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.
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.
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.
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.
The most direct approach for characterizing the quantum dynamics of a strongly-interacting system is to measure the time-evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate framework is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Our work centers on the following question: What can the decoherence dynamics of such a probe tell us about the many-body system? In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly-interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in diamond: nitrogen-vacancy (NV) color centers (probe spins) and substitutional nitrogen impurities (many-body system). We demonstrate that signatures of the many-body system's dimensionality, dynamics, and disorder are naturally encoded in the functional form of the NV's decoherence profile. Leveraging these insights, we directly characterize the two-dimensional nature of a nitrogen delta-doped diamond sample. In addition, we explore two distinct facets of the many-body dynamics: First, we address a persistent debate about the microscopic nature of spin dynamics in strongly-interacting dipolar systems. Second, we demonstrate direct control over the spectral properties of the many-body system, including its correlation time. Our work opens the door to new directions in both quantum sensing and simulation.
Characterizing the intricate structure of entanglement in quantum many-body systems remains a central challenge, as standard measures often obscure underlying geometric details. In this Letter, we introduce a powerful framework, termed multi-bipartition entanglement tomography, which probes the fine structure of entanglement across an exhaustive ensemble of distinct bipartitions. Our cornerstone is the discovery of a ``bond-additive law'', which reveals that the entanglement entropy can be precisely decomposed into a bulk volume-law baseline plus a geometric correction formed by a sum of local contributions from crossed bonds of varying ranges. This law distills complex entanglement landscapes into a concise set of entanglement bond tensions {ωj}, serving as a quantitative fingerprint of interaction locality. By applying this tomography to Hamiltonian dynamics, random quantum circuits, and Floquet dynamics, we resolve a fundamental distinction between thermalization mechanisms: Hamiltonian thermalized states retain a persistent geometric imprint characterized by a significantly non-zero ω1, while this structure is completely erased in random quantum circuit and Floquet dynamics. Our work establishes multi-bipartition entanglement tomography as a versatile toolbox for the geometric structure of quantum information in many-body systems.
Nitrogen vacancy (NV) centers in diamond are widely deployed as local magnetic sensors, using coherent, single qubit control to measure both time-averaged fields and noise with nanoscale spatial resolution. Moving beyond single qubits to multi-qubit control enables new sensing modalities such as measuring nonlocal spatiotemporal correlators, or using entangled states to improve measurement sensitivity. Here, we describe protocols to use optically unresolved NV center pairs and nuclear spins as multi-qubit sensors for measuring correlated noise, enabling covariance magnetometry at nanometer length scales. For NV centers that are optically unresolved but have spectrally resolved spin transitions, we implement a phase-cycling protocol that disambiguates magnetic correlations from variance fluctuations by alternating the relative spin orientations of the two NV centers. For NV centers that are both optically and spectrally unresolved, we leverage the presence of a third qubit, a 13C nucleus that is strongly coupled to one of the NV centers, to effect coherent single-NV spin flips and enable a similar phase-cycling protocol. For length scales around 10 nm, we create maximally entangled Bell states through dipole-dipole coupling between two NV centers, and use these entangled states to directly read out the magnetic field correlation, rather than reconstructing it from independent measurements of unentangled NV centers. Importantly, this changes the scaling of sensitivity with readout noise from quadratic to linear. For conventional off-resonant readout of the NV center spin state (for which the readout noise is roughly 30 times the quantum projection limit), this results in a dramatic sensitivity improvement. Finally, we demonstrate methods for the detection of high spatial- and temporal-resolution correlators with pairs of strongly interacting NV centers.
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.