Meinel, JonasVorobyov, VadimWang, PingYavkin, BorisPfender, MathiasSumiya, HitoshiOnoda, ShinobuIsoya, JunichiLiu, Ren-BaoWrachtrup, Jörg2025-04-2220222041-17231926692853http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-162710https://elib.uni-stuttgart.de/handle/11682/16271https://doi.org/10.18419/opus-16252Conventional nonlinear spectroscopy, which use classical probes, can only access a limited set of correlations in a quantum system. Here we demonstrate that quantum nonlinear spectroscopy, in which a quantum sensor and a quantum object are first entangled and the sensor is measured along a chosen basis, can extract arbitrary types and orders of correlations in a quantum system. We measured fourth-order correlations of single nuclear spins that cannot be measured in conventional nonlinear spectroscopy, using sequential weak measurement via a nitrogen-vacancy center in diamond. The quantum nonlinear spectroscopy provides fingerprint features to identify different types of objects, such as Gaussian noises, random-phased AC fields, and quantum spins, which would be indistinguishable in second-order correlations. This work constitutes an initial step toward the application of higher-order correlations to quantum sensing, to examining the quantum foundation (by, e.g., higher-order Leggett-Garg inequality), and to studying quantum many-body physics.enCC BYinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/530article2024-11-26