- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Overcoming Frequency Resolution Limits Using a Solid-State Spin Quantum Sensor

Qingyun Cao1,*,†, Genko T. Genov1,*, Yaoming Chu2,‡, Jianming Cai2,§, Yu Liu3,∥, Alex Retzker4,5, and Fedor Jelezko1

  • *These authors contributed equally to this work.
  • †Contact author: qingyun.cao@uni-ulm.de
  • ‡Contact author: yaomingchu@hust.edu.cn
  • §Contact author: jianmingcai@hust.edu.cn
  • ∥Contact author: yu.liu@uni-ulm.de
PDF

Phys. Rev. Lett. 135, 250806 – Published 19 December, 2025

DOI: https://doi.org/10.1103/llfg-s4rr

Abstract

The ability to determine precisely the separation of two frequencies is fundamental to spectroscopy, yet the resolution limit poses a critical challenge: distinguishing two incoherent signals becomes impossible when their frequencies are sufficiently close. Here, we demonstrate a simple and powerful approach, dubbed superresolution quantum sensing, which experimentally resolves two nearly identical incoherent signals using a solid-state spin quantum sensor. By carefully choosing interrogation times that satisfy the superresolution condition, we eliminate quantum projection noise, overcoming the vanishing distinguishability of signals with near-identical frequencies. This leads to improved resolution, which scales as t−2 in comparison to the standard t−1 scaling. Together with a greatly reduced classical readout noise assisted by a nuclear spin, we are able to achieve sub-kHz resolution with a signal detection time of 80 μs. Our results highlight the potential of quantum sensing to overcome conventional frequency resolution limitations, with broad implications for precision measurements.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (55)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. J. W. Gardner, T. Gefen, S. A. Haine, J. J. Hope, J. Preskill, Y. Chen, and L. McCuller, Stochastic waveform estimation at the fundamental quantum limit, PRX Quantum 6, 030311 (2025).
  3. M. Tsang, R. Nair, and X.-M. Lu, Quantum theory of superresolution for two incoherent optical point sources, Phys. Rev. X 6, 031033 (2016).
  4. R. Nair and M. Tsang, Far-field superresolution of thermal electromagnetic sources at the quantum limit, Phys. Rev. Lett. 117, 190801 (2016).
  5. C. Lupo and S. Pirandola, Ultimate precision bound of quantum and subwavelength imaging, Phys. Rev. Lett. 117, 190802 (2016).
  6. A. Chrostowski, R. Demkowicz-Dobrzański, M. Jarzyna, and K. Banaszek, On super-resolution imaging as a multiparameter estimation problem, Int. J. Quantum. Inform. 15, 1740005 (2017).
  7. T. Gefen, A. Rotem, and A. Retzker, Overcoming resolution limits with quantum sensing, Nat. Commun. 10, 4992 (2019).
  8. S. L. Mouradian, N. Glikin, E. Megidish, K.-I. Ellers, and H. Haeffner, Quantum sensing of intermittent stochastic signals, Phys. Rev. A 103, 032419 (2021).
  9. H. J. Mamin, M. Kim, M. H. Sherwood, C. T. Rettner, K. Ohno, D. D. Awschalom, and D. Rugar, Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor, Science 339, 557 (2013).
  10. T. Staudacher, F. Shi, S. Pezzagna, J. Meijer, J. Du, C. A. Meriles, F. Reinhard, and J. Wrachtrup, Nuclear magnetic resonance spectroscopy on a (5−nanometer)3 sample volume, Science 339, 561 (2013).
  11. N. Staudenmaier, A. Vijayakumar-Sreeja, G. Genov, D. Cohen, C. Findler, J. Lang, A. Retzker, F. Jelezko, and S. Oviedo-Casado, Optimal sensing protocol for statistically polarized nano-NMR with NV centers, Phys. Rev. Lett. 131, 150801 (2023).
  12. A. Rotem, T. Gefen, S. Oviedo-Casado, J. Prior, S. Schmitt, Y. Burak, L. McGuiness, F. Jelezko, and A. Retzker, Limits on spectral resolution measurements by quantum probes, Phys. Rev. Lett. 122, 060503 (2019).
  13. A. Laraoui, F. Dolde, C. Burk, F. Reinhard, J. Wrachtrup, and C. A. Meriles, High-resolution correlation spectroscopy of C13 spins near a nitrogen-vacancy centre in diamond, Nat. Commun. 4, 1651 (2013).
  14. T. Staudacher, N. Raatz, S. Pezzagna, J. Meijer, F. Reinhard, C. A. Meriles, and J. Wrachtrup, Probing molecular dynamics at the nanoscale via an individual paramagnetic centre, Nat. Commun. 6, 8527 (2015).
  15. X. Kong, A. Stark, J. Du, L. P. McGuinness, and F. Jelezko, Towards chemical structure resolution with nanoscale nuclear magnetic resonance spectroscopy, Phys. Rev. Appl. 4, 024004 (2015).
  16. M. Pfender, N. Aslam, H. Sumiya, S. Onoda, P. Neumann, J. Isoya, C. A. Meriles, and J. Wrachtrup, Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters, Nat. Commun. 8, 1 (2017).
  17. T. Rosskopf, J. Zopes, J. M. Boss, and C. L. Degen, A quantum spectrum analyzer enhanced by a nuclear spin memory, npj Quantum Inf. 3, 33 (2017).
  18. N. Aslam, M. Pfender, P. Neumann, R. Reuter, A. Zappe, F. Fávaro de Oliveira, A. Denisenko, H. Sumiya, S. Onoda, J. Isoya, and J. Wrachtrup, Nanoscale nuclear magnetic resonance with chemical resolution, Science 357, 67 (2017).
  19. M. Pfender, P. Wang, H. Sumiya, S. Onoda, W. Yang, D. B. R. Dasari, P. Neumann, X.-Y. Pan, J. Isoya, R.-B. Liu, and J. Wrachtrup, High-resolution spectroscopy of single nuclear spins via sequential weak measurements, Nat. Commun. 10, 594 (2019).
  20. K. S. Cujia, J. M. Boss, K. Herb, J. Zopes, and C. L. Degen, Tracking the precession of single nuclear spins by weak measurements, Nature (London) 571, 230 (2019).
  21. S. Schmitt, T. Gefen, F. M. Stürner, T. Unden, G. Wolff, C. Müller, J. Scheuer, B. Naydenov, M. Markham, S. Pezzagna, J. Meijer, I. Schwarz, M. Plenio, A. Retzker, L. P. McGuinness, and F. Jelezko, Submillihertz magnetic spectroscopy performed with a nanoscale quantum sensor, Science 356, 832 (2017).
  22. J. M. Boss, K. S. Cujia, J. Zopes, and C. L. Degen, Quantum sensing with arbitrary frequency resolution, Science 356, 837 (2017).
  23. D. R. Glenn, D. B. Bucher, J. Lee, M. D. Lukin, H. Park, and R. L. Walsworth, High-resolution magnetic resonance spectroscopy using a solid-state spin sensor, Nature (London) 555, 351 (2018).
  24. Y. Chu, P. Yang, M. Gong, M. Yu, B. Yu, M. B. Plenio, A. Retzker, and J. Cai, Precise spectroscopy of high-frequency oscillating fields with a single-qubit sensor, Phys. Rev. Appl. 15, 014031 (2021).
  25. I. Lovchinsky, A. O. Sushkov, E. Urbach, N. P. de Leon, S. Choi, K. De Greve, R. Evans, R. Gertner, E. Bersin, C. Müller, L. McGuinness, F. Jelezko, R. L. Walsworth, H. Park, and M. D. Lukin, Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic, Science 351, 836 (2016).
  26. Z. Zhao, X. Ye, S. Xu, P. Yu, Z. Yang, X. Kong, Y. Wang, T. Xie, F. Shi, and J. Du, Sub-nanotesla sensitivity at the nanoscale with a single spin, Natl. Sci. Rev. 10, nwad100 (2023).
  27. J. Meinel, M. Kwon, R. Maier, D. Dasari, H. Sumiya, S. Onoda, J. Isoya, V. Vorobyov, and J. Wrachtrup, High-resolution nanoscale NMR for arbitrary magnetic fields, Commun. Phys. 6, 01419 (2023).
  28. See Supplemental Material at http://link.aps.org/supplemental/10.1103/llfg-s4rr, which includes Refs. [29–37] and more details on the theory of superresolution quantum sensing, derivation of transition probabilities, the sample and experimental setup, the sensing and readout protocol, the signal-to-noise ratio enhancement, and the estimation of the uncertainty of frequency separation.
  29. Y. Chu, X. Li, and J. Cai, Strong quantum metrological limit from many-body physics, Phys. Rev. Lett. 130, 170801 (2023).
  30. Y. Chu, X. Li, and J. Cai, Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation, Phys. Rev. Lett. 133, 110201 (2024).
  31. C. Osterkamp, J. Lang, J. Scharpf, C. Müller, L. P. McGuinness, T. Diemant, R. J. Behm, B. Naydenov, and F. Jelezko, Stabilizing shallow color centers in diamond created by nitrogen delta-doping using SF6 plasma treatment, Appl. Phys. Lett. 106, 113109 (2015).
  32. J. M. Binder, A. Stark, N. Tomek, J. Scheuer, F. Frank, K. D. Jahnke, C. Müller, S. Schmitt, M. H. Metsch, T. Unden, T. Gehring, A. Huck, U. L. Andersen, L. J. Rogers, and F. Jelezko, qudi: A modular python suite for experiment control and data processing, SoftwareX 6, 85 (2017).
  33. T. Häberle, T. Oeckinghaus, D. Schmid-Lorch, M. Pfender, F. F. de Oliveira, S. A. Momenzadeh, A. Finkler, and J. Wrachtrup, Nuclear quantum-assisted magnetometer, Rev. Sci. Instrum. 88, 013702 (2017).
  34. S. Schmitt, T. Gefen, D. Louzon, C. Osterkamp, N. Staudenmaier, J. Lang, M. Markham, A. Retzker, L. P. McGuinness, and F. Jelezko, Optimal frequency measurements with quantum probes, npj Quantum Inf. 7, 55 (2021).
  35. G.-Q. Liu, J. Xing, W.-L. Ma, P. Wang, C.-H. Li, H. C. Po, Y.-R. Zhang, H. Fan, R.-B. Liu, and X.-Y. Pan, Single-shot readout of a nuclear spin weakly coupled to a nitrogen-vacancy center at room temperature, Phys. Rev. Lett. 118, 150504 (2017).
  36. M. H. Levitt, Composite pulses, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986).
  37. G. T. Genov, D. Schraft, T. Halfmann, and N. V. Vitanov, Correction of arbitrary field errors in population inversion of quantum systems by universal composite pulses, Phys. Rev. Lett. 113, 043001 (2014).
  38. P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R. Hemmer, J. Wrachtrup, and F. Jelezko, Single-shot readout of a single nuclear spin, Science 329, 542 (2010).
  39. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Observation of coherent oscillations in a single electron spin, Phys. Rev. Lett. 92, 076401 (2004).
  40. B. J. Shields, Q. P. Unterreithmeier, N. P. de Leon, H. Park, and M. D. Lukin, Efficient readout of a single spin state in diamond via spin-to-charge conversion, Phys. Rev. Lett. 114, 136402 (2015).
  41. P. Siyushev, M. Nesladek, E. Bourgeois, M. Gulka, J. Hruby, T. Yamamoto, M. Trupke, T. Teraji, J. Isoya, and F. Jelezko, Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond, Science 363, 728 (2019).
  42. J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for NV-diamond magnetometry, Rev. Mod. Phys. 92, 015004 (2020).
  43. P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, Monolithic diamond optics for single photon detection, Appl. Phys. Lett. 97, 241902 (2010).
  44. J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. O’Brien, and J. G. Rarity, Strongly enhanced photon collection from diamond defect centers under microfabricated integrated solid immersion lenses, Appl. Phys. Lett. 97, 241901 (2010).
  45. L. Jiang, J. S. Hodges, J. R. Maze, P. Maurer, J. M. Taylor, D. G. Cory, P. R. Hemmer, R. L. Walsworth, A. Yacoby, A. S. Zibrov, and M. D. Lukin, Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae, Science 326, 267 (2009).
  46. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Ultralong spin coherence time in isotopically engineered diamond, Nat. Mater. 8, 383 (2009).
  47. E. D. Herbschleb, H. Kato, Y. Maruyama, T. Danjo, T. Makino, S. Yamasaki, I. Ohki, K. Hayashi, H. Morishita, M. Fujiwara, and N. Mizuochi, Ultra-long coherence times amongst room-temperature solid-state spins, Nat. Commun. 10, 3766 (2019).
  48. A. Salhov, Q. Cao, J. Cai, A. Retzker, F. Jelezko, and G. Genov, Protecting quantum information via destructive interference of correlated noise, Phys. Rev. Lett. 132, 223601 (2024).
  49. P. Cappellaro and M. D. Lukin, Quantum correlation in disordered spin systems: Applications to magnetic sensing, Phys. Rev. A 80, 032311 (2009).
  50. S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, Phonon-induced spin-spin interactions in diamond nanostructures: Application to spin squeezing, Phys. Rev. Lett. 110, 156402 (2013).
  51. W. Wu, E. J. Davis, L. B. Hughes, B. Ye, Z. Wang, D. Kufel, T. Ono, S. A. Meynell, M. Block, C. Liu, H. Yang, A. C. Bleszynski Jayich, and N. Y. Yao, Spin squeezing in an ensemble of nitrogen–vacancy centres in diamond, Nature (London) 646, 74 (2025).
  52. W. Jia et al. (LIGO Scientific Collaboration), Squeezing the quantum noise of a gravitational-wave detector below the standard quantum limit, Science 385, 1318 (2024).
  53. Y. Feng, Z. Zeng, J. Cheng, Z. You, H. Lu, Z. Yan, X. Jia, C. Xie, and K. Peng, Quantum-enhanced interferometer for multiphase sensing, Phys. Rev. Lett. 135, 183602 (2025).
  54. C. Troullinou, R. Jiménez-Martínez, J. Kong, V. G. Lucivero, and M. W. Mitchell, Squeezed-light enhancement and backaction evasion in a high sensitivity optically pumped magnetometer, Phys. Rev. Lett. 127, 193601 (2021).
  55. J.-M. Cai, B. Naydenov, R. Pfeiffer, L. P. McGuinness, K. D. Jahnke, F. Jelezko, M. B. Plenio, and A. Retzker, Robust dynamical decoupling with concatenated continuous driving, New J. Phys. 14, 113023 (2012).

Outline

Information

Phys. Rev. Lett. 135, 250806– Published 19 December, 2025
  • Received 25 June 2025
  • Revised 21 October 2025
  • Accepted 24 November 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation