APS/Cheng Chin and Erich Mueller
Schematic of the experiments by Aidelsburger et al.  and by Miyake et al. . Rubidium atoms hop between sites in a two-dimensional square lattice in a regime where tunneling requires absorbing and emitting photons produced by lasers. Interaction with these lasers produces path-dependent phases for the atoms, mimicking the effect of a magnetic field on electrons. The phase accumulated when moving around a single unit cell, ϕ, is of order π/2 for these experiments.