Low temperatures and precision probes in cold atom-based simulations of the Hubbard model

Ultracold atoms in optical lattices can provide faithful analog realizations of the Hubbard model and many of its variants. Recently, these simulators have been augmented with improved programmable controls that enable new routes to state preparation, new kinds of dynamics, and, by extension, access to new observables. I will discuss two examples where such tools have enabled simulations that challenge classical numerical techniques: first, a sampling problem involving non-interacting bosons on a lattice that is closely related to boson sampling; and second, the preparation of low temperature equilibrium states of interacting spinful fermions on a lattice. These simulations have the potential to enhance our understanding of quantum many body physics, including practical problems of interest in material design relating to strongly correlated quantum materials. However, fully harnessing their capabilities in the regime where exact classical numerical simulations are absent requires new, precision probes of the relevant microscopic or thermodynamic quantities.