Gaussian-to-Non-Gaussian Transition of a Quantum Spin Bath Revealed by Fourth-Order Correlation

Non-Gaussian fluctuations are one of the essential properties of quantum systems. However, the direct detection of non-Gaussian fluctuations has not yet been achieved in experiments since the specific order of correlation has to be isolated from the complex dynamics of the whole system. In this Letter, we measure the second- and fourth-order correlations of ^{13}C nuclear spins around a nitrogen vacancy center in diamond, using the recently developed quantum nonlinear spectroscopy. By adjusting the detection window and the spectral resolution, we observe the Gaussian to non-Gaussian transition of the multispin system. We find that the fourth-order correlation provides a fingerprint signal that can be used to identify individual spins with the same precession frequency, suggesting that Gaussianity is a potential quantum resource for quantum sensing. Our results shed light on the study of nonequilibrium quantum many-body dynamics and quantum materials at the nanoscale.