Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Quantum-limited metrology of macroscopic spin ensembles

Nature Physics (2026)Cite this article

Subjects

Abstract

Quantum effects are usually observed and utilized in microscopic systems, where qubits can be manipulated and measured with precise control. However, larger qubit ensembles should, in principle, enhance performance in sensing and metrology applications. There is an inherent tension between the sensitivity afforded by large-scale experiments and the ability to use quantum protocols, since quantum phenomena are usually rapidly swamped by classical noise as the system size is scaled up. Here we show that spin quantum fluctuations are present in macroscopic spin qubit ensembles that might be expected to behave classically. Quantum-limited detection sensitivity enables us to perform magnetic resonance spectroscopy of quantum spin fluctuations without any external excitation. We demonstrate non-equilibrium spin-state preparation and single-shot measurements of subsequent ultraslow thermalization dynamics. Quantum-limited metrology of millimole-scale ensemble dynamics brings the tools of quantum sensing into the macroscopic regime. This enables truly non-invasive magnetic resonance spectroscopy and precision searches for fundamental physics.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental setup.
Fig. 2: Magnetic resonance detection with and without external excitation.
Fig. 3: Noise-driven magnetic resonance spectroscopy of thermally polarized spin ensembles.
Fig. 4: Spin-state preparation, relaxation and quantum fluctuations.

Data availability

Source data are provided with this paper.

References

  1. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  2. Bothwell, T. et al. Resolving the gravitational redshift across a millimetre-scale atomic sample. Nature 602, 420–424 (2022).

    Article  ADS  Google Scholar 

  3. LIGO Scientific Collaboration and Virgo Collaboration et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  4. Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).

    Article  ADS  Google Scholar 

  5. Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).

    Article  ADS  Google Scholar 

  6. Virgo Collaboration et al. Increasing the astrophysical reach of the Advanced Virgo Detector via the application of squeezed vacuum states of light. Phys. Rev. Lett. 123, 231108 (2019).

    Article  ADS  Google Scholar 

  7. Robinson, J. M. et al. Direct comparison of two spin-squeezed optical clock ensembles at the 10−17 level. Nat. Phys. 20, 208–213 (2024).

    Article  Google Scholar 

  8. Aprile, E. et al. Observation of two-neutrino double electron capture in 124Xe with XENON1T. Nature 568, 532–535 (2019).

    Article  ADS  Google Scholar 

  9. Abe, K. et al. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature 580, 339–344 (2020).

    Article  Google Scholar 

  10. Ning, X. et al. Limits on the luminance of dark matter from xenon recoil data. Nature 618, 47–50 (2023).

    Article  ADS  Google Scholar 

  11. IceCube Collaboration. Observation of high-energy neutrinos from the Galactic plane. Science 380, 1338–1343 (2023).

    Article  ADS  Google Scholar 

  12. Budker, D. & Romalis, M. Optical magnetometry. Nat. Phys. 3, 227–234 (2007).

    Article  Google Scholar 

  13. Budker, D., Graham, P. W., Ledbetter, M., Rajendran, S. & Sushkov, A. O. Proposal for a cosmic axion spin precession experiment (CASPEr). Phys. Rev. X 4, 021030 (2014).

    Google Scholar 

  14. Safronova, M. S. et al. Search for new physics with atoms and molecules. Rev. Mod. Phys. 90, 025008 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  15. Bloch, F. Nuclear induction. Phys. Rev. 70, 460–474 (1946).

    Article  ADS  Google Scholar 

  16. Aybas, D. et al. Quantum sensitivity limits of nuclear magnetic resonance experiments searching for new fundamental physics. Quantum Sci. Technol. 6, 034007 (2021).

    Article  ADS  Google Scholar 

  17. Sleater, T., Hahn, E. L., Hilbert, C. & Clarke, J. Nuclear-spin noise. Phys. Rev. Lett. 55, 1742–1745 (1985).

    Article  ADS  Google Scholar 

  18. McCoy, M. A. & Ernst, R. R. Nuclear spin noise at room temperature. Chem. Phys. Lett. 159, 587–593 (1989).

    Article  ADS  Google Scholar 

  19. Guéron, M. & Leroy, J. L. NMR of water protons. The detection of their nuclear-spin noise, and a simple determination of absolute probe sensitivity based on radiation damping. J. Magn. Reson. 85, 209–215 (1989).

    ADS  Google Scholar 

  20. Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005).

    Article  ADS  Google Scholar 

  21. Sushkov, A. O. et al. Magnetic resonance detection of individual proton spins using quantum reporters. Phys. Rev. Lett. 113, 197601 (2014).

    Article  ADS  Google Scholar 

  22. Aslam, N. et al. Nanoscale nuclear magnetic resonance with chemical resolution. Science 357, 67–71 (2017).

    Article  ADS  Google Scholar 

  23. Glenn, D. R. et al. High-resolution magnetic resonance spectroscopy using a solid-state spin sensor. Nature 555, 351–354 (2018).

    Article  ADS  Google Scholar 

  24. Sels, D., Dashti, H., Mora, S., Demler, O. & Demler, E. Quantum approximate Bayesian computation for NMR model inference. Nat. Mach. Intell. 2, 396–402 (2020).

    Article  Google Scholar 

  25. Crooker, S. A., Rickel, D. G., Balatsky, A. V. & Smith, D. L. Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance. Nature 431, 49–52 (2004).

    Article  ADS  Google Scholar 

  26. Hübner, J., Berski, F., Dahbashi, R. & Oestreich, M. The rise of spin noise spectroscopy in semiconductors: from acoustic to GHz frequencies. Phys. Stat. Sol. (b) 251, 1824–1838 (2014).

    Article  ADS  Google Scholar 

  27. Lovchinsky, I. et al. Nuclear magnetic resonance detection and spectroscopy of single proteins using quantum logic. Science 351, 836–841 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  28. Shah, V., Vasilakis, G. & Romalis, M. V. High bandwidth atomic magnetometery with continuous quantum nondemolition measurements. Phys. Rev. Lett. 104, 013601 (2010).

    Article  ADS  Google Scholar 

  29. Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).

    Article  ADS  Google Scholar 

  30. Hosten, O., Engelsen, N. J., Krishnakumar, R. & Kasevich, M. A. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).

    Article  ADS  Google Scholar 

  31. Marciniak, C. D. et al. Optimal metrology with programmable quantum sensors. Nature 603, 604–609 (2022).

    Article  ADS  Google Scholar 

  32. Li, Z. et al. Improving metrology with quantum scrambling. Science 380, 1381–1384 (2023).

    Article  ADS  MathSciNet  Google Scholar 

  33. Bao, H. et al. Spin squeezing of 1,011 atoms by prediction and retrodiction measurements. Nature 581, 159–163 (2020).

    Article  ADS  Google Scholar 

  34. Boyers, E., Goldstein, G. & Sushkov, A. O. Spin squeezing of macroscopic nuclear spin ensembles. Phys. Rev. D 111, 052004 (2025).

    Article  ADS  Google Scholar 

  35. Giraudeau, P., Müller, N., Jerschow, A. & Frydman, L. 1H NMR noise measurements in hyperpolarized liquid samples. Chem. Phys. Lett. 489, 107–112 (2010).

    Article  ADS  Google Scholar 

  36. Schlagnitweit, J. & Müller, N. The first observation of carbon-13 spin noise spectra. J. Magn. Reson. 224, 78–81 (2012).

    Article  ADS  Google Scholar 

  37. Kronenbitter, J. & Schwenk, A. A new technique for measuring the relaxation times T1 and T2 and the equilibrium magnetization M0 of slowly relaxing systems with weak NMR signals. J. Magn. Reson. 25, 147–165 (1977).

    ADS  Google Scholar 

  38. Tycko, R. NMR at low and ultralow temperatures. Acc. Chem. Res. 46, 1923–1932 (2013).

    Article  Google Scholar 

  39. Bucher, D. B., Glenn, D. R., Park, H., Lukin, M. D. & Walsworth, R. L. Hyperpolarization-enhanced NMR spectroscopy with femtomole sensitivity using quantum defects in diamond. Phys. Rev. X 10, 021053 (2020).

    Google Scholar 

  40. Du, J., Shi, F., Kong, X., Jelezko, F. & Wrachtrup, J. Single-molecule scale magnetic resonance spectroscopy using quantum diamond sensors. Rev. Mod. Phys. 96, 025001 (2024).

    Article  ADS  Google Scholar 

  41. Dusad, R. et al. Magnetic monopole noise. Nature 571, 234–239 (2019).

    Article  Google Scholar 

  42. Reif, B., Ashbrook, S. E., Emsley, L. & Hong, M. Solid-state NMR spectroscopy. Nat. Rev. Methods Primers 1, 2 (2021).

    Article  Google Scholar 

  43. Morineau, F. et al. Satisfaction and violation of the fluctuation-dissipation relation in spin ice materials. Phys. Rev. Lett. 134, 096702 (2025).

    Article  ADS  Google Scholar 

  44. Chen, P. et al. Magic angle spinning spheres. Sci. Adv. 4, eaau1540 (2018).

    Article  ADS  Google Scholar 

  45. Scott, F. J. et al. A versatile custom cryostat for dynamic nuclear polarization supports multiple cryogenic magic angle spinning transmission line probes. J. Magn. Reson. 297, 23–32 (2018).

    Article  ADS  Google Scholar 

  46. Matsuki, Y. & Fujiwara, T. Cryogenic platforms and optimized DNP sensitivity. eMagRes 7, 9–24 (2018).

    Google Scholar 

  47. Muñoz-Arias, M. H., Poggi, P. M., Jessen, P. S. & Deutsch, I. H. Simulating nonlinear dynamics of collective spins via quantum measurement and feedback. Phys. Rev. Lett. 124, 110503 (2020).

    Article  ADS  Google Scholar 

  48. Lei, M. et al. Many-body cavity quantum electrodynamics with driven inhomogeneous emitters. Nature 617, 271–276 (2023).

    Article  ADS  Google Scholar 

  49. DeMille, D., Doyle, J. M. & Sushkov, A. O. Probing the frontiers of particle physics with tabletop-scale experiments. Science 357, 990–994 (2017).

    Article  ADS  Google Scholar 

  50. Aybas, D. et al. Search for axionlike dark matter using solid-state nuclear magnetic resonance. Phys. Rev. Lett. 126, 141802 (2021).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge valuable discussions with G. Randall, L. Rava, D. Budker, D. Jackson-Kimball, A. Wickenbrock and H. Bekker. This work was supported by US National Science Foundation CAREER grant PHY-2145162 (A.O.S.), the US Department of Energy, Office of High Energy Physics, under the QuantISED programme FWP 100667 (A.O.S.), the Gordon and Betty Moore Foundation grant (https://doi.org/10.37807/gbmf12248) (A.O.S.) and NSF REU grant 2244795 (A.M.).

Author information

Author notes

  1. Alexander O. Sushkov

    Present address: Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA

  2. Stephen E. Kuenstner

    Present address: Center for Nuclear Physics and Astrophysics, University of Washington, Seattle, WA, USA

  3. Declan W. Smith, Andrew J. Winter, Eren Ozdemir & Tanja Marić

    Present address: Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA

  4. Alyssa Matthews

    Present address: Department of Physics, University of California, Berkeley, Berkeley, CA, USA

  5. These authors contributed equally: Stephen E. Kuenstner, Declan W. Smith.

Authors and Affiliations

  1. Department of Physics, Boston University, Boston, MA, USA

    Stephen E. Kuenstner, Declan W. Smith, Andrew J. Winter, Eren Ozdemir, Tanja Marić, Alyssa Matthews & Alexander O. Sushkov

  2. Photonics Center, Boston University, Boston, MA, USA

    Alexander O. Sushkov

  3. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA

    Alexander O. Sushkov

Authors
  1. Stephen E. Kuenstner
    View author publications

    Search author on:PubMed Google Scholar

  2. Declan W. Smith
    View author publications

    Search author on:PubMed Google Scholar

  3. Andrew J. Winter
    View author publications

    Search author on:PubMed Google Scholar

  4. Eren Ozdemir
    View author publications

    Search author on:PubMed Google Scholar

  5. Tanja Marić
    View author publications

    Search author on:PubMed Google Scholar

  6. Alyssa Matthews
    View author publications

    Search author on:PubMed Google Scholar

  7. Alexander O. Sushkov
    View author publications

    Search author on:PubMed Google Scholar

Contributions

S.E.K. and D.W.S. constructed the experiment, performed the measurements and analysed the data. A.J.W. constructed the experiment and performed the theoretical modelling. E.O. constructed the experiment and analysed the data. T.M. and A.M. constructed the experiment and performed the measurements. A.O.S. analysed the data, performed the theoretical modelling and supervised the project. All authors contributed to drafting the manuscript.

Corresponding author

Correspondence to Alexander O. Sushkov.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Juergen Haase 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.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6, Tables 1–4, description of the experimental apparatus and control, data acquisition, calibrations and data analysis.

Source data

Source Data Fig. 2

Measurement data.

Source Data Fig. 3

Measurement data.

Source Data Fig. 4

Measurement data.

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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuenstner, S.E., Smith, D.W., Winter, A.J. et al. Quantum-limited metrology of macroscopic spin ensembles. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03187-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • DOI: https://doi.org/10.1038/s41567-026-03187-6

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing