Insulating BECs, pattern formation, and emergent gauge fields in strongly tilted optical lattices

We Bose- and Fermi-Hubbard models whose dynamics conserves total center of mass, a situation which can arise in strongly tilted optical lattices. The bosonic models realize a phase of matter which contains a Bose-Einstein condensate, but which is not a superfluid. They also possess a universal tendency to "fracture" into an exotic glassy state that exhibits spontaneous pattern formation, with implications for experiments on spinning BECs. The fermionic models are described at low energies by fermions that strongly interact with an emergent gauge field, offering a novel route towards studying non-Fermi liquids and gauge theories. I will give an overview of the analytic and numerical work behind these results, with a particular focus given on experimental protocols for realizing these exotic phases in the lab.