic transport parameters in the regime of weak disorder: mean free path, transport mean free path, diffusion constant, localization length. A crucial quantity for these analytical calculations is the spatial correlation function of speckle fluctuations. It determines the degree of anisotropy of a scattering event. We consider in particular the transition from weak localization to strong localization. In this case the diffusion constant of matter waves decreases and approaches zero at the threshold of strong localization. We calculate the renormalization of the diffusion constant due to the interference of matter waves by explicitly considering the correlation of fluctuations of the disordered potential.