Simulating magnetic fields in Rydberg-dressed neutral atoms

A Rydberg interaction that can effectively exchange the states of two atoms may be used to transfer the optical phase of laser fields to the atomic pair wave function. A similar phase mapping may occur for many neutral atoms in a two-dimensional lattice when subjected to off-resonant optical Rydberg dressing fields, simulating the effect of a magnetic field. This all-optical method of simultaneously simulating magnetic fields and strong two-body interaction may have application to the study of quantum magnetism and topological physics.