Subdiffusion and Heat Transport in a Tilted 2D Fermi-Hubbard System

We study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a “tilt”). We do this 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 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.