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Search for axion-like dark matter with spin-based amplifiers


Ultralight axion-like particles are well-motivated dark matter candidates introduced by theories beyond the standard model of particle physics. However, directly constraining their parameter space with laboratory experiments usually yields weaker limits than indirect approaches relying on astrophysical observations. Here we report the search for axion-like particles with a quantum sensor in the mass range of 8.3–744.0 feV. The sensor makes use of hyperpolarized long-lived nuclear spins as a pre-amplifier that effectively enhances a coherently oscillating axion-like dark matter field by a factor of more than 100. Using these spin-based amplifiers, we achieve an ultrahigh magnetic sensitivity of 18 fT Hz–(1/2), which exceeds the performance of state-of-the-art nuclear spin magnetometers. Our experiment constrains the parameter space describing the coupling of axion-like particles to nucleons over the aforementioned mass range, namely, at 67.5 feV reaching 2.9 × 10−9 GeV−1, improving on previous laboratory constraints by at least five orders of magnitude. Our measurements also constrain the quadratic interaction between axion-like particles and nucleons as well as interactions between dark photons and nucleons, exceeding bounds from astrophysical observations.

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Fig. 1: Basic principle of the spin-based amplifier.
Fig. 2: Proof-of-principle demonstrations of the spin-based amplifier.
Fig. 3: Amplification and sensitivity of magnetic-field measurement assisted with a spin-based amplifier.
Fig. 4: Results of axion-like dark matter search.

Data availability

Source data are provided with this paper. All other data that support the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code that supports the plots in this paper is available from the corresponding author upon reasonable request.


  1. 1.

    Bertone, G. & Hooper, D. History of dark matter. Rev. Mod. Phys. 90, 045002 (2018).

    ADS  Google Scholar 

  2. 2.

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

    ADS  Google Scholar 

  3. 3.

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

    ADS  MathSciNet  Google Scholar 

  4. 4.

    Bertone, G. & Tait, T. M. A new era in the search for dark matter. Nature 562, 51–56 (2018).

    ADS  Google Scholar 

  5. 5.

    Ambrosi, G. et al. Direct detection of a break in the teraelectronvolt cosmic-ray spectrum of electrons and positrons. Nature 552, 63–66 (2017).

    ADS  Google Scholar 

  6. 6.

    Aprile, E. et al. First dark matter search results from the XENON1T experiment. Phys. Rev. Lett. 119, 181301 (2017).

    ADS  Google Scholar 

  7. 7.

    Liu, J., Chen, X. & Ji, X. Current status of direct dark matter detection experiments. Nat. Phys. 13, 212–216 (2017).

    Google Scholar 

  8. 8.

    Peccei, R. D. & Quinn, H. R. CP conservation in the presence of pseudoparticles. Phys. Rev. Lett. 38, 1440–1443 (1977).

    ADS  Google Scholar 

  9. 9.

    Preskill, J., Wise, M. B. & Wilczek, F. Cosmology of the invisible axion. Phys. Lett. B 120, 127–132 (1983).

    ADS  Google Scholar 

  10. 10.

    Kim, J. E. & Carosi, G. Axions and the strong CP problem. Rev. Mod. Phys. 82, 557–601 (2010); erratum 91, 049902 (2019).

    ADS  Google Scholar 

  11. 11.

    Irastorza, I. G. & Redondo, J. New experimental approaches in the search for axion-like particles. Prog. Part. Nucl. Phys. 102, 89–159 (2018).

    ADS  Google Scholar 

  12. 12.

    Svrcek, P. & Witten, E. Axions in string theory. J. High Energ. Phys. 2006, 051 (2006).

    ADS  MathSciNet  Google Scholar 

  13. 13.

    Anastassopoulos, V. et al. New CAST limit on the axion–photon interaction. Nat. Phys. 13, 584–590 (2017).

    Google Scholar 

  14. 14.

    Bradley, R. et al. Microwave cavity searches for dark-matter axions. Rev. Mod. Phys. 75, 777–817 (2003).

    ADS  Google Scholar 

  15. 15.

    Zhong, L. et al. Results from phase 1 of the HAYSTAC microwave cavity axion experiment. Phys. Rev. D 97, 092001 (2018).

    ADS  Google Scholar 

  16. 16.

    Braine, T. et al. Extended search for the invisible axion with the axion dark matter experiment. Phys. Rev. Lett. 124, 101303 (2020).

    ADS  Google Scholar 

  17. 17.

    Ouellet, J. L. et al. First results from ABRACADABRA-10 cm: a search for sub-μeV axion dark matter. Phys. Rev. Lett. 122, 121802 (2019).

    ADS  Google Scholar 

  18. 18.

    Gramolin, A. V., Aybas, D., Johnson, D., Adam, J. & Sushkov, A. O. Search for axion-like dark matter with ferromagnets. Nat. Phys. 17, 79–84 (2020).

    Google Scholar 

  19. 19.

    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 

  20. 20.

    Roberts, B. et al. Limiting P-odd interactions of cosmic fields with electrons, protons, and neutrons. Phys. Rev. Lett. 113, 081601 (2014).

    ADS  Google Scholar 

  21. 21.

    Graham, P. W. & Rajendran, S. Axion dark matter detection with cold molecules. Phys. Rev. D 84, 055013 (2011).

    ADS  Google Scholar 

  22. 22.

    Stadnik, Y. & Flambaum, V. Axion-induced effects in atoms, molecules, and nuclei: parity nonconservation, anapole moments, electric dipole moments, and spin-gravity and spin-axion momentum couplings. Phys. Rev. D 89, 043522 (2014).

    ADS  Google Scholar 

  23. 23.

    Kimball, D. F. J. et al. Overview of the cosmic axion spin precession experiment (CASPEr). In Microwave Cavities and Detectors for Axion Research 105–121 (Springer, 2020).

  24. 24.

    Jiang, M., Su, H., Wu, Z., Peng, X. & Budker, D. Floquet maser. Sci. Adv. 7, eabe0719 (2021).

    ADS  Google Scholar 

  25. 25.

    Abel, C. et al. Search for axionlike dark matter through nuclear spin precession in electric and magnetic fields. Phys. Rev. X 7, 041034 (2017).

    Google Scholar 

  26. 26.

    Wu, T. et al. Search for axionlike dark matter with a liquid-state nuclear spin comagnetometer. Phys. Rev. Lett. 122, 191302 (2019).

    ADS  Google Scholar 

  27. 27.

    Smorra, C. et al. Direct limits on the interaction of antiprotons with axion-like dark matter. Nature 575, 310–314 (2019).

    ADS  Google Scholar 

  28. 28.

    Garcon, A. et al. Constraints on bosonic dark matter from ultralow-field nuclear magnetic resonance. Sci. Adv. 5, eaax4539 (2019).

    ADS  Google Scholar 

  29. 29.

    Graham, P. W. et al. Spin precession experiments for light axionic dark matter. Phys. Rev. D 97, 055006 (2018).

    ADS  Google Scholar 

  30. 30.

    Graham, P. W. & Rajendran, S. New observables for direct detection of axion dark matter. Phys. Rev. D 88, 035023 (2013).

    ADS  Google Scholar 

  31. 31.

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

    ADS  Google Scholar 

  32. 32.

    Bloch, I. M., Hochberg, Y., Kuflik, E. & Volansky, T. Axion-like relics: new constraints from old comagnetometer data. J. High Energ. Phys. 2020, 167 (2020).

    Google Scholar 

  33. 33.

    Vysotsskii, M., Zel’Dovich, Y. B., Khlopov, M. Y. & Chechetkin, V. Some astrophysical limitations on the axion mass. JETP Lett. 27, 502–505 (1978).

    ADS  Google Scholar 

  34. 34.

    Raffelt, G. G. Astrophysical axion bounds. In Axions 51–71 (Springer, 2008).

  35. 35.

    Arias, P. et al. WISPy cold dark matter. J. Cosmol. Astropart. Phys. 2012, 013 (2012).

    ADS  Google Scholar 

  36. 36.

    Beznogov, M. V., Rrapaj, E., Page, D. & Reddy, S. Constraints on axion-like particles and nucleon pairing in dense matter from the hot neutron star in HESS J1731-347. Phys. Rev. C 98, 035802 (2018).

    ADS  Google Scholar 

  37. 37.

    Carenza, P. et al. Improved axion emissivity from a supernova via nucleon-nucleon bremsstrahlung. J. Cosmol. Astropart. Phys. 2019, 016 (2019).

    Google Scholar 

  38. 38.

    Kominis, I., Kornack, T., Allred, J. & Romalis, M. V. A subfemtotesla multichannel atomic magnetometer. Nature 422, 596–599 (2003).

    ADS  Google Scholar 

  39. 39.

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

    Google Scholar 

  40. 40.

    Arvanitaki, A. & Geraci, A. A. Resonantly detecting axion-mediated forces with nuclear magnetic resonance. Phys. Rev. Lett. 113, 161801 (2014).

    ADS  Google Scholar 

  41. 41.

    Walker, T. G. & Happer, W. Spin-exchange optical pumping of noble-gas nuclei. Rev. Mod. Phys. 69, 629–642 (1997).

    ADS  Google Scholar 

  42. 42.

    Marsh, D. J. Axion cosmology. Phys. Rep. 643, 1–79 (2016).

    ADS  MathSciNet  Google Scholar 

  43. 43.

    Dine, M. & Fischler, W. The not-so-harmless axion. Phys. Lett. B 120, 137–141 (1983).

    ADS  Google Scholar 

  44. 44.

    Kornack, T., Ghosh, R. & Romalis, M. Nuclear spin gyroscope based on an atomic comagnetometer. Phys. Rev. Lett. 95, 230801 (2005).

    ADS  Google Scholar 

  45. 45.

    Centers, G. P. et al. Stochastic fluctuations of bosonic dark matter. Preprint at (2019).

  46. 46.

    Bar, N., Blum, K. & D’amico, G. Is there a supernova bound on axions? Phys. Rev. D 101, 123025 (2020).

    ADS  Google Scholar 

  47. 47.

    DeRocco, W., Graham, P. W. & Rajendran, S. Exploring the robustness of stellar cooling constraints on light particles. Phys. Rev. D 102, 075015 (2020).

    ADS  Google Scholar 

  48. 48.

    Pospelov, M. et al. Detecting domain walls of axionlike models using terrestrial experiments. Phys. Rev. Lett. 110, 021803 (2013).

    ADS  Google Scholar 

  49. 49.

    Graham, P. W., Irastorza, I. G., Lamoreaux, S. K., Lindner, A. & van Bibber, K. A. Experimental searches for the axion and axion-like particles. Annu. Rev. Nucl. Part. Sci. 65, 485–514 (2015).

    ADS  Google Scholar 

  50. 50.

    Aggarwal, N. et al. Characterization of magnetic field noise in the ARIADNE source mass rotor. Preprint at (2020).

  51. 51.

    Ji, W. et al. New experimental limits on exotic spin-spin-velocity-dependent interactions by using SmCo5 spin sources. Phys. Rev. Lett. 121, 261803 (2018).

    ADS  Google Scholar 

  52. 52.

    Kim, Y. J., Chu, P.-H., Savukov, I. & Newman, S. Experimental limit on an exotic parity-odd spin- and velocity-dependent interaction using an optically polarized vapor. Nat. Commun. 10, 2245 (2019).

    ADS  Google Scholar 

  53. 53.

    Cai, B. et al. Herriott-cavity-assisted all-optical atomic vector magnetometer. Phys. Rev. A 101, 053436 (2020).

    ADS  Google Scholar 

  54. 54.

    Dailey, C. et al. Quantum sensor networks as exotic field telescopes for multi-messenger astronomy. Nat. Astron. 5, 150–158 (2020).

    ADS  Google Scholar 

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M.J., H.S. and X.P. were supported by the National Key Research and Development Program of China (grant no. 2018YFA0306600), National Natural Science Foundation of China (grants nos. 11661161018, 11927811 and 12004371), Anhui Initiative in Quantum Information Technologies (grant no. AHY050000) and USTC Research Funds of the Double First-Class Initiative (grant no. YD3540002002). D.B. and A.G. were supported by the Cluster of Excellence PRISMA+ funded by the German Research Foundation (DFG) within the German Excellence Strategy (project ID 39083149), by the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (Dark-OsT project; grant agreement no. 695405), by the DFG Reinhart Koselleck project, and by the Emergent AI Center funded by Carl-Zeiss-Stiftung.

Author information




M.J. designed the experimental protocols, analysed the data and wrote the manuscript. H.S. performed the experiments, analysed the data and wrote the manuscript. A.G. analysed the data and edited the manuscript. X.P. proposed the experimental concept, devised the experimental protocols and edited the manuscript. D.B. contributed to the design of the experiment, and proofread and edited the manuscript. All the authors contributed with discussions and checking the manuscript.

Corresponding author

Correspondence to Xinhua Peng.

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Peer review informationNature Physics thanks Claudio Gatti, Maurizio Giannotti and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–15, text and references.

Source data

Source Data Fig. 2

Data for plotting Fig. 2d.

Source Data Fig. 3

Data for plotting Fig. 3a,b.

Source Data Fig. 4

Data for plotting Fig. 4b–d.

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Jiang, M., Su, H., Garcon, A. et al. Search for axion-like dark matter with spin-based amplifiers. Nat. Phys. 17, 1402–1407 (2021).

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