Gradiometry provides a versatile alternative to passive environmental shielding in quasi-static magnetometry, effectively suppressing background noise through differential signal extraction. Nevertheless, traditional implementations rely on multi-sensor architectures restricted to spatial gradients, where subtracting signals from independent detectors involves imperfect suppression of common-mode noise and artifacts, limiting their sensitivity. To overcome these limitations, we introduce a quantum control sequence that enables intrinsic temporal and spatial vectorial gradiometry of magnetic fields using a single quantum sensor. Our method provides direct access to first and higher-order derivatives of the magnetic field and extended applicability via auxiliary nuclear spin memory. We showcase this protocol on an ensemble of nitrogen-vacancy (NV) centers in diamond and combine it with mechanical control to realize high-precision differential sensing. Through detailed numerical simulations, we demonstrate the performance of our scheme in two critical DC magnetometry applications: (i) vector magnetic anomaly detection and (ii) non-invasive gradiometry of neuronal action potentials.
Gradiometry provides a versatile alternative to passive environmental shielding in quasi-static magnetometry, effectively suppressing background noise through differential signal extraction. Nevertheless, traditional implementations rely on multi-sensor architectures restricted to spatial gradients, where subtracting signals from independent detectors involves imperfect suppression of common-mode noise and artifacts, limiting their sensitivity. To overcome these limitations, we introduce a quantum control sequence that enables intrinsic temporal and spatial vectorial gradiometry of magnetic fields using a single quantum sensor. Our method provides direct access to first and higher-order derivatives of the magnetic field and extended applicability via auxiliary nuclear spin memory. We showcase this protocol on an ensemble of nitrogen-vacancy (NV) centers in diamond and combine it with mechanical control to realize high-precision differential sensing. Through detailed numerical simulations, we demonstrate the performance of our scheme in two critical DC magnetometry applications: (i) vector magnetic anomaly detection and (ii) non-invasive gradiometry of neuronal action potentials.
Sensing static magnetic fields with high sensitivity and spatial resolution is critical to many applications in fundamental physics, bioimaging, and materials science. Even more beneficial would be full vector magnetometry with nanoscale spatial resolution. Several versatile magnetometry platforms have emerged over the past decade, such as electronic spins associated with nitrogen vacancy (NV) centers in diamond. Achieving vector magnetometry has, however, often required using an ensemble of sensors or degrading the sensitivity. Here we introduce a hybrid magnetometry platform, consisting of a sensor and an ancillary qubit, that allows vector magnetometry of static fields. While more generally applicable, we demonstrate the method for an electronic NV sensor and a nuclear spin qubit. In particular, sensing transverse fields relies on frequency up-conversion of the dc fields through the ancillary qubit, allowing quantum lock-in detection with low-frequency noise rejection. In combination with the Ramsey detection of longitudinal fields, our frequency up-conversion scheme delivers a sensitive technique for vector dc magnetometry at the nanoscale.
Nitrogen vacancy (NV) centers in diamond are atom-scale defects that can be used to sense magnetic fields with high sensitivity and spatial resolution. Typically, the magnetic field is measured by averaging sequential measurements of single NV centers, or by spatial averaging over ensembles of many NV centers, which provides mean values that contain no nonlocal information about the relationship between two points separated in space or time. Here, we propose and implement a sensing modality whereby two or more NV centers are measured simultaneously, and we extract temporal and spatial correlations in their signals that would otherwise be inaccessible. We demonstrate measurements of correlated applied noise using spin-to-charge readout of two NV centers and implement a spectral reconstruction protocol for disentangling local and nonlocal noise sources.
We demonstrate direct, non-invasive and non-contact detection of human cardiac magnetic signals using quantum sensors based on nitrogen-vacancy (NV) centers in diamond. Three configurations were employed recording magnetocardiography (MCG) signals in various shielded and unshielded environments. The signals were averaged over a few hundreds up to several thousands of heart beats to detect the MCG traces. The compact room-temperature NV sensors exhibit sensitivities of 6-26 pT/Hz^(1/2) with active sensing volumes below 0.5 mm^3, defining the performance level of the demonstrated MCG measurements. While the present signals are obtained by averaging, this performance already indicates a clear path toward single-shot MCG sensing. To move beyond shielded environments toward practical clinical use, strong noise suppression is required. To this end, we implement NV-based gradiometry and achieve efficient common-mode noise rejection, enabled by the intrinsically small sensing volume of NV sensors. Together, these multi-platform results obtained across diverse magnetic environments provide a solid foundation for translating quantum sensors into human medical diagnostics such as MCG and magnetoencephalography (MEG).
In modern-day quantum metrology, quantum sensors are widely employed to detect weak magnetic fields or nanoscale signals. Quantum devices, exploiting quantum coherence, are inevitably connected to physical constants and can achieve accuracy, repeatability, and precision approaching fundamental limits. As a result, these sensors have shown utility in a wide range of research domains spanning both science and technology. A rapidly emerging quantum sensing platform employs atomic-scale defects in crystals. In particular, magnetometry using nitrogen-vacancy (NV) color centers in diamond has garnered increasing interest. NV systems possess a combination of remarkable properties, optical addressability, long coherence times, and biocompatibility. Sensors based on NV centers excel in spatial resolution and magnetic sensitivity. These diamond-based sensors promise comparable combination of high spatial resolution and magnetic sensitivity without cryogenic operation. The above properties of NV magnetometers promise increasingly integrated quantum measurement technology, as a result, they have been extensively developed with various protocols and find use in numerous applications spanning materials characterization, nuclear magnetic resonance (NMR), condensed matter physics, paleomagnetism, neuroscience and living systems biology, and industrial vector magnetometry. In this chapter, NV centers are explored for magnetic sensing in a number of contexts. In general, we introduce novel regimes for magnetic-field probes with NV ensembles. Specifically, NV centers are developed for sensitive magnetometers for applications where microwaves (MWs) are prohibitively invasive and operations need to be carried out under zero ambient magnetic field. The primary goal of our discussion is to improve the utility of these NV center-based magnetometers.
Practical performance of quantum sensors is often curtailed by uncontrolled environmental drift (bias-field instability, temperature fluctuations, mechanical vibration), background fields, and imperfect control pulses. This motivates developing physical mechanisms that intrinsically compensate for such perturbations while retaining high sensitivity to target fields. We introduce an interaction-protected magnetometry scheme where periodic driving steers the collective magnetization onto two long-lived, prethermal Floquet "orbit" axes well-separated on the Bloch sphere. Rapid toggling between these axes encodes target fields as a differential signal, whereas background fields appear as common-mode motion that is strongly rejected, achieving >1000-fold suppression while canceling prethermal transients. This enables accurate reconstruction of rapidly varying audio-band magnetic signals without predictive filtering or spectral tuning. We provide an experimental proof-of-principle using a dense ensemble of coupled nuclear spins, operated here as a broadband (0-1 kHz) magnetometer. The protocol is remarkably tolerant to imperfections, operating robustly across millions of pulses under pulse-angle (~10°) and pulse frequency (>1 kHz) errors, large bias-field drifts (>50 μT), temperature variations over 150 K, and harsh mechanical vibrations. These results establish Floquet prethermalization as a resource for robust quantum sensors that combines broadband magnetic-field sensitivity with intrinsic immunity to diverse environmental and control perturbations, opening a path toward stable quantum metrology beyond controlled laboratory conditions.
High-fidelity quantum operation of qubits plays an important role in magnetometry based on nitrogen-vacancy (NV) centers in diamonds. However, the nontrivial spin-spin coupling of the NV center decreases signal contrast and sensitivity. Here, we overcome this limitation by exploiting the amplitude modulation of microwaves, which allows us to perfectly detect magnetic signals at low fields. Compared with the traditional double-quantum sensing protocol, the full contrast of the detection signal was recovered, and the sensitivity was enhanced three times in the experiment. Our method is applicable to a wide range of sensing tasks, such as temperature, strain, and electric field.