Towards low temperatures and extensions of Fermi-Hubbard models in a quantum gas microscope

The Fermi-Hubbard model is the simplest model of strongly-correlated quantum materials, and believed to capture the physics of high-Tc cuprates. However, the most widely studied square lattice Hubbard model may actually miss several important features of the cuprate phase diagram (particle-hole asymmetry of antiferromagnetism, finite interaction Mott transition, and high-Tc superconductivity). Recent numerical studies suggest that adding frustration to the model in the form of a diagonal tunneling, or expanding to a multi-site unit cell might be necessary ingredients to reproduce the behavior of real materials. Ultracold fermionic atoms in tunable optical lattices, combined with arbitrary projected light potentials are ideal realizations of the Hubbard model in various lattice geometries. Recent experimental progress has allowed us to prepare very low entropy initial states, and dynamically transform them to low temperature regimes of the square lattice Hubbard model. Here we report on progress towards studies of magnetism and low temperature phases in extensions of the Hubbard model. We further explore new measurements and experimental protocols to probe the emergent low temperature physics in these models.