Spin Transport in a Mott Insulator of Ultracold Fermions

Understanding transport in strongly interacting Fermi systems is among the most pressing but difficult tasks of many-body physics. The Fermi-Hubbard model serves as a prototypical example of a strongly correlated fermionic quantum system, and is believed to hold the key to high-temperature superconductivity. However, the transport properties in the various regions of its phase diagram are far from understood. We realize the Fermi-Hubbard model using a gas of fermionic atoms in an optical lattice, confined in a homogeneous box trap. In this setting, we study spin and charge transport using a quantum gas microscope, able to resolve individual atoms. In particular, at half filling, the charge degree of freedom is frozen, while spins are still able to move. Spin transport is induced by applying a spin-dependent magnetic field gradient. We observe spin dynamics which are diffusive in nature, and obtain the spin conductivity and spin diffusivity. These findings can be compared to existing theoretical approaches, such as the numerical-linked-cluster expansion (NLCE).