The past decades have seen rapid advances in our capabilities to probe and manipulate atoms. Novel cooling methods have led to quantum degeneracy of large ensembles of atoms. Combined with the ability to tune interactions via Feshbach resonances and energy landscapes via optical potentials, ultracold fermionic atoms have emerged as a flexible platform for "quantum simulation" of condensed matter models. In recent years, the advent of quantum gas microscopy has even allowed one to measure and control single atoms trapped within an optical lattice, enabling novel studies of correlations in lattice systems.
In this talk, I will describe three experiments that highlight the unique capabilities of ultracold fermions as a platform for quantum simulation. First, I will describe how fermions near a Feshbach resonance have made possible precise thermodynamic measurements of a strongly-interacting s-wave superfluid. Next, I will describe how we have realized and detected spin-orbit coupling. Combined with s-wave interactions, spin-orbit coupling allows one to create a single component Fermi sea that has effective p-wave interactions, a potential route towards topologically protected states. Thirdly, I will describe quantum gas microscopy of fermionic atoms in a 2D optical lattice. This system realizes the Hubbard model on a square lattice, believed to capture essential aspects of high-Tc cuprates. Using a quantum gas microscope, we have directly observed the Mott and band insulating states. The ability to resolve the spin and occupation of every lattice site has also allowed us to observe anti-ferromagnetic spin correlations and non-trivial charge correlations as a function of doping.