Topological Phases in Atomic, Molecular, and Optical Systems

We will first review schemes for taking advantage of the tremendous degree of control recently achieved in AMO (atomic, molecular, and optical) systems to realize topological phenomena. In particular, we will emphasize unique features of AMO systems such the abundance of bosonic platforms, accessibility of far-out-of-equilibrium dynamics, and natural occurrence of interactions decaying as tunable power laws. We will then focus on a few examples such as symmetry protected topological phases with ion crystals, various fractional quantum Hall states with dipoles, and parafermionic zero modes with ultracold neutral bosons.