Abstract: The normal state of high-temperature superconductors exhibits anomalous transport and spectral properties that are poorly understood. Cold atoms in optical lattices have been used to realize the celebrated Fermi-Hubbard model, widely believed to capture the essential physics of these materials. The recent development of fermionic quantum gas microscopes has enabled studying Hubbard systems with single-site resolution and extracting equilibrium charge and spin correlations. In this talk, I will report on using a quantum gas microscope to probe the transport and spectral properties of atomic Fermi-Hubbard systems. First, I will describe the development of a technique to measure microscopic charge diffusion, and hence resistivity, in doped Mott insulators. We have found that this resistivity exhibits a linear dependence on temperature and violates the Mott-Ioffe-Regel limit, two signatures of strange metallic behavior . Next, I will discuss how we used the same technique to observe sub- diffusive charge transport in tilted Hubbard systems and present a hydrodynamic model that explains this observation in terms of an interplay of charge and heat transport, allowing the extraction of the infinite temperature heat diffusivity of the system . Finally, I will describe the development of angle-resolved photoemission spectroscopy (ARPES) for Hubbard systems and its application to studying pseudogap physics in an attractive Hubbard system across the BEC-BCS crossover , setting the stage for future studies of the pseudogap regime in repulsive Hubbard systems.
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