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.
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.
Conventional 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.
Understanding the nonequilibrium dynamics of isolated quantum many-body systems is a central goal of modern physics. Measuring genuine many-body correlations in quantum systems is central to this aim, while it remains a fundamental challenge for systems lacking individual addressability. We introduce a multidimensional correlation imprinting technique that encodes the structure of a many-body state into the temporal fluctuation spectrum of a local quantum probe. This allows direct measurement of arbitrary-order correlations in nonequilibrium quantum states. Using a nitrogen-vacancy center in diamond coupled to a ^{13}C nuclear spin bath, we experimentally reconstruct many-body correlation landscape to third order. Furthermore, by analyzing the spectral structure of correlation cumulants, we directly visualize the dynamics of quantum entanglement. Our Letter establishes a general approach to probing complex nonequilibrium phenomena and entanglement in quantum many-body systems at the nanoscale.
Abstract Nitrogen-vacancy (NV) center decoherence is often interpreted with effective Gaussian noise models, which encode only second-order environmental correlations and can obscure intrinsically non-Gaussian nuclear-bath dynamics. Here we show that entangled NV qutrit pairs provide an operational probe of this non-Gaussianity via the time-dependent d = 3 Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell parameter , built from joint outcome probabilities using two fixed local measurement settings per party. We derive a cumulant expansion for and isolate contributions from third- and fourth-order Overhauser-field cumulants that are absent in a Gaussian model whose second cumulant is fixed by standard qubit-coherence inference under identical conditions. Exact simulations of few-spin central-spin clusters show that these higher-order bath statistics generate a structured residual at the few-percent level relative to the qubit-constrained Gaussian prediction, even when qubit coherence is accurately described by a Gaussian envelope. Our results provide an operational non-Gaussianity witness beyond qubit-constrained Gaussian inference.
Atomic scale qubits, as may be realized in nitrogen vacancy (NV) centers in diamond, offer the opportunity to study magnetic field noise with nanometer scale spatial resolution. Using these spin qubits, one can learn a great deal about the magnetic-field noise correlations, and correspondingly the collective-mode spectra, in quantum materials and devices. However, to date these tools have been essentially restricted to studying Gaussian noise processes – equivalent to linear-response. In this work we will show how to extend these techniques beyond the Gaussian regime and show how to unambiguously measure higher-order magnetic noise cumulants in a local, spatially resolved way. We unveil two protocols for doing this; the first uses a single spin-qubit and different dynamical decoupling sequences to extract non-Markovian and non-Gaussian spin-echo noise. The second protocol uses two-qubit coincidence measurements to study spatially non-local cumulants in the magnetic noise. We then demonstrate the utility of these protocols by considering a model of a bath of non-interacting two-level systems, as well as a model involving spatially correlated magnetic fluctuations near a second-order Ising phase transition. In both cases, we highlight how this technique can be used to measure in a real many-body system how fluctuation dynamics converge towards the central limit theorem as a function of effective bath size. We then conclude by discussing some promising applications and extensions of this method.
Central spin decoherence caused by nuclear spin baths is often a critical issue in various quantum computing schemes, and it has also been used for sensing single-nuclear spins. Recent theoretical studies suggest that central spin decoherence can act as a probe of many-body physics in spin baths; however, identification and detection of many-body correlations of nuclear spins in nanoscale systems are highly challenging. Here, taking a phosphorus donor electron spin in a 29Si nuclear spin bath as our model system, we discover both theoretically and experimentally that many-body correlations in nanoscale nuclear spin baths produce identifiable signatures in decoherence of the central spin under multiple-pulse dynamical decoupling control. We demonstrate that under control by an odd or even number of pulses, the central spin decoherence is principally caused by second- or fourth-order nuclear spin correlations, respectively. This study marks an important step toward studying many-body physics using spin qubits. Detecting many-body correlations is a long-standing challenge in many-body physics. By studying their effects on the decoherence of the central spin under dynamical decoupling, Ma et al.provide an experimental demonstration of detection of many-body correlations in nanoscale nuclear spin bath.
Central spin systems, in which a central spin is singled out and interacts nonlocally with several bath spins, are paradigmatic models for nitrogen-vacancy centers and quantum dots. They show complex emergent dynamics and stationary phenomena which, despite the collective nature of their interaction, are still largely not understood. Here, we derive exact results on the emergent behavior of open quantum central spin systems. The latter crucially depends on the scaling of the interaction strength with the bath size. For scalings with the inverse square root of the bath size (typical of one-to-many interactions), the system behaves, in the thermodynamic limit, as an open quantum Jaynes-Cummings model, whose bosonic mode encodes the quantum fluctuations of the bath spins. In this case, non-Gaussian correlations are dynamically generated and persist at stationarity. For scalings with the inverse bath size, the emergent dynamics is instead of mean-field type. Our Letter provides a fundamental understanding of the different dynamical regimes of central spin systems and a simple theory for efficiently exploring their nonequilibrium behavior. Our findings may become relevant for developing fully quantum descriptions of many-body solid-state devices and their applications.