Physics with Ring Lattices

Toroidal or ring-shaped lattices can be used to study a broad range of physical phenomena often with novel features due to the combination of two different kinds of periodicities - the lattice and the boundary condition. Such phenomena include, rotation sensing, nonlienear criticality and spin-squeezing and various topological and synthetic gauge structures. We examine several of these in the context of possible implementation in experiments with ultracold atoms.