Bilayer microscopy of spin and charge in a Fermi-Hubbard lattice

Quantum gas microscopes have provided unique opportunities to investigate correlations and thermodynamics of strongly interacting fermionic systems with unprecedented accuracy, including in-situ measurement of magnetic order with repulsive interactions and charge-density wave order with attractive interactions. In this work, we demonstrate the ability to extract the full charge information of a single band Fermi-Hubbard model. The method provides access to local correlations of the total density, enabling model-independent thermometry of low entropy samples through the fluctuation-dissipation theorem. We here also extract both spin and charge simultaneously from images of large, strongly-correlated systems by creating an additional spin-dependent potential during the separation of atoms. In addition, we show that this perpendicular superlattice can be used to coherently prepare equilibrium many-body states, and explore the crossover from single-layer to bilayer Fermi-Hubbard systems.