Insulating BECs, fractured Bose glasses, and other surprises in strongly tilted optical lattices

We consider versions of Bose- and Fermi-Hubbard models whose dynamics conserves both total charge and total dipole moment, a situation which can be engineered in strongly tilted optical lattices. Related models have received significant attention recently for their interesting out-of-equilibrium dynamics, but analytic and numeric studies reveal that they also possess rather unusual ground states. As an example, the dipole-conserving Bose-Hubbard model realizes a phase of matter which contains a Bose-Einstein condensate, but which is not a superfluid. This model also exhibits an interesting dynamic instability towards an exotic type of glassy state, with implications for experiments on spinning BECs. This talk will present a survey of recent results on these models, as well as discuss connections to current and future AMO experiments.