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. .

GALILEO: Galactic Axion Laser Interferometer Leveraging Electro-Optics.

We propose a novel experimental method for probing light dark matter candidates. We show that an electro-optical material's refractive index is modified in the presence of a coherently oscillating dark matter background. A high-precision resonant Michelson interferometer can be used to read out this signal. The proposed detection scheme allows for the exploration of an uncharted parameter space of dark matter candidates over a wide range of masses-including masses exceeding a few tens of microelectronvolts, which is a challenging parameter space for microwave cavity haloscopes.

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 sensors for biomedical applications.

Quantum sensors are finding their way from laboratories to the real world, as witnessed by the increasing number of start-ups in this field. The atomic length scale of quantum sensors and their coherence properties enable unprecedented spatial resolution and sensitivity. Biomedical applications could benefit from these quantum technologies, but it is often difficult to evaluate the potential impact of the techniques. This Review sheds light on these questions, presenting the status of quantum sensing applications and discussing their path towards commercialization. The focus is on two promising quantum sensing platforms: optically pumped atomic magnetometers, and nitrogen-vacancy centres in diamond. The broad spectrum of biomedical applications is highlighted by four case studies ranging from brain imaging to single-cell spectroscopy.

NMR of 31P nuclear spin singlet states in organic diphosphates.

31P NMR and MRI are commonly used to study organophosphates that are central to cellular energy metabolism. In some molecules of interest, such as adenosine diphosphate (ADP) and nicotinamide adenine dinucleotide (NAD), pairs of coupled 31P nuclei in the diphosphate moiety should enable the creation of nuclear spin singlet states, which may be long-lived and can be selectively detected via quantum filters. Here, we show that 31P singlet states can be created on ADP and NAD, but their lifetimes are shorter than T1 and are strongly sensitive to pH. Nevertheless, the singlet states were used with a quantum filter to successfully isolate the 31P NMR spectra of those molecules from the adenosine triphosphate (ATP) background signal.

Milky Way Accelerometry via Millisecond Pulsar Timing.

The temporal stability of millisecond pulsars is remarkable, rivaling even some terrestrial atomic clocks at long timescales. Using this property, we show that millisecond pulsars distributed in the galactic neighborhood form an ensemble of accelerometers from which we can directly extract the local galactic acceleration. From pulsar spin period measurements, we demonstrate acceleration sensitivity with about 1σ precision using 117 pulsars. We also present a complementary analysis using orbital periods of 13 binary pulsar systems that eliminates the systematics associated with pulsar braking and results in a local acceleration of (1.7±0.5)×10^{-10} m/s^{2} in good agreement with expectations. This work is a first step toward dynamically measuring acceleration gradients that will eventually inform us about the dark matter density distribution in the Milky Way galaxy.

Imaging viscous flow of the Dirac fluid in graphene.

The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system in which electrical transport features a universal hydrodynamic description, even at room temperature1,2. This quantum critical 'Dirac fluid' is expected to have a shear viscosity close to a minimum bound3,4, with an interparticle scattering rate saturating1 at the Planckian time, the shortest possible timescale for particles to relax. Although electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene5-8, a clear demonstration of viscous flow at the charge-neutrality point remains elusive. Here we directly image viscous Dirac fluid flow in graphene at room temperature by measuring the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy centres in diamond. Scanning single-spin and wide-field magnetometry reveal a parabolic Poiseuille profile for electron flow in a high-mobility graphene channel near the charge-neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in a metallic conductor and also in a low-mobility graphene channel. Via combined imaging and transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly ideal electron fluid in charge-neutral, high-mobility graphene at room temperature4. Our results will enable the study of hydrodynamic transport in quantum critical fluids relevant to strongly correlated electrons in high-temperature superconductors9. This work also highlights the capability of quantum spin magnetometers to probe correlated electronic phenomena at the nanoscale.

Probing Dark Matter Using Precision Measurements of Stellar Accelerations.

Dark matter comprises the bulk of the matter in the Universe, but its particle nature and cosmological origin remain mysterious. Knowledge of the dark matter density distribution in the Milky Way Galaxy is crucial both to our understanding of the standard cosmological model and for grounding direct and indirect searches for the particles comprising dark matter. Current measurements of Galactic dark matter content rely on model assumptions to infer the forces acting upon stars from the distribution of observed velocities. Here, we propose to apply the precision radial velocity method, optimized in recent years for exoplanet astronomy, to measure the change in the velocity of stars over time, thereby providing a direct probe of the local gravitational potential in the Galaxy. Using numerical simulations, we develop a realistic strategy to observe the differential accelerations of stars in our Galactic neighborhood with next-generation telescopes, at the level of 10^{-8} cm/s^{2}. Our simulations show that detecting accelerations at this level with an ensemble of 10^{3} stars requires the effect of stellar noise on radial velocity measurements to be reduced to <10 cm/s. The measured stellar accelerations may then be used to extract the local dark matter density and morphological parameters of the density profile.

Quantum diamond spectrometer for nanoscale NMR and ESR spectroscopy.

Nitrogen-vacancy (NV) quantum defects in diamond are sensitive detectors of magnetic fields. Owing to their atomic size and optical readout capability, they have been used for magnetic resonance spectroscopy of nanoscale samples on diamond surfaces. Here, we present a protocol for fabricating NV diamond chips and for constructing and operating a simple, low-cost 'quantum diamond spectrometer' for performing NMR and electron spin resonance (ESR) spectroscopy in nanoscale volumes. The instrument is based on a commercially available diamond chip, into which an NV ensemble is ion-implanted at a depth of ~10 nm below the diamond surface. The spectrometer operates at low magnetic fields (~300 G) and requires standard optical and microwave (MW) components for NV spin preparation, manipulation, and readout. We demonstrate the utility of this device for nanoscale proton and fluorine NMR spectroscopy, as well as for the detection of transition metals via relaxometry. We estimate that the full protocol requires 2-3 months to implement, depending on the availability of equipment, diamond substrates, and user experience.

Fundamental Precision Bounds for Three-Dimensional Optical Localization Microscopy with Poisson Statistics.

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter depth localization is more challenging than lateral localization, considerable effort has been spent on engineering the response of the microscope in a way that reveals increased depth information. Here, we prove the (sub)optimality of these approaches by deriving and comparing to the measurement-independent quantum Cramér-Rao bound (QCRB). We show that existing methods for depth localization with single-objective collection exceed the QCRB, and we gain insight into the bound by proposing an interferometer arrangement that approaches it. We also show that for light collection with two opposed objectives, an established interferometric technique globally reaches the QCRB in all three dimensions simultaneously, and so this represents an interesting case study from the point of view of quantum multiparameter estimation.

High-resolution magnetic resonance spectroscopy using a solid-state spin sensor.

Quantum systems that consist of solid-state electronic spins can be sensitive detectors of nuclear magnetic resonance (NMR) signals, particularly from very small samples. For example, nitrogen-vacancy centres in diamond have been used to record NMR signals from nanometre-scale samples, with sensitivity sufficient to detect the magnetic field produced by a single protein. However, the best reported spectral resolution for NMR of molecules using nitrogen-vacancy centres is about 100 hertz. This is insufficient to resolve the key spectral identifiers of molecular structure that are critical to NMR applications in chemistry, structural biology and materials research, such as scalar couplings (which require a resolution of less than ten hertz) and small chemical shifts (which require a resolution of around one part per million of the nuclear Larmor frequency). Conventional, inductively detected NMR can provide the necessary high spectral resolution, but its limited sensitivity typically requires millimetre-scale samples, precluding applications that involve smaller samples, such as picolitre-volume chemical analysis or correlated optical and NMR microscopy. Here we demonstrate a measurement technique that uses a solid-state spin sensor (a magnetometer) consisting of an ensemble of nitrogen-vacancy centres in combination with a narrowband synchronized readout protocol to obtain NMR spectral resolution of about one hertz. We use this technique to observe NMR scalar couplings in a micrometre-scale sample volume of approximately ten picolitres. We also use the ensemble of nitrogen-vacancy centres to apply NMR to thermally polarized nuclear spins and resolve chemical-shift spectra from small molecules. Our technique enables analytical NMR spectroscopy at the scale of single cells.

Mapping the microscale origins of magnetic resonance image contrast with subcellular diamond magnetometry.

Magnetic resonance imaging (MRI) is a widely used biomedical imaging modality that derives much of its contrast from microscale magnetic field patterns in tissues. However, the connection between these patterns and the appearance of macroscale MR images has not been the subject of direct experimental study due to a lack of methods to map microscopic fields in biological samples. Here, we optically probe magnetic fields in mammalian cells and tissues with submicron resolution and nanotesla sensitivity using nitrogen-vacancy diamond magnetometry, and combine these measurements with simulations of nuclear spin precession to predict the corresponding MRI contrast. We demonstrate the utility of this technology in an in vitro model of macrophage iron uptake and histological samples from a mouse model of hepatic iron overload. In addition, we follow magnetic particle endocytosis in live cells. This approach bridges a fundamental gap between an MRI voxel and its microscopic constituents.

Superresolution optical magnetic imaging and spectroscopy using individual electronic spins in diamond.

Nitrogen vacancy (NV) color centers in diamond are a leading modality for both superresolution optical imaging and nanoscale magnetic field sensing. In this work, we address the key challenge of performing optical magnetic imaging and spectroscopy selectively on multiple NV centers that are located within a diffraction-limited field-of-view. We use spin-RESOLFT microscopy to enable precision nanoscale mapping of magnetic field patterns with resolution down to ~20 nm, while employing a low power optical depletion beam. Moreover, we use a shallow NV to demonstrate the detection of proton nuclear magnetic resonance (NMR) signals exterior to the diamond, with 50 nm lateral imaging resolution and without degrading the proton NMR linewidth.

Control and local measurement of the spin chemical potential in a magnetic insulator.

The spin chemical potential characterizes the tendency of spins to diffuse. Probing this quantity could provide insight into materials such as magnetic insulators and spin liquids and aid optimization of spintronic devices. Here we introduce single-spin magnetometry as a generic platform for nonperturbative, nanoscale characterization of spin chemical potentials. We experimentally realize this platform using diamond nitrogen-vacancy centers and use it to investigate magnons in a magnetic insulator, finding that the magnon chemical potential can be controlled by driving the system's ferromagnetic resonance. We introduce a symmetry-based two-fluid theory describing the underlying magnon processes, measure the local thermomagnonic torque, and illustrate the detection sensitivity using electrically controlled spin injection. Our results pave the way for nanoscale control and imaging of spin transport in mesoscopic systems.

Nanodiamond-enhanced MRI via in situ hyperpolarization.

Nanodiamonds are of interest as nontoxic substrates for targeted drug delivery and as highly biostable fluorescent markers for cellular tracking. Beyond optical techniques, however, options for noninvasive imaging of nanodiamonds in vivo are severely limited. Here, we demonstrate that the Overhauser effect, a proton-electron polarization transfer technique, can enable high-contrast magnetic resonance imaging (MRI) of nanodiamonds in water at room temperature and ultra-low magnetic field. The technique transfers spin polarization from paramagnetic impurities at nanodiamond surfaces to 1H spins in the surrounding water solution, creating MRI contrast on-demand. We examine the conditions required for maximum enhancement as well as the ultimate sensitivity of the technique. The ability to perform continuous in situ hyperpolarization via the Overhauser mechanism, in combination with the excellent in vivo stability of nanodiamond, raises the possibility of performing noninvasive in vivo tracking of nanodiamond over indefinitely long periods of time.

Efficiency of Cathodoluminescence Emission by Nitrogen-Vacancy Color Centers in Nanodiamonds.

Correlated electron microscopy and cathodoluminescence (CL) imaging using functionalized nanoparticles is a promising nanoscale probe of biological structure and function. Nanodiamonds (NDs) that contain CL-emitting color centers are particularly well suited for such applications. The intensity of CL emission from NDs is determined by a combination of factors, including particle size, density of color centers, efficiency of energy deposition by electrons passing through the particle, and conversion efficiency from deposited energy to CL emission. This paper reports experiments and numerical simulations that investigate the relative importance of each of these factors in determining CL emission intensity from NDs containing nitrogen-vacancy (NV) color centers. In particular, it is found that CL can be detected from NV-doped NDs with dimensions as small as ≈40 nm, although CL emission decreases significantly for smaller NDs.

Optical magnetic detection of single-neuron action potentials using quantum defects in diamond.

Magnetic fields from neuronal action potentials (APs) pass largely unperturbed through biological tissue, allowing magnetic measurements of AP dynamics to be performed extracellularly or even outside intact organisms. To date, however, magnetic techniques for sensing neuronal activity have either operated at the macroscale with coarse spatial and/or temporal resolution-e.g., magnetic resonance imaging methods and magnetoencephalography-or been restricted to biophysics studies of excised neurons probed with cryogenic or bulky detectors that do not provide single-neuron spatial resolution and are not scalable to functional networks or intact organisms. Here, we show that AP magnetic sensing can be realized with both single-neuron sensitivity and intact organism applicability using optically probed nitrogen-vacancy (NV) quantum defects in diamond, operated under ambient conditions and with the NV diamond sensor in close proximity (∼10 µm) to the biological sample. We demonstrate this method for excised single neurons from marine worm and squid, and then exterior to intact, optically opaque marine worms for extended periods and with no observed adverse effect on the animal. NV diamond magnetometry is noninvasive and label-free and does not cause photodamage. The method provides precise measurement of AP waveforms from individual neurons, as well as magnetic field correlates of the AP conduction velocity, and directly determines the AP propagation direction through the inherent sensitivity of NVs to the associated AP magnetic field vector.

Probing scalar coupling differences via long-lived singlet states.

We probe small scalar coupling differences via the coherent interactions between two nuclear spin singlet states in organic molecules. We show that the spin-lock induced crossing (SLIC) technique enables the coherent transfer of singlet order between one spin pair and another. The transfer is mediated by the difference in syn and anti vicinal or long-range J couplings among the spins. By measuring the transfer rate, we calculate a J coupling difference of 8±2mHz in phenylalanine-glycine-glycine and 2.57±0.04Hz in glutamate. We also characterize a coherence between two singlet states in glutamate, which may enable the creation of a long-lived quantum memory.

Nanoscale NMR spectroscopy and imaging of multiple nuclear species.

Nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging (MRI) provide non-invasive information about multiple nuclear species in bulk matter, with wide-ranging applications from basic physics and chemistry to biomedical imaging. However, the spatial resolution of conventional NMR and MRI is limited to several micrometres even at large magnetic fields (>1 T), which is inadequate for many frontier scientific applications such as single-molecule NMR spectroscopy and in vivo MRI of individual biological cells. A promising approach for nanoscale NMR and MRI exploits optical measurements of nitrogen-vacancy (NV) colour centres in diamond, which provide a combination of magnetic field sensitivity and nanoscale spatial resolution unmatched by any existing technology, while operating under ambient conditions in a robust, solid-state system. Recently, single, shallow NV centres were used to demonstrate NMR of nanoscale ensembles of proton spins, consisting of a statistical polarization equivalent to ∼100-1,000 spins in uniform samples covering the surface of a bulk diamond chip. Here, we realize nanoscale NMR spectroscopy and MRI of multiple nuclear species ((1)H, (19)F, (31)P) in non-uniform (spatially structured) samples under ambient conditions and at moderate magnetic fields (∼20 mT) using two complementary sensor modalities.

A genetic strategy for probing the functional diversity of magnetosome formation.

Model genetic systems are invaluable, but limit us to understanding only a few organisms in detail, missing the variations in biological processes that are performed by related organisms. One such diverse process is the formation of magnetosome organelles by magnetotactic bacteria. Studies of model magnetotactic α-proteobacteria have demonstrated that magnetosomes are cubo-octahedral magnetite crystals that are synthesized within pre-existing membrane compartments derived from the inner membrane and orchestrated by a specific set of genes encoded within a genomic island. However, this model cannot explain all magnetosome formation, which is phenotypically and genetically diverse. For example, Desulfovibrio magneticus RS-1, a δ-proteobacterium for which we lack genetic tools, produces tooth-shaped magnetite crystals that may or may not be encased by a membrane with a magnetosome gene island that diverges significantly from those of the α-proteobacteria. To probe the functional diversity of magnetosome formation, we used modern sequencing technology to identify hits in RS-1 mutated with UV or chemical mutagens. We isolated and characterized mutant alleles of 10 magnetosome genes in RS-1, 7 of which are not found in the α-proteobacterial models. These findings have implications for our understanding of magnetosome formation in general and demonstrate the feasibility of applying a modern genetic approach to an organism for which classic genetic tools are not available.