High-resolution correlation spectroscopy of ¹³C spins near a nitrogen-vacancy centre in diamond

Selective Detection of Dynamics-Complete Set of Correlations via Quantum Channels

Correlations of fluctuations are essential to understanding many-body systems and key information for advancing quantum technologies. To fully describe the dynamics of a physical system, all time-ordered correlations (TOCs), i.e., the dynamics-complete set of correlations are needed. The current measurement techniques can only access a limited set of TOCs, and there has been no systematic and feasible solution for extracting the dynamic-complete set of correlations hitherto. Here we propose a platform-universal protocol to selectively detect arbitrary types of TOCs via quantum channels. In our method, the quantum channels are synthesized with various controls, and engineer the evolution of a sensor-target system along a specific path that corresponds to a desired correlation. Using nuclear magnetic resonance, we experimentally demonstrate this protocol by detecting a specific type of fourth-order TOC that has never been accessed previously. We also show that the knowledge of the TOCs can be used to significantly improve the precision of quantum optimal control. Our method provides a new toolbox for characterizing the quantum many-body states and quantum noise, and hence for advancing the fields of quantum sensing and quantum computing.

A scanning probe microscope compatible with quantum sensing at ambient conditions

We designed and built up a new type of ambient scanning probe microscope (SPM), which is fully compatible with state-of-the-art quantum sensing technology based on the nitrogen-vacancy (NV) centers in diamond. We chose a qPlus-type tuning fork (Q up to ∼4400) as the current/force sensor of SPM for its high stiffness and stability under various environments, which yields atomic resolution under scanning tunneling microscopy mode and 1.2-nm resolution under atomic force microscopy mode. The tip of SPM can be used to directly image the topography of nanoscale targets on diamond surfaces for quantum sensing and to manipulate the electrostatic environment of NV centers to enhance their sensitivity up to a single proton spin. In addition, we also demonstrated scanning magnetometry and electrometry with a spatial resolution of ∼20 nm. Our new system not only paves the way for integrating atomic/molecular-scale color-center qubits onto SPM tips to produce quantum tips but also provides the possibility of fabricating color-center qubits with nanoscale or atomic precision.

Multidimensional Spectroscopy of Nuclear Spin Clusters in Diamond

Optically active spin defects in solids offer promising platforms to investigate nuclear spin clusters with high sensitivity and atomic-site resolution. To leverage near-surface defects for molecular structure analysis in chemical and biological contexts using nuclear magnetic resonance (NMR), further advances in spectroscopic characterization of nuclear environments are essential. Here, we report Fourier spectroscopy techniques to improve localization and mapping of the test bed ^{13}C nuclear spin environment of individual, shallow nitrogen-vacancy centers at room temperature. We use multidimensional spectroscopy, well-known from classical NMR, in combination with weak measurements of single-nuclear-spin precession. We demonstrate two examples of multidimensional NMR: (i) improved nuclear spin localization by separate encoding of the two hyperfine components along spectral dimensions and (ii) spectral editing of nuclear-spin pairs, including measurement of internuclear coupling constants. Our work adds important tools for the spectroscopic analysis of molecular structures by single-spin probes.

Diamond surface functionalization via visible light-driven C-H activation for nanoscale quantum sensing

Nitrogen-vacancy (NV) centers in diamond are a promising platform for nanoscale NMR sensing. Despite significant progress toward using NV centers to detect and localize nuclear spins down to the single spin level, NV-based spectroscopy of individual, intact, arbitrary target molecules remains elusive. Such sensing requires that target molecules are immobilized within nanometers of NV centers with long spin coherence. The inert nature of diamond typically requires harsh functionalization techniques such as thermal annealing or plasma processing, limiting the scope of functional groups that can be attached to the surface. Solution-phase chemical methods can be readily generalized to install diverse functional groups, but they have not been widely explored for single-crystal diamond surfaces. Moreover, realizing shallow NV centers with long spin coherence times requires highly ordered single-crystal surfaces, and solution-phase functionalization has not yet been shown with such demanding conditions. In this work, we report a versatile strategy to directly functionalize C-H bonds on single-crystal diamond surfaces under ambient conditions using visible light, forming C-F, C-Cl, C-S, and C-N bonds at the surface. This method is compatible with NV centers within 10 nm of the surface with spin coherence times comparable to the state of the art. As a proof-of-principle demonstration, we use shallow ensembles of NV centers to detect nuclear spins from surface-bound functional groups. Our approach to surface functionalization opens the door to deploying NV centers as a tool for chemical sensing and single-molecule spectroscopy.

Suppression of Pulsed Dynamic Nuclear Polarization by Many-Body Spin Dynamics

We study a mechanism by which nuclear hyperpolarization due to the polarization transfer from a microwave-pulse-controlled electron spin is suppressed. From analytical and numerical calculations of the unitary dynamics of multiple nuclear spins, we uncover that, combined with the formation of the dark state within a cluster of nuclei, coherent higher-order nuclear spin dynamics impose limits on the efficiency of the polarization transfer even in the absence of mundane depolarization processes such as nuclear spin diffusion and relaxation. Furthermore, we show that the influence of the dark state can be partly mitigated by introducing a disentangling operation. Our analysis is applied to the nuclear polarizations observed in ^{13}C nuclei coupled with a single nitrogen-vacancy center in diamond [Randall et al., Science 374, 1474 (2021)SCIEAS0036-807510.1126/science.abk0603]. Our Letter sheds light on collective engineering of nuclear spins as well as future designs of pulsed dynamic nuclear polarization protocols.

P1 Center Electron Spin Clusters Are Prevalent in Type Ib Diamonds

Understanding the spatial distribution of the P1 centers is crucial for diamond-based sensors and quantum devices. P1 centers serve as polarization sources for dynamic nuclear polarization (DNP) quantum sensing and play a significant role in the relaxation of nitrogen vacancy (NV) centers. Additionally, the distribution of NV centers correlates with the distribution of P1 centers, as NV centers are formed through the conversion of P1 centers. We utilized DNP and pulsed electron paramagnetic resonance (EPR) techniques that revealed strong clustering of a significant population of P1 centers that exhibit exchange coupling and produce asymmetric line shapes. The 13C DNP frequency profile at a high magnetic field revealed a pattern that requires an asymmetric EPR line shape of the P1 clusters with electron-electron (e-e) coupling strengths exceeding the 13C nuclear Larmor frequency. EPR and DNP characterization at high magnetic fields was necessary to resolve energy contributions from different e-e couplings. We employed a two-frequency pump-probe pulsed electron double resonance technique to show cross-talk between the isolated and clustered P1 centers. This finding implies that the clustered P1 centers affect all of the P1 populations. Direct observation of clustered P1 centers and their asymmetric line shape offers a novel and crucial insight into understanding magnetic noise sources for quantum information applications of diamonds and for designing diamond-based polarizing agents with optimized DNP efficiency for 13C and other nuclear spins of analytes. We propose that room temperature 13C DNP at a high field, achievable through straightforward modifications to existing solution-state NMR systems, is a potent tool for evaluating and controlling diamond defects.

Nitrogen-Vacancy Magnetic Relaxometry of Nanoclustered Cytochrome C Proteins

Nitrogen-vacancy (NV) magnetometry offers an alternative tool to detect paramagnetic centers in cells with a favorable combination of magnetic sensitivity and spatial resolution. Here, we employ NV magnetic relaxometry to detect cytochrome C (Cyt-C) nanoclusters. Cyt-C is a water-soluble protein that plays a vital role in the electron transport chain of mitochondria. Under ambient conditions, the heme group in Cyt-C remains in the Fe3+ state, which is paramagnetic. We vary the concentration of Cyt-C from 6 to 54 μM and observe a reduction of the NV spin-lattice relaxation time (T1) from 1.2 ms to 150 μs, which is attributed to the spin noise originating from the Fe3+ spins. NV T1 imaging of Cyt-C drop-casted on a nanostructured diamond chip allows us to detect the relaxation rates from the adsorbed Fe3+ within Cyt-C.

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.

Optimal Sensing Protocol for Statistically Polarized Nano-NMR with NV Centers

Diffusion noise represents a major constraint to successful liquid state nano-NMR spectroscopy. Using the Fisher information as a faithful measure, we theoretically calculate and experimentally show that phase sensitive protocols are superior in most experimental scenarios, as they maximize information extraction from correlations in the sample. We derive the optimal experimental parameters for quantum heterodyne detection (Qdyne) and present the most accurate statistically polarized nano-NMR Qdyne detection experiments to date, leading the way to resolve chemical shifts and J couplings at the nanoscale.

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ∼10^{9} two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

Quantum sensing of radio-frequency signal with NV centers in SiC

Silicon carbide is an emerging platform for quantum technologies that provides wafer scale and low-cost industrial fabrication. The material also hosts high-quality defects with long coherence times that can be used for quantum computation and sensing applications. Using an ensemble of nitrogen-vacancy centers and an XY8-2 correlation spectroscopy approach, we demonstrate a room-temperature quantum sensing of an artificial AC field centered at ~900 kHz with a spectral resolution of 10 kHz. Implementing the synchronized readout technique, we further extend the frequency resolution of our sensor to 0.01 kHz. These results pave the first steps for silicon carbide quantum sensors toward low-cost nuclear magnetic resonance spectrometers with a wide range of practical applications in medical, chemical, and biological analysis.

Nitrogen-Vacancy Magnetometry of Individual Fe-Triazole Spin Crossover Nanorods

[Fe(Htrz)₂(trz)](BF₄) (Fe-triazole) spin crossover molecules show thermal, electrical, and optical switching between high spin (HS) and low spin (LS) states, making them promising candidates for molecular spintronics. The LS and HS transitions originate from the electronic configurations of Fe(II) and are considered to be diamagnetic and paramagnetic, respectively. The Fe(II) LS state has six paired electrons in the ground states with no interaction with the magnetic field and a diamagnetic behavior is usually observed. While the bulk magnetic properties of Fe-triazole compounds are widely studied by standard magnetometry techniques, their magnetic properties at the individual level are missing. Here we use nitrogen vacancy (NV) based magnetometry to study the magnetic properties of the Fe-triazole LS state of nanoparticle clusters and individual nanorods of size varying from 20 to 1000 nm. Scanning electron microscopy (SEM) and Raman spectroscopy are performed to determine the size of the nanoparticles/nanorods and to confirm their respective spin states. The magnetic field patterns produced by the nanoparticles/nanorods are imaged by NV magnetic microscopy as a function of applied magnetic field (up to 350 mT) and correlated with SEM and Raman. We found that in most of the nanorods the LS state is slightly paramagnetic, possibly originating from the surface oxidation and/or the greater Fe(III) presence along the nanorods' edges. NV measurements on the Fe-triazole LS state nanoparticle clusters revealed both diamagnetic and paramagnetic behavior. Our results highlight the potential of NV quantum sensors to study the magnetic properties of spin crossover molecules and molecular magnets.

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.

Using Metal-Organic Frameworks to Confine Liquid Samples for Nanoscale NV-NMR

Atomic-scale magnetic field sensors based on nitrogen vacancy (NV) defects in diamonds are an exciting platform for nanoscale nuclear magnetic resonance (NMR) spectroscopy. The detection of NMR signals from a few zeptoliters to single molecules or even single nuclear spins has been demonstrated using NV centers close to the diamond surface. However, fast molecular diffusion of sample molecules in and out of the nanoscale detection volumes impedes their detection and limits current experiments to solid-state or highly viscous samples. Here, we show that restricting diffusion by confinement enables nanoscale NMR spectroscopy of liquid samples. Our approach uses metal-organic frameworks (MOF) with angstrom-sized pores on a diamond chip to trap sample molecules near the NV centers. This enables the detection of NMR signals from a liquid sample, which would not be detectable without confinement. These results set the route for nanoscale liquid-phase NMR with high spectral resolution.

Nanoscale covariance magnetometry with diamond quantum sensors

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.

Quantum nonlinear spectroscopy of single nuclear spins

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.

Signals that look the same from their low-order correlations can often be distinguished by looking at higher-order ones. Here, the authors exploit the sensitivity of quantum nonlinear spectroscopy to fourth-order correlations to identify Gaussian noises, random-phased AC fields, and quantum spins.

Surface NMR using quantum sensors in diamond

NMR is a noninvasive, molecular-level spectroscopic technique widely used for chemical characterization. However, it lacks the sensitivity to probe the small number of spins at surfaces and interfaces. Here, we use nitrogen vacancy (NV) centers in diamond as quantum sensors to optically detect NMR signals from chemically modified thin films. To demonstrate the method's capabilities, aluminum oxide layers, common supports in catalysis and materials science, are prepared by atomic layer deposition and are subsequently functionalized by phosphonate chemistry to form self-assembled monolayers. The surface NV-NMR technique detects spatially resolved NMR signals from the monolayer, indicates chemical binding, and quantifies molecular coverage. In addition, it can monitor in real time the formation kinetics at the solid-liquid interface. With our approach, we show that NV quantum sensors are a surface-sensitive NMR tool with femtomole sensitivity for in situ analysis in catalysis, materials, and biological research.

Detecting initial correlations via correlated spectroscopy in hybrid quantum systems

Generic mesoscopic quantum systems that interact with their environment tend to display appreciable correlations with environment that often play an important role in the physical properties of the system. However, the experimental methods needed to characterize such systems either ignore the role of initial correlations or scale unfavourably with system dimensions. Here, we present a technique that is agnostic to system-environment correlations and can be potentially implemented experimentally. Under a specific set of constraints, we demonstrate the ability to detect and measure specific correlations. We apply the technique to two cases related to Nitrogen Vacancy Centers (NV). Firstly, we use the technique on an NV coupled to a P1 defect centre in the environment to demonstrate the ability to detect dark spins. Secondly, we implement the technique on a hybrid quantum system of NV coupled to an optical cavity with initial correlations. We extract the interaction strength and effective number of interacting NVs from the initial correlations using our technique.

Low Field Nano-NMR via Three-Level System Control

Conventional control strategies for nitrogen-vacancy centers in quantum sensing are based on a two-level model of their triplet ground state. However, this approach fails in regimes of weak bias magnetic fields or strong microwave pulses, as we demonstrate. To overcome this limitation, we propose a novel control sequence that exploits all three levels by addressing a hidden Raman configuration with microwave pulses tuned to the zero-field transition. We report excellent performance in typical dynamical decoupling sequences, opening up the possibility for nano-NMR operation in low field environments.

Correlated noise in Brownian motion allows for super resolution

Diffusion broadening of spectral lines is the main limitation to frequency resolution in non-polarized liquid state nano-NMR. This problem arises from the limited amount of information that can be extracted from the signal before losing coherence. For liquid state NMR as with most generic sensing experiments, the signal is thought to decay exponentially, severely limiting resolution. However, there is theoretical evidence that predicts a power law decay of the signal’s correlations due to diffusion noise in the non-polarized nano-NMR scenario. In this work we show that in the NV based nano-NMR setup such diffusion noise results in high spectral resolution.

Robustness of the NV-NMR Spectrometer Setup to Magnetic Field Inhomogeneities

The NV-NMR spectrometer is a promising candidate for detection of NMR signals at the nanoscale. Field inhomogeneities, however, are a major source of noise that limits spectral resolution in state of the art NV-NMR experiments and constitutes a major bottleneck in the development of nanoscale NMR. Here we propose, a route in which this limitation could be circumvented in NV-NMR spectrometer experiments, by utilizing the nanometric scale and the quantumness of the detector.

Measurement of Backaction from Electron Spins in a Gate-Defined GaAs Double Quantum dot Coupled to a Mesoscopic Nuclear Spin Bath

Decoherence of a quantum system arising from its interaction with an environment is a key concept for understanding the transition between the quantum and classical world as well as performance limitations in quantum technology applications. The effects of large, weakly coupled environments are often described as a classical, fluctuating field whose dynamics is unaffected by the qubit, whereas a fully quantum description still implies some backaction from the qubit on the environment. Here we show direct experimental evidence for such a backaction for an electron-spin qubit in a GaAs quantum dot coupled to a mesoscopic environment of order 10^{6} nuclear spins. By means of a correlation measurement technique, we detect the backaction of a single qubit-environment interaction whose duration is comparable to the qubit's coherence time, even in such a large system. We repeatedly let the qubit interact with the spin bath and measure its state. Between such cycles, the qubit is reinitialized to different states. The correlations of the measurement outcomes are strongly affected by the intermediate qubit state, which reveals the action of a single electron spin on the nuclear spins.

Kilohertz electron paramagnetic resonance spectroscopy of single nitrogen centers at zero magnetic field

Electron paramagnetic resonance (EPR) spectroscopy is among the most important analytical tools in physics, chemistry, and biology. The emergence of nitrogen-vacancy (NV) centers in diamond, serving as an atomic-sized magnetometer, has promoted this technique to single-spin level, even under ambient conditions. Despite the enormous progress in spatial resolution, the current megahertz spectral resolution is still insufficient to resolve key heterogeneous molecular information. A major challenge is the short coherence times of the sample electron spins. Here, we address this challenge by using a magnetic noise-insensitive transition between states of different symmetry. We demonstrate a 27-fold narrower spectrum of single substitutional nitrogen (P1) centers in diamond with a linewidth of several kilohertz, and then some weak couplings can be resolved. Those results show both spatial and spectral advances of NV center-based EPR and provide a route toward analytical (EPR) spectroscopy at the single-molecule level.

Hyperpolarized relaxometry based nuclear T1 noise spectroscopy in diamond

The origins of spin lifetimes in quantum systems is a matter of importance in several areas of quantum information. Spectrally mapping spin relaxation processes provides insight into their origin and motivates methods to mitigate them. In this paper, we map nuclear relaxation in a prototypical system of [Formula: see text] nuclei in diamond coupled to Nitrogen Vacancy (NV) centers over a wide field range (1 mT-7 T). Nuclear hyperpolarization through optically pumped NV electrons allows signal measurement savings exceeding million-fold over conventional methods. Through a systematic study with varying substitutional electron (P1 center) and [Formula: see text] concentrations, we identify the operational relaxation channels for the nuclei at different fields as well as the dominant role played by [Formula: see text] coupling to the interacting P1 electronic spin bath. These results motivate quantum control techniques for dissipation engineering to boost spin lifetimes in diamond, with applications including engineered quantum memories and hyperpolarized [Formula: see text] imaging.

Overcoming resolution limits with quantum sensing

The field of quantum sensing explores the use of quantum phenomena to measure a broad range of physical quantities, of both static and time-dependent types. While for static signals the main figure of merit is sensitivity, for time dependent signals it is spectral resolution, i.e. the ability to resolve two different frequencies. Here we study this problem, and develop new superresolution methods that rely on quantum features. We first formulate a general criterion for superresolution in quantum problems. Inspired by this, we show that quantum detectors can resolve two frequencies from incoherent segments of the signal, irrespective of their separation, in contrast to what is known about classical detection schemes. The main idea behind these methods is to overcome the vanishing distinguishability in resolution problems by nullifying the projection noise.

Standard resolution limits reflect the fact that two objects, frequencies etc. cannot be told apart when they get too close. Here, the authors show theoretically that, if one is able to reduce projection noise by suitable control of the probe, these limits can be overcome.

Triple nitrogen-vacancy centre fabrication by C5N4Hn ion implantation

Quantum information processing requires quantum registers based on coherently interacting quantum bits. The dipolar couplings between nitrogen vacancy (NV) centres with nanometre separation makes them a potential platform for room-temperature quantum registers. The fabrication of quantum registers that consist of NV centre arrays has not advanced beyond NV pairs for several years. Further scaling up of coupled NV centres by using nitrogen implantation through nanoholes has been hampered because the shortening of the separation distance is limited by the nanohole size and ion straggling. Here, we demonstrate the implantation of C₅N₄H_n from an adenine ion source to achieve further scaling. Because the C₅N₄H_n ion may be regarded as an ideal point source, the separation distance is solely determined by straggling. We successfully demonstrate the fabrication of strongly coupled triple NV centres. Our method may be extended to fabricate small quantum registers that can perform quantum information processing at room temperature.

Randomization of Pulse Phases for Unambiguous and Robust Quantum Sensing

We develop theoretically and demonstrate experimentally a universal dynamical decoupling method for robust quantum sensing with unambiguous signal identification. Our method uses randomization of control pulses to simultaneously suppress two types of errors in the measured spectra that would otherwise lead to false signal identification. These are spurious responses due to finite-width π pulses, as well as signal distortion caused by π pulse imperfections. For the cases of nanoscale nuclear-spin sensing and ac magnetometry, we benchmark the performance of the protocol with a single nitrogen vacancy center in diamond against widely used nonrandomized pulse sequences. Our method is general and can be combined with existing multipulse quantum sensing sequences to enhance their performance.

Quantum Control and Sensing of Nuclear Spins by Electron Spins under Power Limitations

State of the art quantum sensing experiments targeting frequency measurements or frequency addressing of nuclear spins require one to drive the probe system at the targeted frequency. In addition, there is a substantial advantage to performing these experiments in the regime of high magnetic fields, in which the Larmor frequency of the measured spins is large. In this scenario we are confronted with a natural challenge of controlling a target system with a very high frequency when the probe system cannot be set to resonance with the target frequency. In this contribution we present a set of protocols that are capable of confronting this challenge, even at large frequency mismatches between the probe system and the target system, both for polarization and for quantum sensing.

Limits on Spectral Resolution Measurements by Quantum Probes

The limits of frequency resolution in nano-NMR experiments have been discussed extensively in recent years. It is believed that there is a crucial difference between the ability to resolve a few frequencies and the precision of estimating a single one. Whereas the efficiency of single frequency estimation gradually increases with the square root of the number of measurements, the ability to resolve two frequencies is limited by the specific timescale of the signal and cannot be compensated for by extra measurements. Here we show theoretically and demonstrate experimentally that the relationship between these quantities is more subtle and both are only limited by the Cramér-Rao bound of a single frequency estimation.

High-resolution spectroscopy of single nuclear spins via sequential weak measurements

Nuclear magnetic resonance (NMR) of single spins have recently been detected by quantum sensors. However, the spectral resolution has been limited by the sensor’s relaxation to a few kHz at room temperature. This can be improved by using quantum memories, at the expense of sensitivity. In contrast, classical signals can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. When applied to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurement. Here we report sequential weak measurements on a single ¹³C nuclear spin. The back-action causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.

Quantum sensors can have exceptional properties but the limits on their performance involve nonclassical effects such as quantum backaction. Here the authors show how to mitigate the effects of backaction on the spectral resolution of an NV centre nuclear spin sensor by controlling the measurement strength.

Wide dynamic range magnetic field cycler: Harnessing quantum control at low and high fields

We describe the construction of a fast field cycling device capable of sweeping a 4-order-of-magnitude range of magnetic fields, from ∼1 mT to 7 T, in under 700 ms, and which is further extendable to a 1 nT-7 T range. Central to this system is a high-speed sample shuttling mechanism between a superconducting magnet and a magnetic shield, with the capability to access arbitrary fields in between with high resolution. Our instrument serves as a versatile platform to harness the inherent dichotomy of spin dynamics on offer at low and high fields-in particular, the low anisotropy, fast spin manipulation, and rapid entanglement growth at low field as well as the long spin lifetimes, spin specific control, and efficient inductive measurement possible at high fields. Exploiting these complementary capabilities in a single device opens up applications in a host of problems in quantum control, sensing, and information storage, besides in nuclear hyperpolarization, relaxometry, and imaging. In particular, in this paper, we focus on the ability of the device to enable low-field hyperpolarization of ¹³C nuclei in diamond via optically pumped electronic spins associated with nitrogen vacancy defect centers.

Three-dimensional localization spectroscopy of individual nuclear spins with sub-Angstrom resolution

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method for analyzing the chemical composition and molecular structure of materials. At the nanometer scale, NMR has the prospect of mapping the atomic-scale structure of individual molecules, provided a method that can sensitively detect single nuclei and measure inter-atomic distances. Here, we report on precise localization spectroscopy experiments of individual 13C nuclear spins near the central electronic sensor spin of a nitrogen-vacancy (NV) center in a diamond chip. By detecting the nuclear free precession signals in rapidly switchable external magnetic fields, we retrieve the three-dimensional spatial coordinates of the nuclear spins with sub-Angstrom resolution and for distances beyond 10 Å. We further show that the Fermi contact contribution can be constrained by measuring the nuclear g-factor enhancement. The presented method will be useful for mapping atomic positions in single molecules, an ambitious yet important goal of nanoscale nuclear magnetic resonance spectroscopy.

Three-Dimensional Nuclear Spin Positioning Using Coherent Radio-Frequency Control

Distance measurements via the dipolar interaction are fundamental to the application of nuclear magnetic resonance (NMR) to molecular structure determination, but they provide information on only the absolute distance r and polar angle θ between spins. In this Letter, we present a protocol to also retrieve the azimuth angle ϕ. Our method relies on measuring the nuclear precession phase after the application of a control pulse with a calibrated external radio-frequency coil. We experimentally demonstrate three-dimensional positioning of individual ^{13}C nuclear spins in a diamond host crystal relative to the central electronic spin of a single nitrogen-vacancy center. The ability to pinpoint three-dimensional nuclear locations is central for realizing a nanoscale NMR technique that can image the structure of single molecules with atomic resolution.

Quantum measurement of a rapidly rotating spin qubit in diamond

A controlled qubit in a rotating frame opens new opportunities to probe fundamental quantum physics, such as geometric phases in physically rotating frames, and can potentially enhance detection of magnetic fields. Realizing a single qubit that can be measured and controlled during physical rotation is experimentally challenging. We demonstrate quantum control of a single nitrogen-vacancy (NV) center within a diamond rotated at 200,000 rpm, a rotational period comparable to the NV spin coherence time T₂. We stroboscopically image individual NV centers that execute rapid circular motion in addition to rotation and demonstrate preparation, control, and readout of the qubit quantum state with lasers and microwaves. Using spin-echo interferometry of the rotating qubit, we are able to detect modulation of the NV Zeeman shift arising from the rotating NV axis and an external DC magnetic field. Our work establishes single NV qubits in diamond as quantum sensors in the physically rotating frame and paves the way for the realization of single-qubit diamond-based rotation sensors.

Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor

Precise timekeeping is critical to metrology, forming the basis by which standards of time, length, and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy because they define the ultimate frequency precision that can be reached. In quantum metrology, the qubit coherence time defines the clock stability, from which the spectral linewidth and frequency precision are determined. We demonstrate a quantum sensing protocol in which the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observed a precision in frequency estimation scaling in time T as T^-3/2 for classical oscillating fields. The narrow linewidth magnetometer based on single spins in diamond is used to sense nanoscale magnetic fields with an intrinsic frequency resolution of 607 microhertz, which is eight orders of magnitude narrower than the qubit coherence time.

Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters

In nanoscale metrology, dissipation of the sensor limits its performance. Strong dissipation has a negative impact on sensitivity, and sensor–target interaction even causes relaxation or dephasing of the latter. The weak dissipation of nitrogen-vacancy (NV) sensors in room temperature diamond enables detection of individual target nuclear spins, yet limits the spectral resolution of nuclear magnetic resonance (NMR) spectroscopy to several hundred Hertz, which typically prevents molecular recognition. Here, we use the NV intrinsic nuclear spin as a nonvolatile classical memory to store NMR information, while suppressing sensor back-action on the target using controlled decoupling of sensor, memory, and target. We demonstrate memory lifetimes up to 4 min and apply measurement and decoupling protocols, which exploit such memories efficiently. Our universal NV-based sensor device records single-spin NMR spectra with 13 Hz resolution at room temperature.

Dissipation of the sensor is a limiting factor in metrology. Here, Pfender et al. suppress this effect employing the nuclear spin of an NV centre for robust intermediate storage of classical NMR information, allowing then to record single-spin NMR spectra with 13 Hz resolution at room temperature.

Solution nuclear magnetic resonance spectroscopy on a nanostructured diamond chip

Sensors using nitrogen-vacancy centers in diamond are a promising tool for small-volume nuclear magnetic resonance (NMR) spectroscopy, but the limited sensitivity remains a challenge. Here we show nearly two orders of magnitude improvement in concentration sensitivity over previous nitrogen-vacancy and picoliter NMR studies. We demonstrate NMR spectroscopy of picoliter-volume solutions using a nanostructured diamond chip with dense, high-aspect-ratio nanogratings, enhancing the surface area by 15 times. The nanograting sidewalls are doped with nitrogen-vacancies located a few nanometers from the diamond surface to detect the NMR spectrum of roughly 1 pl of fluid lying within adjacent nanograting grooves. We perform ¹H and ¹⁹F nuclear magnetic resonance spectroscopy at room temperature in magnetic fields below 50 mT. Using a solution of CsF in glycerol, we determine that 4 ± 2 × 10^{12 19}F spins in a 1 pl volume can be detected with a signal-to-noise ratio of 3 in 1 s of integration.

Nitrogen vacancy (NV) centres in diamond can be used for NMR spectroscopy, but increased sensitivity is needed to avoid long measurement times. Kehayias et al. present a nanostructured diamond grating with a high density of NV centres, enabling NMR spectroscopy of picoliter-volume solutions.

Dissipatively Stabilized Quantum Sensor Based on Indirect Nuclear-Nuclear Interactions

We propose to use a dissipatively stabilized nitrogen vacancy (NV) center as a mediator of interaction between two nuclear spins that are protected from decoherence and relaxation of the NV due to the periodical resets of the NV center. Under ambient conditions this scheme achieves highly selective high-fidelity quantum gates between nuclear spins in a quantum register even at large NV-nuclear distances. Importantly, this method allows for the use of nuclear spins as a sensor rather than a memory, while the NV spin acts as an ancillary system for the initialization and readout of the sensor. The immunity to the decoherence and relaxation of the NV center leads to a tunable sharp frequency filter while allowing at the same time the continuous collection of the signal to achieve simultaneously high spectral selectivity and high signal-to-noise ratio.

Nanoscale nuclear magnetic resonance with chemical resolution

Nuclear magnetic resonance (NMR) spectroscopy is a key analytical technique in chemistry, biology, and medicine. However, conventional NMR spectroscopy requires an at least nanoliter-sized sample volume to achieve sufficient signal. We combined the use of a quantum memory and high magnetic fields with a dedicated quantum sensor based on nitrogen vacancy centers in diamond to achieve chemical shift resolution in 1H and 19F NMR spectroscopy of 20-zeptoliter sample volumes. We demonstrate the application of NMR pulse sequences to achieve homonuclear decoupling and spin diffusion measurements. The best measured NMR linewidth of a liquid sample was ~1 part per million, mainly limited by molecular diffusion. To mitigate the influence of diffusion, we performed high-resolution solid-state NMR by applying homonuclear decoupling and achieved a 20-fold narrowing of the NMR linewidth.

Delayed entanglement echo for individual control of a large number of nuclear spins

Methods to selectively detect and manipulate nuclear spins by single electrons of solid-state defects play a central role for quantum information processing and nanoscale nuclear magnetic resonance (NMR). However, with standard techniques, no more than eight nuclear spins have been resolved by a single defect centre. Here we develop a method that improves significantly the ability to detect, address and manipulate nuclear spins unambiguously and individually in a broad frequency band by using a nitrogen-vacancy (NV) centre as model system. On the basis of delayed entanglement control, a technique combining microwave and radio frequency fields, our method allows to selectively perform robust high-fidelity entangling gates between hardly resolved nuclear spins and the NV electron. Long-lived qubit memories can be naturally incorporated to our method for improved performance. The application of our ideas will increase the number of useful register qubits accessible to a defect centre and improve the signal of nanoscale NMR.

Single electrons of solid-state defects can be used to detect nearby nuclear spins, but so far only a few at a time have been resolved. Here the authors propose an approach based on delayed entanglement echo that demonstrates improved detection and manipulation capabilities of nuclear spins by an NV centre.

Perspective: Structure and dynamics of water at surfaces probed by scanning tunneling microscopy and spectroscopy

The detailed and precise understanding of water-solid interaction largely relies on the development of atomic-scale experimental techniques, among which scanning tunneling microscopy (STM) has proven to be a noteworthy example. In this perspective, we review the recent advances of STM techniques in imaging, spectroscopy, and manipulation of water molecules. We discuss how those newly developed techniques are applied to probe the structure and dynamics of water at solid surfaces with single-molecule and even submolecular resolution, paying particular attention to the ability of accessing the degree of freedom of hydrogen. In the end, we present an outlook on the directions of future STM studies of water-solid interfaces as well as the challenges faced by this field. Some new scanning probe techniques beyond STM are also envisaged.

Single-spin magnetic resonance in the nitrogen-vacancy center of diamond

Magnetic resonance of single spins has flourished mostly because of the unique properties of the NV center in diamond. This review covers the basic physics of this defect center, introduces the techniques for working with single spins and gives an overview of some applications like quantum information and sensing.

A quantum spin-probe molecular microscope

Imaging the atomic structure of a single biomolecule is an important challenge in the physical biosciences. Whilst existing techniques all rely on averaging over large ensembles of molecules, the single-molecule realm remains unsolved. Here we present a protocol for 3D magnetic resonance imaging of a single molecule using a quantum spin probe acting simultaneously as the magnetic resonance sensor and source of magnetic field gradient. Signals corresponding to specific regions of the molecule's nuclear spin density are encoded on the quantum state of the probe, which is used to produce a 3D image of the molecular structure. Quantum simulations of the protocol applied to the rapamycin molecule (C₅₁H₇₉NO₁₃) show that the hydrogen and carbon substructure can be imaged at the angstrom level using current spin-probe technology. With prospects for scaling to large molecules and/or fast dynamic conformation mapping using spin labels, this method provides a realistic pathway for single-molecule microscopy.

Single spin defects can allow high-resolution sensing of molecules under an applied magnetic field. Here, the authors propose a protocol for three-dimensional magnetic resonance imaging with angstrom-level resolution exploiting the dipolar field of a spin qubit, such as a diamond nitrogen-vacancy.