# Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor

## Abstract

Nuclear magnetic resonance (NMR) is a powerful method for determining the structure of molecules and proteins1. Whereas conventional NMR requires averaging over large ensembles, recent progress with single-spin quantum sensors2,3,4,5,6,7,8,9 has created the prospect of magnetic imaging of individual molecules10,11,12,13. As an initial step towards this goal, isolated nuclear spins and spin pairs have been mapped14,15,16,17,18,19,20,21. However, large clusters of interacting spins—such as those found in molecules—result in highly complex spectra. Imaging these complex systems is challenging because it requires high spectral resolution and efficient spatial reconstruction with sub-ångström precision. Here we realize such atomic-scale imaging using a single nitrogen vacancy centre as a quantum sensor, and demonstrate it on a model system of 27 coupled 13C nuclear spins in diamond. We present a multidimensional spectroscopy method that isolates individual nuclear–nuclear spin interactions with high spectral resolution (less than 80 millihertz) and high accuracy (2 millihertz). We show that these interactions encode the composition and inter-connectivity of the cluster, and develop methods to extract the three-dimensional structure of the cluster with sub-ångström resolution. Our results demonstrate a key capability towards magnetic imaging of individual molecules and other complex spin systems9,10,11,12,13.

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## Data availability

The data that support the findings of this study are available from the corresponding author upon request.

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## Acknowledgements

We thank V. V. Dobrovitski, T. van der Sar, W. Hahn, M. Scheer and R. Zia for valuable discussions. We thank R. F. L. Vermeulen and R. N. Schouten for assistance with the RF electronics, and M. Eschen for assistance with the experimental setup. We acknowledge support from the Netherlands Organisation for Scientific Research (NWO/OCW) through a Vidi grant, as part of the Frontiers of Nanoscience (NanoFront) programme and as part of the Quantum Software Consortium programme (project number 024.003.037/3368).

## Author information

M.H.A. and T.H.T. devised the experiments. M.H.A. performed the experiments. J.R. developed the 3D structure analysis method. M.H.A., J.R. and T.H.T. analysed the data. M.H.A., J.R., M.J.D. and C.E.B. prepared the experimental apparatus. C.E.B. and J.R. developed the RF electronics. H.P.B. and M.A.B. performed preliminary experiments. M.H.A., M.J.D., J.R., C.E.B. and T.H.T. developed the magnetic-field alignment procedure and the 14N echo spectroscopy. M.M. and D.J.T. grew the diamond sample. M.H.A., J.R. and T.H.T. wrote the manuscript with input from all authors. T.H.T. supervised the project.

Correspondence to T. H. Taminiau.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Nir Bar-Gill, Vidya Praveen Bhallamudi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Experimental sequence.

The pulse sequence consists of five parts: sensor preparation, sensor initialization, polarization of the probe spin, double resonance, and detection of the probe spin. Sensor preparation: the NV centre is prepared by excitation with two 637-nm lasers for 150 μs and counting of the detected photons (read-out (RO) laser resonant with the Ex transition and initialization (Init) laser resonant with the E′ transition)24,34. If the number of photons exceeds a certain threshold, the NV is in the negative charge state and resonant with both lasers, and we proceed to the next step. If not, we apply a 515-nm laser (charge reset (RS) laser, 1 ms) and repeat the process24,34. Sensor initialization: the NV electron spin is initialized in the ms = 0 state through spin pumping (Init laser, 100 μs)34. Polarization of the probe spin: first, the NV sensor is brought into a superposition state using a π/2 pulse. Then, a dynamical decoupling sequence of N′ equally spaced π pulses of the form (τr − π − τr)N is applied to the electron spin. This sequence correlates the state of the nuclear spin(s) with the phase of the electron spin. We use two different sequences (see Methods). For sequence B, the microwave (MW) π pulses are interleaved with RF pulses (RF1) that resonantly drive the probe spin(s) (dashed box); see Bradley et al.28 for details. A second π/2 pulse maps the electron phase to the population and the electron spin is read out (RO laser). Double resonance: N echo pulses are applied simultaneously on the probe spin(s) (RF1) and the target spin(s) (RF2), so that the coupling between these spins is isolated. To mitigate pulse errors, we alternate the phases of the pulses following the XY8 scheme42. Detection of the probe spin: the detection sequence is the same as the polarization sequence except for the final RO laser pulse, which is applied for 10 μs and with higher power.

### Extended Data Fig. 2 Ramsey experiments and reconstructed spectra.

a, Schematic of the pulse sequence used in the Ramsey experiment (equivalent to correlation spectroscopy); see Methods and Extended Data Fig. 1 for details. b, Ramsey signal for C2 and the corresponding PSD (5 kHz detuning). The red line represents the central frequency f0. Green lines are the 27 frequencies based on the seven strongest coupling strengths extracted from our high-resolution double-resonance spectroscopy (Supplementary Table 4). These frequencies are given by f0 ± f1 ± f2 ± f3 ± f4 ± f5 ± f6 ± f7, where f1 to f7 are the seven largest measured coupling strengths for C2. ce, The same experiment for C3 (c; ~5 kHz detuning), C15 (d; ~1 kHz detuning) and C5 (e; ~2 kHz detuning).

### Extended Data Fig. 3 Strongly coupled subclusters.

3D plots showing the structure of two strongly coupled subclusters (orange boxes) within the larger cluster (shown in the centre). Ramsey measurements performed on spins within these subclusters show clear beating signals within their dephasing time $${T}_{2}^{\ast }$$ (see, for example, Extended Data Fig. 2). a, Eight-spin subcluster. b, Four-spin subcluster. Couplings above 3 Hz are marked blue, above 20 Hz green and above 50 Hz red. Grey points show the 2D projections of the diamond-lattice coordinates.

### Extended Data Fig. 4 Finding the position of the NV centre.

a, 3D plot showing the 27-nuclear-spin cluster shown in Fig. 4, with the position of the nitrogen spin (green) and vacancy (purple) lattice sites calculated from the measured nitrogen–13C couplings. The grey dots show the 2D projections of the diamond-lattice coordinates. b, Bar plot showing the measured couplings fiN between 13C spin i and the nitrogen spin (grey), as well as the theoretically calculated couplings |CiN|/4π (green). Error bars are one standard deviation. See Supplementary Table 4 for the numerical values. c, Bar plots of Δr for the fitted position of the nitrogen spin (black) and fit errors δx (blue), δy (orange) and δz (green), where the 13C spins are fixed at the diamond-lattice solution. d, Plot of z versus $${r}_{xy}=\sqrt{{x}^{2}+{y}^{2}}$$ for all lattice positions used in the DFT calculation from Nizovtsev et al.33 (blue) and for the appropriately transformed 13C coordinates found in this work (orange). Spins 5, 6, 9, 12 and 19 match a DFT lattice position, whereas the rest of the identified spins are outside the 510 lattice sites simulated. e, Measured electron–13C parallel (top) and perpendicular (bottom) hyperfine couplings for the five spins that are within the DFT calculation volume (red; from Supplementary Table 1), compared with the DFT results from ref. 33 (blue).

### Extended Data Fig. 5 Aligning the magnetic field using a thermal echo sequence.

a, Pulse sequence used for the thermal echo measurement35. The electron spin is prepared in a superposition of the states ms = 0 and ms = −1 in the first half of the sequence and then swapped to a superposition of ms = 0 and ms = +1 for the second half, using a sequence of three closely spaced π pulses. By sweeping τ, the average frequency fTE = (f+1 + f−1)/2 is obtained, which is minimized when B = 0. f±1 are the ms = 0 ↔ ms = ±1 transition frequencies. The NV nitrogen spin is initialized in mI = 0 (ref. 34). b, Magnetic-field alignment by scanning the magnet position in two orthogonal directions. The obtained thermal echo frequencies are fitted with a parabolic function to find the optimum position (that is, minimal fTE). The plots show the frequency difference fTE − 2.877652 GHz. c, The magnet is placed at the optimum position and the measurement is repeated 200 times (over a 10-h period). The obtained average frequency difference is 0.13 kHz, with a standard deviation of 0.27 kHz, which is consistent with the statistical measurement error. Therefore, the total uncertainty for the magnet alignment is ~0.4 kHz, which corresponds to a perpendicular field of 0.5 G or a misalignment angle of 0.07°.

## Supplementary information

### Supplementary Information

This file contains additional details of the methods used in the paper, including supplementary discussion and derivations. In addition, it includes six supplementary figures and five supplementary tables, which summarize the experimental parameters used, nuclear spin properties, measured coupling strengths and obtained spatial coordinates of the spins in the cluster.

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Abobeih, M.H., Randall, J., Bradley, C.E. et al. Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor. Nature 576, 411–415 (2019). https://doi.org/10.1038/s41586-019-1834-7