Publication Search Results

ID: 158884
Type: article
Authors: Bauch, Erik; Singh, Swati; Lee, Junghyun; Hart, Connor A.; Schloss, Jennifer M.; Turner, Matthew J.; Barry, John F.; Pham, Linh M.; Bar-Gill, Nir; Yelin, Susanne F.; Walsworth, Ronald L.
Abstract: We present a combined theoretical and experimental study of solid-state spin decoherence in an electronic spin bath, focusing specifically on ensembles of nitrogen-vacancy (NV) centers in diamond and the associated substitutional nitrogen spin bath. We perform measurements of NV spin free-induction decay (FID) times T₂^* and spin-echo coherence times T₂ in 25 diamond samples with nitrogen concentrations [N] ranging from 0.01 to 300 ppm. We introduce a microscopic model and perform numerical simulations to quantitatively explain the degradation of both T₂^* and T₂ over four orders of magnitude in [N]. Our analysis enables us to describe the NV ensemble spin coherence decay shapes as emerging consistently from the contribution of many individual NV centers.

ID: 156478
Type: article
Authors: Ku, Mark J. H.; Zhou, Tony X.; Li, Qing; Shin, Young J.; Shi, Jing K.; Burch, Claire; Anderson, Laurel E.; Pierce, Andrew T.; Xie, Yonglong; Hamo, Assaf; Vool, Uri; Zhang, Huiliang; Casola, Francesco; Taniguchi, Takashi; Watanabe, Kenji; Fogler, Michael M.; Kim, Philip; Yacoby, Amir; Walsworth, Ronald L.

ID: 155695
Type: article
Authors: Miklos, M.; Milbourne, Timothy W.; Haywood, Raphaëlle D.; Phillips, David F.; Saar, Steven H.; Meunier, N.; Cegla, H. M.; Dumusque, X.; Langellier, Nicholas; Maldonado, J.; Malavolta, L.; Mortier, A.; Thompson, S.; Watson, C. A.; Cecconi, M.; Cosentino, R.; Ghedina, A.; Li, C. -H; López-Morales, Mercedes; Molinari, E.; Poretti, Ennio; Sasselov, Dimitar; Sozzetti, A.; Walsworth, Ronald L.
Abstract: Efforts to detect low-mass exoplanets using stellar radial velocities (RVs) are currently limited by magnetic photospheric activity. Suppression of convective blueshift is the dominant magnetic contribution to RV variability in low-activity Sun-like stars. Due to convective plasma motion, the magnitude of RV contributions from the suppression of convective blueshift is related to the depth of formation of photospheric spectral lines for a given species used to compute the RV time series. Meunier et al. used this relation to demonstrate a method for spectroscopic extraction of the suppression of convective blueshift in order to isolate RV contributions, including planetary RVs, that contribute equally to the time series for each spectral line. Here, we extract disk-integrated solar RVs from observations over a 2.5 yr time span made with the solar telescope integrated with the HARPS-N spectrograph at the Telescopio Nazionale Galileo (La Palma, Canary Islands, Spain). We apply the methods outlined by Meunier et al. We are not, however, able to isolate physically meaningful contributions due to the suppression of convective blueshift from this solar data set, potentially because our data set is taken during solar minimum when the suppression of convective blueshift may not sufficiently dominate activity contributions to RVs. This result indicates that, for low- activity Sun-like stars, one must include additional RV contributions from activity sources not considered in the Meunier et al. model at different timescales, as well as instrumental variation, in order to reach the submeter per second RV sensitivity necessary to detect low- mass planets in orbit around Sun-like stars.

ID: 157129
Type: article
Authors: Thompson, A. P. G.; Watson, C. A.; Haywood, Raphaëlle D.; Costes, J. C.; de Mooij, E.; Collier Cameron, A.; Dumusque, X.; Phillips, David F.; Saar, Steven H.; Mortier, A.; Milbourne, T. W.; Aigrain, S.; Cegla, H. M.; Charbonneau, David; Cosentino, R.; Ghedina, A.; Latham, David W.; López-Morales, M.; Micela, G.; Molinari, E.; Poretti, E.; Sozzetti, A.; Thompson, S.; Walsworth, Ronald L.
Abstract: Stellar activity is the major roadblock on the path to finding true Earth-analogue planets with the Doppler technique. Thus, identifying new indicators that better trace magnetic activity (I.e. faculae and spots) is crucial to aid in disentangling these signals from that of a planet's Doppler wobble. In this work, we investigate activity related features as seen in disc-integrated spectra from the HARPS-N solar telescope. We divide high-activity spectral echelle orders by low-activity master templates (as defined using both $\log {R^{\prime }_{HK}}$ and images from the Solar Dynamics Observatory, SDO), creating 'relative spectra'. With resolved images of the surface of the Sun (via SDO), the faculae and spot filling factors can be calculated, giving a measure of activity independent of, and in addition to, $\log {R^{\prime }_{HK}}$ . We find pseudo-emission (and pseudo-absorption) features in the relative spectra that are similar to those reported in our previous work on α Cen B. In α Cen B, the features are shown to correlate better to changes in faculae filling factor than spot filling factor. In this work, we more confidently identify changes in faculae coverage of the visible hemisphere of the Sun as the source of features produced in the relative spectra. Finally, we produce trailed spectra to observe the radial velocity component of the features, which show that the features move in a redward direction as one would expect when tracking active regions rotating on the surface of a star.

ID: 154146
Type: article
Authors: Collier Cameron, A.; Mortier, A.; Phillips, David; Dumusque, X.; Haywood, Raphaëlle D.; Langellier, Nicholas; Watson, C. A.; Cegla, H. M.; Costes, J.; Charbonneau, David; Coffinet, A.; Latham, David W.; Lopez-Morales, Mercedes; Malavolta, L.; Maldonado, J.; Micela, G.; Milbourne, Timothy; Molinari, Emilio; Saar, S. H.; Thompson, S.; Buchschacher, Nicholas; Cecconi, M.; Cosentino, R.; Ghedina, A.; Glenday, Alexander G.; Gonzalez, M.; Li, C. -H; Lodi, M.; Lovis, C.; Pepe, F.; Poretti, E.; Rice, K.; Sasselov, Dimitar; Sozzetti, A.; Szentgyorgyi, Andrew; Udry, S.; Walsworth, Ronald L.
Abstract: The time-variable velocity fields of solar-type stars limit the precision of radial-velocity determinations of their planets' masses, obstructing detection of Earth twins. Since 2015 July, we have been monitoring disc-integrated sunlight in daytime using a purpose-built solar telescope and fibre feed to the HARPS-N stellar radial-velocity spectrometer. We present and analyse the solar radial-velocity measurements and cross-correlation function (CCF) parameters obtained in the first 3 yr of observation, interpreting them in the context of spatially resolved solar observations. We describe a Bayesian mixture- model approach to automated data-quality monitoring. We provide dynamical and daily differential-extinction corrections to place the radial velocities in the heliocentric reference frame, and the CCF shape parameters in the sidereal frame. We achieve a photon-noise-limited radial-velocity precision better than 0.43 m s^-1 per 5-min observation. The day-to-day precision is limited by zero-point calibration uncertainty with an RMS scatter of about 0.4 m s^-1. We find significant signals from granulation and solar activity. Within a day, granulation noise dominates, with an amplitude of about 0.4 m s^-1 and an autocorrelation half-life of 15 min. On longer time-scales, activity dominates. Sunspot groups broaden the CCF as they cross the solar disc. Facular regions temporarily reduce the intrinsic asymmetry of the CCF. The radial-velocity increase that accompanies an active-region passage has a typical amplitude of 5 m s^-1 and is correlated with the line asymmetry, but leads it by 3d. Spectral line-shape variability thus shows promise as a proxy for recovering the true radial velocity.

ID: 152920
Type: article
Authors: Jaskula, J. -C; Shields, B. J.; Bauch, E.; Lukin, M. D.; Trifonov, Andrey S.; Walsworth, Ronald L.
Abstract: Efficient optical read-out of single, solid-state electronic spins at room temperature is a key challenge for nanoscale quantum sensing. Nitrogen-vacancy color centers in diamond have a fast optical spin-state read-out mechanism, but it provides little information in a single shot, because the spin state is destroyed before many photons can be collected. Recently, a technique based on spin-to-charge conversion (SCC) was demonstrated that circumvents this problem by converting the spin state to a long-lived charge state. Here, we study how the choice of spin read-out technique impacts the performance of a single nitrogen-vacancy center in bulk diamond for quantum-sensing applications. Specifically, we show that the SCC technique results in an order-of-magnitude reduction in spin read-out noise per shot and a factor of 5 increase in ac-magnetometry sensitivity compared with the conventional optical read-out method. Crucially, these improvements are obtained for a low collection efficiency and bulk diamond geometry, which opens up the SCC technique to a wide array of sensing applications. We identify applications where single-shot spin read-out noise, rather than sensitivity, is the limiting factor (e.g., low duty cycle pulsed sequences in biomagnetometry involving long dead times).

ID: 154587
Type: article
Authors: Kehayias, Pauli; Turner, M. J.; Trubko, R.; Schloss, J. M.; Hart, C. A.; Wesson, M.; Glenn, D. R.; Walsworth, Ronald L.
Abstract: We present a micrometer-scale-resolution stress imaging method with millimeter field-of-view for diamonds containing a thin surface layer of nitrogen-vacancy (NV) centers. In this method, we reconstruct stress tensor elements over a two-dimensional field of view from NV optically detected magnetic resonance (ODMR) spectra. We use this technique to study how stress inhomogeneity affects NV magnetometry performance and show how NV M_{z ,κ} imaging is a useful and direct way to assess these effects. This tool for mapping stress in diamond will aid optimization of NV-diamond sensing, with wide-ranging applications in the physical and life sciences.

ID: 154385
Type: article
Authors: Levine, Edlyn V.; Turner, Matthew J.; Kehayias, Pauli; Hart, Connor A.; Langellier, Nicholas; Trubko, Raisa; Glenn, David R.; Fu, Roger R.; Walsworth, Ronald L.
Abstract: We provide an overview of the experimental techniques, measurement modalities, and diverse applications of the quantum diamond microscope (QDM). The QDM employs a dense layer of fluorescent nitrogen-vacancy (NV) color centers near the surface of a transparent diamond chip on which a sample of interest is placed. NV electronic spins are coherently probed with microwaves and optically initialized and read out to provide spatially resolved maps of local magnetic fields. NV fluorescence is measured simultaneously across the diamond surface, resulting in a wide-field, two-dimensional magnetic field image with adjustable spatial pixel size set by the parameters of the imaging system. NV measurement protocols are tailored for imaging of broadband and narrowband fields, from DC to GHz frequencies. Here we summarize the physical principles common to diverse implementations of the QDM and review example applications of the technology in geoscience, biology, and materials science.

ID: 155443
Type: article
Authors: Milbourne, Timothy W.; Haywood, Raphaëlle D.; Phillips, David F.; Saar, Steve H.; Cegla, H. M.; Cameron, A. C.; Costes, J.; Dumusque, X.; Langellier, Nicholas; Latham, David W.; Maldonado, J.; Malavolta, L.; Mortier, A.; Palumbo, Michael L.,III; Thompson, S.; Watson, C. A.; Bouchy, F.; Buchschacher, N.; Cecconi, M.; Charbonneau, David; Cosentino, R.; Ghedina, A.; Glenday, Alexander G.; Gonzalez, M.; Li, C. -H; Lodi, M.; López-Morales, Mercedes; Lovis, C.; Mayor, M.; Micela, G.; Molinari, E.; Pepe, F.; Piotto, G.; Rice, K.; Sasselov, Dimitar; Ségransan, D.; Sozzetti, A.; Szentgyorgyi, Andrew; Udry, S.; Walsworth, Ronald L.
Abstract: State-of-the-art radial-velocity (RV) exoplanet searches are currently limited by RV signals arising from stellar magnetic activity. We analyze solar observations acquired over a 3 yr period during the decline of Carrington Cycle 24 to test models of RV variation of Sun-like stars. A purpose-built solar telescope at the High Accuracy Radial-velocity Planet Searcher for the Northern hemisphere (HARPS-N) provides disk- integrated solar spectra, from which we extract RVs and {log}{R}_HK}^{\prime }. The Solar Dynamics Observatory (SDO) provides disk-resolved images of magnetic activity. The Solar Radiation and Climate Experiment (SORCE) provides near- continuous solar photometry, analogous to a Kepler light curve. We verify that the SORCE photometry and HARPS-N {log}{R}_HK}^{\prime } correlate strongly with the SDO-derived magnetic filling factor, while the HARPS-N RV variations do not. To explain this discrepancy, we test existing models of RV variations. We estimate the contributions of the suppression of convective blueshift and the rotational imbalance due to brightness inhomogeneities to the observed HARPS-N RVs. We investigate the time variation of these contributions over several rotation periods, and how these contributions depend on the area of active regions. We find that magnetic active regions smaller than 60 Mm² do not significantly suppress convective blueshift. Our area-dependent model reduces the amplitude of activity-induced RV variations by a factor of two. The present study highlights the need to identify a proxy that correlates specifically with large, bright magnetic regions on the surfaces of exoplanet-hosting stars.

ID: 154254
Type: article
Authors: Ravi, Aakash; Langellier, Nicholas; Phillips, David F.; Buschmann, Malte; Safdi, Benjamin R.; Walsworth, Ronald L.
Abstract: 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 /s² . Our simulations show that detecting accelerations at this level with an ensemble of 10³ 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.

ID: 147883
Type: article
Authors: Backlund, Mikael P.; Shechtman, Yoav; Walsworth, Ronald L.
Abstract: 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.

ID: 144791
Type: article
Authors: Backlund, Mikael P.; Kehayias, Pauli; Walsworth, Ronald L.
Abstract: Diamond-based magnetic field sensors have attracted great interest in recent years. In particular, wide-field magnetic imaging using nitrogen-vacancy (NV) centers in diamond has been previously demonstrated in condensed matter, biological, and paleomagnetic applications. Vector magnetic imaging with NV ensembles typically requires a significant applied field (>10 G ) to resolve the contributions from four crystallographic orientations, hindering studies of magnetic samples that require measurement in low or independently specified bias fields. Here we model and measure the complex amplitude distribution of NV emission at the microscope's Fourier plane and show that by modulating this collected light at the Fourier plane, one can decompose the NV ensemble magnetic resonance spectrum into its constituent orientations by purely optical means. This decomposition effectively extends the dynamic range at a given bias field and enables wide-field vector magnetic imaging at arbitrarily low bias fields, thus broadening potential applications of NV imaging and sensing. Our results demonstrate that NV-based microscopy stands to benefit greatly from Fourier optical approaches, which have already found widespread utility in other branches of microscopy.

ID: 143783
Type: article
Authors: Du, Chunhui; van der Sar, Toeno; Zhou, Tony X.; Upadhyaya, Pramey; Casola, Francesco; Zhang, Huiliang; Onbasli, Mehmet C.; Ross, Caroline A.; Walsworth, Ronald L.; Tserkovnyak, Yaroslav; Yacoby, Amir
Abstract: 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.

ID: 142313
Type: article
Authors: Fu, Roger R.; Weiss, Benjamin P.; Lima, Eduardo A.; Kehayias, Pauli; Araujo, Jefferson F. D. F.; Glenn, David R.; Gelb, Jeff; Einsle, Joshua F.; Bauer, Ann M.; Harrison, Richard J.; Ali, Guleed A. H.; Walsworth, Ronald L.
Abstract: Zircon crystals offer a unique combination of suitability for high-precision radiometric dating and high resistance to alteration. Paleomagnetic experiments on ancient zircons may potentially constrain the history of the earliest geodynamo, which would hold broad implications for the early Earth's interior and atmosphere. However, the ability of zircons to record accurately the geomagnetic field has not been demonstrated. Here we conduct thermal and alternating field (AF) paleointensity experiments on 767.1 thousand year old (ka) zircons from the Bishop Tuff, California. The rapid emplacement of these zircons in a well-characterized magnetic field provides a high-fidelity test of the zircons' intrinsic paleomagnetic recording accuracy. Successful dual heating experiments on eleven zircons measured using a superconducting quantum interference device (SQUID) microscope yield a mean paleointensity of 54.1 ± 6.8?T (1?; 42.6 ± 5.3?T after excluding possible maghemite-bearing zircons), which is consistent with high-precision results from Bishop Tuff whole rock (43.0 ± 3.2?T). High-resolution quantum diamond magnetic (QDM) mapping, electron microscopy, and X-ray tomography indicate that the bulk of the remanent magnetization in Bishop Tuff zircons is carried by Fe oxides associated with apatite inclusions, which may be susceptible to destruction via metamorphism and aqueous alteration in older zircons. As such, while zircons can reliably record the geomagnetic field, robust zircon-derived paleomagnetic results require careful characterization of the ferromagnetic carrier and demonstration of their occurrence in primary inclusions. We further conclude that a combination of quantum diamond magnetometry and high-resolution imaging can provide detailed, direct characterization of the ferromagnetic mineralogy of geological samples.

ID: 143261
Type: article
Authors: Waddington, David E. J.; Sarracanie, Mathieu; Zhang, Huiliang; Salameh, Najat; Glenn, David R.; Rej, Ewa; Gaebel, Torsten; Boele, Thomas; Walsworth, Ronald L.; Reilly, David J.; Rosen, Matthew S.
Abstract: 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.

ID: 138758
Type: article
Authors: Devience, Stephen J.; Walsworth, Ronald L.; Rosen, Matthew S.
Abstract: 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 ± 2 mHz in phenylalanine-glycine-glycine and 2.57 ± 0.04 Hz in glutamate. We also characterize a coherence between two singlet states in glutamate, which may enable the creation of a long-lived quantum memory.

ID: 141936
Type: article
Authors: Kolkowitz, S.; Pikovski, I.; Langellier, N.; Lukin, M. D.; Walsworth, Ronald L.; Ye, J.
Abstract: We propose a space-based gravitational wave (GW) detector consisting of two spatially separated, drag-free satellites sharing ultrastable optical laser light over a single baseline. Each satellite contains an optical lattice atomic clock, which serves as a sensitive, narrowband detector of the local frequency of the shared laser light. A synchronized two-clock comparison between the satellites will be sensitive to the effective Doppler shifts induced by incident GWs at a level competitive with other proposed space-based GW detectors, while providing complementary features. The detected signal is a differential frequency shift of the shared laser light due to the relative velocity of the satellites, and the detection window can be tuned through the control sequence applied to the atoms' internal states. This scheme enables the detection of GWs from continuous, spectrally narrow sources, such as compact binary inspirals, with frequencies ranging from ˜3 mHz - 10 Hz without loss of sensitivity, thereby bridging the detection gap between space-based and terrestrial optical interferometric GW detectors. Our proposed GW detector employs just two satellites, is compatible with integration with an optical interferometric detector, and requires only realistic improvements to existing ground-based clock and laser technologies.

ID: 139125
Type: article
Authors: Lovchinsky, I.; Sushkov, A. O.; Urbach, E.; de Leon, N. P.; Choi, S.; de Greve, K.; Evans, R.; Gertner, R.; Bersin, E.; Müller, C.; McGuinness, L.; Jelezko, F.; Walsworth, Ronald L.; Park, H.; Lukin, M. D.
Abstract: Nuclear magnetic resonance spectroscopy is a powerful tool for the structural analysis of organic compounds and biomolecules but typically requires macroscopic sample quantities. We use a sensor, which consists of two quantum bits corresponding to an electronic spin and an ancillary nuclear spin, to demonstrate room temperature magnetic resonance detection and spectroscopy of multiple nuclear species within individual ubiquitin proteins attached to the diamond surface. Using quantum logic to improve readout fidelity and a surface-treatment technique to extend the spin coherence time of shallow nitrogen-vacancy centers, we demonstrate magnetic field sensitivity sufficient to detect individual proton spins within 1 second of integration. This gain in sensitivity enables high-confidence detection of individual proteins and allows us to observe spectral features that reveal information about their chemical composition.

ID: 138740
Type: article
Authors: Pham, Linh M.; Devience, Stephen J.; Casola, Francesco; Lovchinsky, Igor; Sushkov, Alexander O.; Bersin, Eric; Lee, Junghyun; Urbach, Elana; Cappellaro, Paola; Park, Hongkun; Yacoby, Amir; Lukin, Mikhail; Walsworth, Ronald L.
Abstract: We demonstrate a robust experimental method for determining the depth of individual shallow nitrogen-vacancy (NV) centers in diamond with ˜1 nm uncertainty. We use a confocal microscope to observe single

ID: 140561
Type: article
Authors: Arai, K.; Belthangady, C.; Zhang, H.; Bar-Gill, N.; Devience, S. J.; Cappellaro, P.; Yacoby, A.; Walsworth, Ronald L.
Abstract: Optically detected magnetic resonance using nitrogen-vacancy (NV) colour centres in diamond is a leading modality for nanoscale magnetic field imaging, as it provides single electron spin sensitivity, three-dimensional resolution better than 1 nm (ref. 5) and applicability to a wide range of physical and biological samples under ambient conditions. To date, however, NV-diamond magnetic imaging has been performed using 'real-space' techniques, which are either limited by optical diffraction to ~250 nm resolution or require slow, point-by-point scanning for nanoscale resolution, for example, using an atomic force microscope, magnetic tip, or super-resolution optical imaging. Here, we introduce an alternative technique of Fourier magnetic imaging using NV-diamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phase-encode spatial information on NV electronic spins in wavenumber or 'k-space' followed by a fast Fourier transform to yield real-space images with nanoscale resolution, wide field of view and compressed sensing speed-up.