Abstract
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 samples1,2,3, with sensitivity sufficient to detect the magnetic field produced by a single protein4. However, the best reported spectral resolution for NMR of molecules using nitrogen–vacancy centres is about 100 hertz5. 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 hertz6) 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 protocol7,8,9 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.
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Acknowledgements
This material is based on work supported by, or supported in part by, the US Army Research Laboratory and the US Army Research Office under contract/grant number W911NF1510548. D.B.B. was partially supported by the German Research Foundation (BU 3257/1-1). M.D.L. acknowledges support from the Gordon and Betty Moore foundation. We thank R. Fu for assisting with acquisition of the electromagnet used to apply the bias field, M. Rosen for guidance on NMR techniques and S. DeVience for assisting with SpinDynamica calculations of NMR spectra at low B0.
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R.L.W., D.R.G. and D.B.B. devised the synchronized readout technique. D.R.G., D.B.B. and R.L.W. conceived the application of the technique to picolitre-scale NMR measurements, designed the experiments and analysed the data. D.B.B. and D.R.G. designed and constructed the ensemble NV magnetometer and wrote the accompanying control software. J.L. carried out the single-NV synchronized readout experiments with incoherent averaging. M.D.L., H.P. and R.L.W. conceived the application of NV diamond magnetometry to NMR detection at short length scales. All authors discussed the results and participated in writing the manuscript.
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Extended data figures and tables
Extended Data Figure 1 Sensitivity of the NV-ensemble sensor.
a, Synchronized readout (SR) measurements of magnetic test signals from a nearby coil antenna at fcoil = 3.742 MHz (Supplementary Methods 1). The control voltage for the AC current source of the coil was varied from Vc = 0 to Vc = 0.35 V. Each blue trace corresponds to a different value of the control voltage. The amplitude of the oscillating magnetic field that is produced by the coil (bac) is proportional to Vc. The amplitude of the measured synchronized readout signal increases with Vc. b, Synchronized readout signal data (blue points) as a function of control voltage Vc at constant time tmin ≈ 0.53 ms, obtained by cutting the data shown in a along the dashed line. The red line is a sinusoidal fit to the data, from which we obtain the control voltage Vc = 0.22 V that produces a π/2 NV phase accumulation in a single magnetometry subsequence. The π/2 NV phase accumulation occurs when the fluorescence signal is at its minimum, S(π/2). This provides a calibration for the amplitude of the applied test signal. c, Synchronized readout amplitude spectrum of a 10.0-nT test signal (fcoil = 3.752 MHz), recorded in T = 0.96 s. The calibrated signal amplitude defines the vertical axis of the plot. The rectangular window shows the frequency range used to estimate the noise in the spectrum. The noise amplitude σB is determined by comparing with the calibrated test signal. d, Synchronized readout noise measurements as a function of averaging time for acquisition durations of 0.96 s (blue circles) and 0.05 s (grey boxes). A power-law fit to the 0.96 s data (red line) indicates an inverse square-root scaling with time and a sensitivity of ηB = 32 ± 4 pT Hz−1/2. AU, arbitrary units; RMS, root-mean-square.
Extended Data Figure 2 Electromagnet stabilization.
a, Time-series data of magnetic field (B0) deviations, recorded at the primary (NMR) NV-diamond-ensemble sensor, once every 5 min, over 48 h. b, Histogram of the data in a, showing a Gaussian distribution of magnetic-field deviations with a standard deviation of 46 nT. Because the measurement precision of the sensors and the current precision of the coil used to correct B0 were both much smaller than the actual B0 fluctuations, the deviation from the set-point was effectively zero immediately after every feedback adjustment. Assuming linear drift of the magnetic field during each (5-min) feedback interval, the average magnetic-field deviation from the set-point during the interval was approximately half the value recorded at the end of the interval. The real standard deviation of the magnetic-field fluctuations at the primary NV-NMR sensor was therefore estimated to be about 23 nT. c, Schematic of the electromagnet and sensors, drawn to scale. The black coils are the main magnet coils (88 mT); copper coils are the correction coils for fast control of B0.
Extended Data Figure 3 Estimate of NMR measurement volume.
a, Fluorescence image of the NV sensing volume. The image shown has been stretched by 21/2 in the horizontal (x) direction to account for the 45° angle between the imaging plane and the diamond surface. Scale bar, 30 μm. b, c, Cuts through the image in a (horizontal, b; vertical, c) fitted to Gaussian line shapes. The extracted spot size was 27 μm FWHM in x and 20 μm in y. d, Example random configuration of NV centres (purple) and sample protons (grey) generated by the Monte Carlo calculation (Supplementary Note 3) used to estimate the total NMR signal magnitude integrated over the sensor. The NV-sensor volume is modelled as an elliptic cylinder with semi-axes of 14 μm in x and 10 μm in y and a height of 13 μm in z. The set of protons shown corresponds to a 25 pl half-ellipsoid measurement volume. The diamond surface is at z = 0. e, Calculated NMR signal, integrated over the NV-sensor volume and normalized to the asymptotic NMR signal at large sample volume. The integral over the sample was carried out using half-ellipsoid, hemispheric and cube-shaped volumes; the volume at which the protons contained therein produced a normalized signal of 0.5 was less than 10 pl in each case. Error bars are numerical uncertainties (1σ) obtained from 10 repetitions of the Monte Carlo calculation. A.U., arbitrary units.
Extended Data Figure 4 Scaling of the NV magnetic back-action calculated as a function of the position in the NMR sample.
a–d, The position-dependent back-action magnetic field in the NMR sample volume, produced by spin-polarized NV centres during CASR sensing, is calculated numerically (Supplementary Note 4). The B-field integral factors into an NV-density-dependent constant (74 nT for the present sensor) and a dimensionless, position-dependent geometric factor (colour scale). The NV magnetization is approximated as a two-dimensional Gaussian in x and y (with FWHMs of 28 μm and 20 μm, respectively) to represent the laser-intensity-dependent NV polarization, and as a step function in z (so that it is non-zero only between z = −13 μm and 0 μm) to represent the finite extent of the NV layer below the diamond surface. The geometric factor is calculated in several planes above the diamond surface, including z = 2 μm (a), z = 5 μm (b), z = 8 μm (c) and z = 10 μm (d). Even at a distance of only about 2 μm above the diamond surface, the maximum range of the geometric factor is approximately between −1 and +1. This corresponds to an approximately ±74-nT (or about ±1 p.p.m. of B0) shift in the magnetic field seen by the protons during each CASR magnetometry subsequence due to the NV centres. The back-action shift is much smaller than this magnetic-field shift in most of the measurement volume.
Extended Data Figure 5 Synchronized readout spectral resolution measured using signals from a coil antenna.
a, Power spectrum of the synchronized readout signal obtained with a single-NV magnetic sensor in a confocal microscope (Supplementary Methods 5). The synchronized readout protocol used an iteration time of τSR = 75 μs and the total experiment duration was T = nτSR = 112.5 s, for n = 1.5 × 106 iterations. Data shown are the average of Navg = 100 experiments. The observed spectral width was 5.2 mHz (FWHM). Independent, spectrally narrow signal sources were used to drive each of the three detected frequencies. Successive synchronized readout sequences were incoherently averaged, resulting in poor a signal-to-noise ratio compared to CASR. b, Power spectrum of the synchronized readout signal obtained with an NV-ensemble magnetic sensor. The synchronized readout protocol used an iteration time of τSR = 75 μs and the total experiment duration was T = nτSR = 112.5 s, for n = 1.5 × 106 iterations. The spectrum shown is for a single average (Navg = 1). The observed spectral width was again 5.2 mHz (FWHM). c, Power spectrum of the synchronized readout signal obtained with an NV-ensemble magnetic sensor. The synchronized readout protocol used an iteration time of τSR = 1.2 ms and the total experiment duration was T = nτSR = 3,000 s, for n = 2.5 × 106 iterations. The observed spectral width was 0.4 mHz (FWHM), substantially broader than the Fourier limit. The measured line widths for the three signals were consistent to within about 10%, suggesting that the spectral resolution in this measurement was limited by the stability of the timing source used to control the synchronized readout protocol.
Extended Data Figure 6 Spatial inhomogeneity of B0.
a, b, Transverse gradients in the magnetic bias field B0, sampled in the vicinity of the NMR measurement volume using pulsed ESR applied to the NV centres (Supplementary Methods 6). Local magnetic fields are determined by scanning the excitation laser across the diamond surface in the u direction (parallel to the diamond face, along the line with maximum projection on the cylindrical axis of the magnet poles; a) and the v direction (parallel to the diamond face, along the line perpendicular to the magnet axis; b). NV-ensemble ESR spectra were recorded at each scan position and the scan was repeated three times (n = 3). Error bars were estimated by computing the standard error in the mean 
of magnetic-field values over the repeated measurements at each scan position. The observed magnetic-field gradient in the v direction, dB0/dv ≈ 10 μT mm−1, is expected to yield a FNP spectral signal width of about 8.5 Hz (or about 2.3 p.p.m.) for the NMR measurement volume of diameter about 20 μm. This value is consistent with the observed FNP line widths of 8–10 Hz for water (Fig. 2c).
Extended Data Figure 7 Calculated and measured ethyl formate spectra.
a, Measured and calculated CASR NMR power spectra (offset for clarity) of ethyl formate at B0 = 88 mT. The blue trace is the original measurement, reproduced from Fig. 3c. The grey trace is a second measurement, carried out under the same conditions and with a fresh sample, to verify repeatability. The red trace is the calculated spectrum (Supplementary Note 8), obtained using the molecular parameters measured in bulk NMR at high field. b, High-field (reference proton frequency fref = 500 MHz) NMR amplitude spectra of ethyl formate. Spectral constants extracted from these data were used to calculate the low-field spectrum in a. The top-left panel shows the full spectrum; the other panels show zoomed-in regions of the spectrum corresponding to one chemical-shift group. The blue circles are the recorded data; the red lines are fits to sums of Lorentzian line shapes used to extract the molecular parameters. Because the expected triplet for the isolated proton (group III) is unresolved, we used the largest J-coupling consistent with the data. The dotted grey lines show the underlying triplet line shapes.
Extended Data Figure 8 Comparison of NV-ensemble CASR to micrometre-scale inductive NMR detector technologies.
Figure adapted from ref. 33 with permission of The Royal Society of Chemistry (https://doi.org/10.1039/C2SM26065D). Two additional inductive NMR data points from more recent studies have also been included25,34. The limit of detection is defined as the minimum number of nuclear spins in the sample volume needed to obtain a signal-to-noise ratio of 3 in 1 s of averaging. The sensitivity of the inductive detectors is scaled to a common bias field of B0 = 14.1 T, according to the convention of ref. 33. The CASR NMR sensitivity for our experiments (large red square) is calculated from the glycerol FNP measurements at B0 = 0.088 T, without scaling the bias field. Projected CASR sensitivities (small red squares) are calculated for both the 10-pl measurement volume at B0 = 3 T and a scaled-up sensor with a measurement volume of about 10 nl (Supplementary Note 9), also at B0 = 3 T. Realizing NV-ensemble CASR measurements at even higher bias fields would be very challenging technically owing to the large NV Rabi frequencies required; we therefore do not extrapolate CASR NMR to B0 = 14.1 T for this comparison.
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Glenn, D., Bucher, D., Lee, J. et al. High-resolution magnetic resonance spectroscopy using a solid-state spin sensor. Nature 555, 351–354 (2018). https://doi.org/10.1038/nature25781
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DOI: https://doi.org/10.1038/nature25781
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