Roadmap on nanoscale magnetic resonance imaging.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications. .

Qudit-Based Spectroscopy for Measurement and Control of Nuclear-Spin Qubits in Silicon Carbide.

Nuclear spins with hyperfine coupling to single electron spins are highly valuable quantum bits. Here we probe and characterize the particularly rich nuclear-spin environment around single silicon vacancy color centers (V2) in 4H-SiC. By using the electron spin-3/2 qudit as a four level sensor, we identify several sets of ^{29}Si and ^{13}C nuclear spins through their hyperfine interaction. We extract the major components of their hyperfine coupling via optical detected nuclear magnetic resonance, and assign them to shells in the crystal via the density function theory simulations. We utilize the ground-state level anticrossing of the electron spin for dynamic nuclear polarization and achieve a nuclear-spin polarization of up to 98±6%. We show that this scheme can be used to detect the nuclear magnetic resonance signal of individual spins and demonstrate their coherent control. Our work provides a detailed set of parameters and first steps for future use of SiC as a multiqubit memory and quantum computing platform.

Observation of plaid-like spin splitting in a noncoplanar antiferromagnet.

Spatial, momentum and energy separation of electronic spins in condensed-matter systems guides the development of new devices in which spin-polarized current is generated and manipulated1-3. Recent attention on a set of previously overlooked symmetry operations in magnetic materials4 leads to the emergence of a new type of spin splitting, enabling giant and momentum-dependent spin polarization of energy bands on selected antiferromagnets5-10. Despite the ever-growing theoretical predictions, the direct spectroscopic proof of such spin splitting is still lacking. Here we provide solid spectroscopic and computational evidence for the existence of such materials. In the noncoplanar antiferromagnet manganese ditelluride (MnTe2), the in-plane components of spin are found to be antisymmetric about the high-symmetry planes of the Brillouin zone, comprising a plaid-like spin texture in the antiferromagnetic (AFM) ground state. Such an unconventional spin pattern, further found to diminish at the high-temperature paramagnetic state, originates from the intrinsic AFM order instead of spin-orbit coupling (SOC). Our finding demonstrates a new type of quadratic spin texture induced by time-reversal breaking, placing AFM spintronics on a firm basis and paving the way for studying exotic quantum phenomena in related materials.

Quantum-enhanced diamond molecular tension microscopy for quantifying cellular forces.

The constant interplay and information exchange between cells and the microenvironment are essential to their survival and ability to execute biological functions. To date, a few leading technologies such as traction force microscopy, optical/magnetic tweezers, and molecular tension-based fluorescence microscopy are broadly used in measuring cellular forces. However, the considerable limitations, regarding the sensitivity and ambiguities in data interpretation, are hindering our thorough understanding of mechanobiology. Here, we propose an innovative approach, namely, quantum-enhanced diamond molecular tension microscopy (QDMTM), to precisely quantify the integrin-based cell adhesive forces. Specifically, we construct a force-sensing platform by conjugating the magnetic nanotags labeled, force-responsive polymer to the surface of a diamond membrane containing nitrogen-vacancy centers. Notably, the cellular forces will be converted into detectable magnetic variations in QDMTM. After careful validation, we achieved the quantitative cellular force mapping by correlating measurement with the established theoretical model. We anticipate our method can be routinely used in studies like cell-cell or cell-material interactions and mechanotransduction.

Widefield Diamond Quantum Sensing with Neuromorphic Vision Sensors.

Despite increasing interest in developing ultrasensitive widefield diamond magnetometry for various applications, achieving high temporal resolution and sensitivity simultaneously remains a key challenge. This is largely due to the transfer and processing of massive amounts of data from the frame-based sensor to capture the widefield fluorescence intensity of spin defects in diamonds. In this study, a neuromorphic vision sensor to encode the changes of fluorescence intensity into spikes in the optically detected magnetic resonance (ODMR) measurements is adopted, closely resembling the operation of the human vision system, which leads to highly compressed data volume and reduced latency. It also results in a vast dynamic range, high temporal resolution, and exceptional signal-to-background ratio. After a thorough theoretical evaluation, the experiment with an off-the-shelf event camera demonstrated a 13× improvement in temporal resolution with comparable precision of detecting ODMR resonance frequencies compared with the state-of-the-art highly specialized frame-based approach. It is successfully deploy this technology in monitoring dynamically modulated laser heating of gold nanoparticles coated on a diamond surface, a recognizably difficult task using existing approaches. The current development provides new insights for high-precision and low-latency widefield quantum sensing, with possibilities for integration with emerging memory devices to realize more intelligent quantum sensors.

Detection of Quantum Signals Free of Classical Noise via Quantum Correlation.

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the quantum correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our Letter demonstrates the quantum or classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.

Anti-Zeno purification of spin baths by quantum probe measurements.

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature.

Quantum-assisted distortion-free audio signal sensing.

Quantum sensors are known for their high sensitivity in sensing applications. However, this sensitivity often comes with severe restrictions on other parameters which are also important. Examples are that in measurements of arbitrary signals, limitation in linear dynamic range could introduce distortions in magnitude and phase of the signal. High frequency resolution is another important feature for reconstructing unknown signals. Here, we demonstrate a distortion-free quantum sensing protocol that combines a quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the capability of reconstructing audio frequency signals with an extended linear dynamic range and high frequency resolution. Melody and speech based signals are used for demonstrating the features. The methods could broaden the horizon for quantum sensors towards applications, e.g. telecommunication in challenging environment, where low-distortion measurements are required at multiple frequency bands within a limited volume.

Thermodynamics of a Minimal Algorithmic Cooling Refrigerator.

We investigate, theoretically and experimentally, the thermodynamic performance of a minimal three-qubit heat-bath algorithmic cooling refrigerator. We analytically compute the coefficient of performance, the cooling power, and the polarization of the target qubit for an arbitrary number of cycles, taking realistic experimental imperfections into account. We determine their fundamental upper bounds in the ideal reversible limit and show that these values may be experimentally approached using a system of three qubits in a nitrogen-vacancy center in diamond.

Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence.

Optically addressable spin defects in silicon carbide (SiC) are an emerging platform for quantum information processing compatible with nanofabrication processes and device control used by the semiconductor industry. System scalability towards large-scale quantum networks demands integration into nanophotonic structures with efficient spin-photon interfaces. However, degradation of the spin-optical coherence after integration in nanophotonic structures has hindered the potential of most colour centre platforms. Here, we demonstrate the implantation of silicon vacancy centres (VSi) in SiC without deterioration of their intrinsic spin-optical properties. In particular, we show nearly lifetime-limited photon emission and high spin-coherence times for single defects implanted in bulk as well as in nanophotonic waveguides created by reactive ion etching. Furthermore, we take advantage of the high spin-optical coherences of VSi centres in waveguides to demonstrate controlled operations on nearby nuclear spin qubits, which is a crucial step towards fault-tolerant quantum information distribution based on cavity quantum electrodynamics.

Optimizing NV magnetometry for Magnetoneurography and Magnetomyography applications.

Magnetometers based on color centers in diamond are setting new frontiers for sensing capabilities due to their combined extraordinary performances in sensitivity, bandwidth, dynamic range, and spatial resolution, with stable operability in a wide range of conditions ranging from room to low temperatures. This has allowed for its wide range of applications, from biology and chemical studies to industrial applications. Among the many, sensing of bio-magnetic fields from muscular and neurophysiology has been one of the most attractive applications for NV magnetometry due to its compact and proximal sensing capability. Although SQUID magnetometers and optically pumped magnetometers (OPM) have made huge progress in Magnetomyography (MMG) and Magnetoneurography (MNG), exploring the same with NV magnetometry is scant at best. Given the room temperature operability and gradiometric applications of the NV magnetometer, it could be highly sensitive in the pT / Hz -range even without magnetic shielding, bringing it close to industrial applications. The presented work here elaborates on the performance metrics of these magnetometers to the state-of-the-art techniques by analyzing the sensitivity, dynamic range, and bandwidth, and discusses the potential benefits of using NV magnetometers for MMG and MNG applications.

Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets.

Moiré superlattices of twisted nonmagnetic two-dimensional (2D) materials are highly controllable platforms for the engineering of exotic correlated and topological states. Here, we report emerging magnetic textures in small-angle twisted 2D magnet chromium triiodide (CrI3). Using single-spin quantum magnetometry, we directly visualized nanoscale magnetic domains and periodic patterns, a signature of moiré magnetism, and measured domain size and magnetization. In twisted bilayer CrI3, we observed the coexistence of antiferromagnetic (AFM) and ferromagnetic (FM) domains with disorder-like spatial patterns. In twisted double-trilayer CrI3, AFM and FM domains with periodic patterns appear, which is in good agreement with the calculated spatial magnetic structures that arise from the local stacking-dependent interlayer exchange interactions in CrI3 moiré superlattices. Our results highlight magnetic moiré superlattices as a platform for exploring nanomagnetism.

Ultra-sensitive hybrid diamond nanothermometer.

Nitrogen-vacancy (NV) centers in diamond are promising quantum sensors because of their long spin coherence time under ambient conditions. However, their spin resonances are relatively insensitive to non-magnetic parameters such as temperature. A magnetic-nanoparticle-nanodiamond hybrid thermometer, where the temperature change is converted to the magnetic field variation near the Curie temperature, were demonstrated to have enhanced temperature sensitivity ([Formula: see text]) (Wang N, Liu G-Q and Leong W-H et al. Phys Rev X 2018; 8: 011042), but the sensitivity was limited by the large spectral broadening of ensemble spins in nanodiamonds. To overcome this limitation, here we show an improved design of a hybrid nanothermometer using a single NV center in a diamond nanopillar coupled with a single magnetic nanoparticle of copper-nickel alloy, and demonstrate a temperature sensitivity of [Formula: see text]. This hybrid design enables detection of 2 mK temperature changes with temporal resolution of 5 ms. The ultra-sensitive nanothermometer offers a new tool to investigate thermal processes in nanoscale systems.

Single-spin resonance in a van der Waals embedded paramagnetic defect.

A plethora of single-photon emitters have been identified in the atomic layers of two-dimensional van der Waals materials1-8. Here, we report on a set of isolated optical emitters embedded in hexagonal boron nitride that exhibit optically detected magnetic resonance. The defect spins show an isotropic ge-factor of ~2 and zero-field splitting below 10 MHz. The photokinetics of one type of defect is compatible with ground-state electron-spin paramagnetism. The narrow and inhomogeneously broadened magnetic resonance spectrum differs significantly from the known spectra of in-plane defects. We determined a hyperfine coupling of ~10 MHz. Its angular dependence indicates an unpaired, out-of-plane delocalized π-orbital electron, probably originating from substitutional impurity atoms. We extracted spin-lattice relaxation times T1 of 13-17 µs with estimated spin coherence times T2 of less than 1 µs. Our results provide further insight into the structure, composition and dynamics of single optically active spin defects in hexagonal boron nitride.

Heterodyne sensing of microwaves with a quantum sensor.

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system's resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.

Magnetic domains and domain wall pinning in atomically thin CrBr3 revealed by nanoscale imaging.

The emergence of atomically thin van der Waals magnets provides a new platform for the studies of two-dimensional magnetism and its applications. However, the widely used measurement methods in recent studies cannot provide quantitative information of the magnetization nor achieve nanoscale spatial resolution. These capabilities are essential to explore the rich properties of magnetic domains and spin textures. Here, we employ cryogenic scanning magnetometry using a single-electron spin of a nitrogen-vacancy center in a diamond probe to unambiguously prove the existence of magnetic domains and study their dynamics in atomically thin CrBr3. By controlling the magnetic domain evolution as a function of magnetic field, we find that the pinning effect is a dominant coercivity mechanism and determine the magnetization of a CrBr3 bilayer to be about 26 Bohr magnetons per square nanometer. The high spatial resolution of this technique enables imaging of magnetic domains and allows to locate the sites of defects that pin the domain walls and nucleate the reverse domains. Our work highlights scanning nitrogen-vacancy center magnetometry as a quantitative probe to explore nanoscale features in two-dimensional magnets.

Nanoscale electric-field imaging based on a quantum sensor and its charge-state control under ambient condition.

Nitrogen-vacancy (NV) centers in diamond can be used as quantum sensors to image the magnetic field with nanoscale resolution. However, nanoscale electric-field mapping has not been achieved so far because of the relatively weak coupling strength between NV and electric field. Here, using individual shallow NVs, we quantitatively image electric field contours from a sharp tip of a qPlus-based atomic force microscope (AFM), and achieve a spatial resolution of ~10 nm. Through such local electric fields, we demonstrated electric control of NV's charge state with sub-5 nm precision. This work represents the first step towards nanoscale scanning electrometry based on a single quantum sensor and may open up the possibility of quantitatively mapping local charge, electric polarization, and dielectric response in a broad spectrum of functional materials at nanoscale.

Nanoscale Vector Electric Field Imaging Using a Single Electron Spin.

The ability to perform nanoscale electric field imaging of elementary charges at ambient temperatures will have diverse interdisciplinary applications. While the nitrogen-vacancy (NV) center in diamond is capable of high-sensitivity electrometry, demonstrations have so far been limited to macroscopic field features or detection of single charges internal to the diamond itself. In this work, we greatly extend these capabilities by using a shallow NV center to image the electric field of a charged atomic force microscope tip with nanoscale resolution. This is achieved by measuring Stark shifts in the NV spin-resonance due to AC electric fields. We demonstrate a near single-charge sensitivity of ηe = 5.3 charges/√Hz and subelementary charge detection (0.68e). This proof-of-concept experiment provides the motivation for further sensing and imaging of electric fields using NV centers in diamond.

Readout and control of an endofullerene electronic spin.

Atomic spins for quantum technologies need to be individually addressed and positioned with nanoscale precision. C60 fullerene cages offer a robust packaging for atomic spins, while allowing in-situ physical positioning at the nanoscale. However, achieving single-spin level readout and control of endofullerenes has so far remained elusive. In this work, we demonstrate electron paramagnetic resonance on an encapsulated nitrogen spin (14N@C60) within a C60 matrix using a single near-surface nitrogen vacancy (NV) center in diamond at 4.7 K. Exploiting the strong magnetic dipolar interaction between the NV and endofullerene electronic spins, we demonstrate radio-frequency pulse controlled Rabi oscillations and measure spin-echos on an encapsulated spin. Modeling the results using second-order perturbation theory reveals an enhanced hyperfine interaction and zero-field splitting, possibly caused by surface adsorption on diamond. These results demonstrate the first step towards controlling single endofullerenes, and possibly building large-scale endofullerene quantum machines, which can be scaled using standard positioning or self-assembly methods.