Conventional nonlinear spectroscopy, using classical probes, accesses limited quantum system correlations. This work demonstrates quantum nonlinear spectroscopy, employing a quantum sensor entangled with a quantum object, enabling extraction of arbitrary correlation types and orders. Fourth-order correlations of single nuclear spins, unmeasurable via conventional methods, were measured using sequential weak measurement via a nitrogen-vacancy center in diamond. This spectroscopy provides fingerprint features to distinguish Gaussian noises, random-phased AC fields, and quantum spins, which are indistinguishable in second-order correlations. This represents an initial step towards applying higher-order correlations to quantum sensing, quantum foundation examination (e.g., higher-order Leggett-Garg inequality), and quantum many-body physics study.

Jonas Meinel, Vadim Vorobyov, Ping Wang, Boris Yavkin, Mathias Pfender, Hitoshi Sumiya, Shinobu Onoda, Junichi Isoya, Ren-Bao Liu, J. Wrachtrup