Abstract
Developing superior quantum sensing strategies ranging from ultrahigh precision measurements to complex structural analyses is at the heart of quantum technologies. Although strategies to enhance the sensing precision using quantum resources, such as entanglement among sensors, have been abundantly demonstrated, the signal correlation among quantum sensors is rarely exploited. Here we develop a new sensing paradigm that exploits the signal correlation among multiple quantum sensors to resolve overlapping signals from multiple targets that individual sensors cannot resolve and complex structural construction techniques struggles with. By using three nitrogen-vacancy centres as a quantum electrometer system, we demonstrate this multisensor paradigm by resolving the fluctuating electric fields of individual defects from ensemble signals. We image the three-dimensional distribution of 16 dark electronic point defects in a diamond with accuracy approaching 1.7 nm via a GPS-like localization method. Furthermore, we obtain the real-time charge dynamics of individual point defects and visualize how the dynamics induce the well-known optical spectral diffusion. The multisensor paradigm extends the quantum sensing toolbox and offers new possibilities for structural analysis.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
All the key data that support the findings of this study are included in the Article and its Supplementary Information. Further datasets and raw measurements are available from the corresponding authors upon reasonable request.
Code availability
All code that support the findings of this study is available from the corresponding authors upon reasonable request.
References
Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).
Nagata, T. et al. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).
Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).
Hosten, O. et al. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).
Mason, D. et al. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).
Rovny, J. et al. Nanoscale covariance magnetometry with diamond quantum sensors. Science 378, 1301–1305 (2022).
Clarke, J. & Braginski, A. I. The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems (Wiley-VCH, 2003).
Fagaly, R. L. Superconducting quantum interference device instruments and applications. Rev. Sci. Instrum. 77, 101101 (2006).
Budker, D. & Romalis, M. Optical magnetometry. Nat. Phys. 3, 227–234 (2007).
Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).
Ludlow, A. D. et al. Optical atomic clocks. Rev. Mod. Phys. 87, 637 (2015).
Boulder Atomic Clock Optical Network (BACON) Collaboration. Frequency ratio measurements at 18-digit accuracy using an optical clock network. Nature 591, 564–569 (2021).
Bothwell, T. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022).
Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).
Mamin, H. J. et al. Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor. Science 339, 557–560 (2013).
Staudacher, T. et al. Nuclear magnetic resonance spectroscopy on a (5-nanometer)3 sample volume. Science 339, 561–563 (2013).
Shi, F. et al. Single-protein spin resonance spectroscopy under ambient conditions. Science 347, 1135–1138 (2015).
Lovchinsky, I. et al. Magnetic resonance spectroscopy of an atomically thin material using a single-spin qubit. Science 355, 503–507 (2017).
Smits, J. et al. Two-dimensional nuclear magnetic resonance spectroscopy with a microfluidic diamond quantum sensor. Sci. Adv. 5, eaaw7895 (2019).
Dolde, F. et al. Electric-field sensing using single diamond spins. Nat. Phys. 7, 459–463 (2011).
Dolde, F. et al. Nanoscale detection of a single fundamental charge in ambient conditions using the NV− center in diamond. Phys. Rev. Lett. 112, 097603 (2014).
Li, R. et al. Nanoscale electrometry based on a magnetic-field-resistant spin sensor. Phys. Rev. Lett. 124, 247701 (2020).
Tamarat, P. et al. Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond. New J. Phys. 10, 045004 (2008).
Bassett, L. C. et al. Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields. Phys. Rev. Lett. 107, 266403 (2011).
Mittiga, T. et al. Imaging the local charge environment of nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 121, 246402 (2018).
Block, M. et al. Optically enhanced electric field sensing using nitrogen-vacancy ensembles. Phys. Rev. Appl. 16, 024024 (2021).
Lozovoi, A. et al. Optical activation and detection of charge transport between individual colour centres in diamond. Nat. Electron. 4, 717–724 (2021).
Aslam, N. et al. Nanoscale nuclear magnetic resonance with chemical resolution. Science 357, 67–71 (2017).
Schmitt, S. et al. Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor. Science 356, 832–837 (2017).
Glenn, D. R. et al. High-resolution magnetic resonance spectroscopy using a solid-state spin sensor. Nature 555, 351–354 (2018).
Zopes, J. et al. Three-dimensional localization spectroscopy of individual nuclear spins with sub-angstrom resolution. Nat. Commun. 9, 4678 (2018).
Abobeih, M. H. et al. A ten-qubit solid-state spin register with quantum memory up to one minute. Nature 576, 411–415 (2019).
Perunicic, V. S. et al. A quantum spin-probe molecular microscope. Nat. Commun. 7, 12667 (2016).
Günther, H. NMR Spectroscopy: Basic Principles, Concepts and Applications in Chemistry (John Wiley & Sons, 2013).
Kost, M., Cai, J. & Plenio, M. B. Resolving single molecule structures with nitrogen-vacancy centers in diamond. Sci. Rep. 5, 11007 (2015).
Kogan, S. Electronic Noise and Fluctuations in Solids (Cambridge Univ. Press, 2008).
de Leon, N. P. et al. Materials challenges and opportunities for quantum computing hardware. Science 372, abb2823 (2021).
Golding, I. et al. Real-time kinetics of gene activity in individual bacteria. Cell 123, 1025–1036 (2005).
Chubb, J. R. et al. Transcriptional pulsing of a developmental gene. Curr. Biol. 16, 1018–1025 (2006).
Suter, D. M. et al. Mammalian genes are transcribed with widely different bursting kinetics. Science 332, 472–474 (2011).
Ribeiro, M. et al. Human breast cancer cells demonstrate electrical excitability. Front. Neurosci. 14, 404 (2020).
Frauenfelder, H., Sligar, S. G. & Wolynes, P. G. The energy landscapes and motions of proteins. Science 254, 1598–1603 (1991).
König, I. et al. Single-molecule spectroscopy of protein conformational dynamics in live eukaryotic cells. Nat. Methods 12, 773–773 (2015).
Lerner, E. et al. Toward dynamic structural biology: two decades of single-molecule Förster resonance energy transfer. Science 359, eaan1133 (2018).
Harroun, S. G. et al. Monitoring protein conformational changes using fluorescent nanoantennas. Nat. Methods 19, 71–80 (2022).
Chen, Y.-C. et al. Laser writing of coherent colour centres in diamond. Nat. Photon. 11, 77–80 (2016).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced positioning and clock synchronization. Nature 412, 417–419 (2001).
Wolfowicz, G. et al. Quantum guidelines for solid-state spin defects. Nat. Rev. Mater. 6, 906–925 (2021).
Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).
Acknowledgements
This work is supported by the National Natural Science Foundation of China (grant nos. 92265204 and T2325023 to Y.W., T2125011 to F.S., 12104446 to W.J. and 12104447 to M.W.), the CAS (GJJSTD20200001 to J.D.), the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302200 to J.D. and Y.W.), the Anhui Initiative in Quantum Information Technologies (grant no. AHY050000 to J.D.) and the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Contributions
J.D. and Y.W. supervised the project. Y.W. designed the experiments. W.J., Z.L. and Y.G. performed the experiments. J.Z., P.Y. and M.W prepared the sample. Z.H., Y.G. and K.X. conducted the STORM measurements. W.J., Z.L., Z.H., S.D. and Y.C. performed the calculations. Y.W., W.J., J.D. and F.S. wrote the paper. All authors discussed the results and commented on the paper.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Photonics thanks Tim Hugo Taminiau and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data
Extended Data Fig. 1 PLE spectrum for the three NVs.
(a) The full spectrum of the three NVs. The peaks are colored according to the corresponding NVs: blue for NV1, orange for NV2 and green for NV3. (b) Fit the spectra for the transverse strain field components. The longitudinal components are set to zero. The expected frequencies of all the transitions depending on the transverse strain field are plotted in solid grey lines.
Extended Data Fig. 2 The flowchart and pulse sequences for the experiments.
(a) The flowchart of the experiments control logic. One of the three NVs is chosen as a reference and labeled as NVA; the other two NVs are labeled as NVB and NVC. A single experiment run is started by checking the resonance and charge state of NVA, namely ‘CR check’49. If NVA passes the resonance check, then the PLE of NVA Ey is measured. If NVA fails the charge check, a 50 µs 532 nm laser pulse is applied to reset the charge state of NVA. If NVA fails the resonance check but passes the charge check, then Ex and E1,2 PLE spectra are measured to calibrate the transition wavelengths. After the wavelength calibration, if NVA still fails resonance check, an auto-focusing process with Ex and \({E}_{\mathrm{1,2}}\) lasers is applied, labeled as ‘637 AF’. These steps are repeated until NVA passes the resonance check, ensuring NVA’s resonance and position are tracked in the experiments. After measuring NVA’s Ey PLE spectrum, the spectra of NVB and NVC are measured. For NVB and NVC, E1,2 PLE spectrum is first measured to determine the charge state. If the E1,2 peak is missing, the subsequent Ex and Ey measurements will be skipped. After measuring all the spectra, another round of CR checks for the three NVs is applied to detect ionization events during the PLE measurements. Finally, a 532 nm laser pulse of 500 µs is applied to disturb the defect charge state deliberately. (b–e) The pulse sequences for the steps in (a).
Extended Data Fig. 3 The 2D differential spectra of (a) NV1, (b) NV2 and (c) NV3.
The color of the points indicates the charge state change of the NVs, and the label \(\Delta {{\bf{f}}}^{i\leftarrow j}\) indicates the spectral shift of NVi caused by adding a charge at NVj. The most evident pattern here is caused by the spectral shift from the other two NVs, as marked by the arrows. The label \(\text{NV}{i}^{a\to b}\) indicates that the NVi charge state changes from a to b. To reveal the defects’ pattern, the spectra results shown in the main text are with the NVs’ electric field removed.
Extended Data Fig. 4 The decomposition of the raw PLE spectra of the three NVs.
(a–c) The raw PLE spectra within consecutive scans of the Ex and Ey transitions of NV2, NV1 and NV3 (in the experiment order). The transition frequencies are relative to 637.2 nm. The blue data points are the raw experimental results of PLE spectra peak position with evident spectral diffusion of a peak-to-peak variation around 200 MHz. The pink, orange and green bars indicate the contributions of spectral shifts due to NVs’ charges, resolved defects’ dynamics (d) and background electric field from distant defects (e). The purple data points are the expected spectra with all the shifts corrected, which are nearly diffusion-free with a peak-to-peak variant close to the natural linewidth of 13 MHz. Arrows mark the spectral shifts caused by the resolved defects. (d) The resolved defect charge dynamics. The p10* and p12* are possibly defects with at least three charge states or two indistinguishable defects. (e) The common-mode background electric field reconstructed by the three NVs.
Supplementary information
Supplementary Information
Supplementary Sections I–VI, Figs. 1–21 and Tables 1–11.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ji, W., Liu, Z., Guo, Y. et al. Correlated sensing with a solid-state quantum multisensor system for atomic-scale structural analysis. Nat. Photon. 18, 230–235 (2024). https://doi.org/10.1038/s41566-023-01352-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41566-023-01352-4
