Strongly correlated electron systems such as high-temperature superconductors, pseudo-gap states and spin liquids are a cornerstone of modern condensed matter research. One method of studying these systems is the construction of a quantum simulator that captures the essential underlying physics. Ultracold fermionic quantum gases in optical lattices provide a clean and tunable implementation of the Hubbard model, which is believed to be the paradigmatic model of the cuprates. Moreover, high-resolution optical microscopy of these systems gives access to site-level observables and correlation functions. However, so far ultracold atom experiments have not been able to reach the low-temperature regime of the doped Hubbard model, where complex many-body phases are expected.
In this talk I will report on the observation of antiferromagnetic long-range order in a repulsively interacting Fermi gas of Li-6 atoms in a 2D square lattice. We detect the ordered state via the emergence of a peak in the spin structure factor and a diverging spin correlation length. When doping away from half-filling into a numerically intractable regime, we find that long-range order extends to doping concentrations of about 15%. I will also show how we can use entropy redistribution to create ultra-low entropy states of fermionic atoms. Furthermore, I will discuss recent efforts on detecting microscopic signatures of magnetic polarons in the doped Hubbard model.