To experimentally measure the critical exponents, one needs to have access to the curvature function with a certain level of accuracy. Good candidates at present are quantum engineered photonics and ultracold atomic systems. In the first case, the curvature function can be extracted from the anomalous displacement of wave packets under optical pulse pumping in coupled fibre loops. For ultracold atoms in optical lattices, the Berry curvature can be achieved through quantum interference or force-induced wave-packet velocity measurements.