Synthetic Magnetism in Ultracold Atoms

Ultra cold atoms are remarkable systems with a truly unprecedented level of experimental control and one application of this control is to engineer many body hamiltonians usually associated with condensed matter physics.  To date this engineering has focused mostly on the real-space potential that the atoms experience, for example, multiple-well traps, optical lattice potentials, or even potentials depending on the internal state of the atom. 

Here I present our experimental work creating a synthetic magnetic field in a Bose-Einstein condensate (BEC) generated by an abelian vector potential and discuss the connection between spin-orbit coupling and non-abelian vector potentials.