Measurement of interacting quantum phases:A band mapping scheme

Band mapping is widely used in various scenarios of cold atom physics to measure the quasi-momentum distribution and band population.However,conventional methods fail in strongly interacting systems.Here we propose and experimentally realize a novel scheme of band mapping that can accurately measure the quasi-momentum of interacting many-body systems.Through an anisotropic control in turning down the three-dimensional optical lattice,we can eliminate the effect of interactions on the band mapping process.Then,based on a precise measurement of the quasi-momentum distribution,we introduce the incoherent fraction as a physical quantity that can quantify the degree of incoherence of quantum many-body states.This method enables precise measurement of processes such as the superfluid to Mott insulator phase transition.Additionally,by analyzing the spatial correlation derived from the quasi-momentum of superfluid-Mott insulator phase transitions,we obtain results consistent with the incoherent fraction.Our scheme broadens the scope of band mapping and provides a method for studying quantum many-body prob-lems.