Subdiffusion and Heat Transport in a Tilted Two-Dimensional Fermi-Hubbard System

Using quantum gas microscopy, we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a "tilt"). The tilt is along one of the principal directions of the two-dimensional square lattice and couples mass transport to local heating through energy conservation. Because of this coupling, the system quickly heats up to near infinite temperature in the lowest band of the lattice. We study the high-temperature transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength λ and tilt strength and find that the associated decay time τ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with τ λ4. In order to explain the underlying physics and emphasize its universal nature, we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models that may exhibit nonergodic dynamics.