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Search for axionlike dark matter using liquid-state nuclear magnetic resonance

Julian Walter1,2,3,*, Olympia Maliaka1,2,3,*, Yuzhe Zhang1,2,3,*, John W. Blanchard4,2,3, Gary Centers1,2,3, Arian Dogan1,2,3, Martin Engler1,2,3, Nataniel L. Figueroa1,2,3, Younggeun Kim1,2,3 et al.

Derek F. Jackson Kimball5, Matthew Lawson6, Declan W. Smith7, Alexander O. Sushkov7,8,9,10, Dmitry Budker1,2,3,11, Hendrik Bekker1,2,3,†, and Arne Wickenbrock1,2,3

  • *These authors contributed equally to this work.
  • †Contact author: hbekker@uni-mainz.de
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Phys. Rev. D 112, 052008 – Published 22 September, 2025

DOI: https://doi.org/10.1103/39nc-vr9m

Abstract

We search for dark matter in the form of axionlike particles (ALPs) in the mass range 5.576741  neV/c2−5.577733  neV/c2 by probing their possible coupling to fermion spins through the ALP field gradient. This is achieved by performing proton nuclear magnetic resonance spectroscopy on a sample of methanol as a technical demonstration of the Cosmic Axion Spin Precession Experiment Gradient (CASPEr-Gradient) Low-Field apparatus. Searching for spin-coupled ALP dark matter in this mass range with associated Compton frequencies in a 240 Hz window centered at 1.348570 MHZ resulted in a sensitivity to the ALP-proton coupling constant of gap≈3×10−2  GeV−1. This narrow-bandwidth search serves as a proof-of-principle and a commissioning measurement, validating our methodology and demonstrating the experiment’s capabilities. CASPEr-Gradient Low-Field will probe the mass range from 4.1  peV/c2 to 17  neV/c2 with hyperpolarized samples to boost the sensitivity beyond the astronomical limits.

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References (72)

  1. Fritz Zwicky et al., The redshift of extragalactic nebulae, Helv. Phys. Acta 6, 138 (1933).
  2. Fritz Zwicky, On the masses of nebulae and of clusters of nebulae, Astrophys. J. 86, 217 (1937).
  3. Vera C. Rubin and W. Kent Ford Jr., Rotation of the andromeda nebula from a spectroscopic survey of emission regions, Astrophys. J. 159, 379 (1970).
  4. P. A. R. Ade, Nabila Aghanim, Yashar Akrami, P. K. Aluri, M. Arnaud, M. Ashdown, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro et al., Planck 2015 results-XVI. Isotropy and statistics of the CMB, Astron. Astrophys. 594, A16 (2016).
  5. Matthias Bartelmann, Gravitational lensing, Classical Quantum Gravity 27, 233001 (2010).
  6. Douglas Clowe, Maruša Bradač, Anthony H. Gonzalez, Maxim Markevitch, Scott W. Randall, Christine Jones, and Dennis Zaritsky, A direct empirical proof of the existence of dark matter, Astrophys. J. 648, L109 (2006).
  7. David Harvey, Richard Massey, Thomas Kitching, Andy Taylor, and Eric Tittley, The nongravitational interactions of dark matter in colliding galaxy clusters, Science 347, 1462 (2015).
  8. Karsten Jedamzik and Maxim Pospelov, Big bang nucleosynthesis and particle dark matter, New J. Phys. 11, 105028 (2009).
  9. Z. G. Berezhiani, A. S. Sakharov, and M. Yu Khlopov, Primordial background of cosmological axions, Sov. J. Nucl. Phys. 55, 1063 (1992).
  10. Peter W. Graham, Igor G. Irastorza, Steven K. Lamoreaux, Axel Lindner, and Karl A. van Bibber, Experimental searches for the axion and axion-like particles, Annu. Rev. Nucl. Part. Sci. 65, 485 (2015).
  11. Francesca Chadha-Day, John Ellis, and David J. E. Marsh, Axion dark matter: What is it and why now?, Sci. Adv. 8, eabj3618 (2022).
  12. Derek F. Jackson Kimball and Karl Van Bibber, The Search for Ultralight Bosonic Dark Matter (Springer Nature, Cham, Switezerland, 2023).
  13. Peter W. Graham and Adam Scherlis, Stochastic axion scenario, Phys. Rev. D 98, 035017 (2018).
  14. John Preskill, Mark B. Wise, and Frank Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  15. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  16. Michael Dine and Willy Fischler, The not-so-harmless axion, Phys. Lett. 120B, 137 (1983).
  17. Peter Svrcek and Edward Witten, Axions in string theory, J. High Energy Phys. 06 (2006) 051.
  18. Z. G. Berezhiani and M. Yu Khlopov, Cosmology of spontaneously broken gauge family symmetry with axion solution of strong CP-problem, Z. Phys. C 49, 73 (1991).
  19. R. D. Peccei and Helen R. Quinn, CP conservation in the presence of pseudoparticles, Phys. Rev. Lett. 38, 1440 (1977).
  20. R. D. Peccei and Helen R. Quinn, Constraints imposed by CP conservation in the presence of pseudoparticles, Phys. Rev. D 16, 1791 (1977).
  21. Lars Bergström, Piero Ullio, and James H. Buckley, Observability of γ rays from dark matter neutralino annihilations in the Milky Way halo, Astropart. Phys. 9, 137 (1998).
  22. Gerard Jungman, Marc Kamionkowski, and Kim Griest, Supersymmetric dark matter, Phys. Rep. 267, 195 (1992).
  23. Yoshiaki Sofue and Vera Rubin, Rotation curves of spiral galaxies, Annu. Rev. Astron. Astrophys. 39, 137 (2001).
  24. Joshua W. Foster, Nicholas L. Rodd, and Benjamin R. Safdi, Revealing the dark matter halo with axion direct detection, Phys. Rev. D 97, 123006 (2018).
  25. Mariangela Lisanti, Matthew Moschella, and William Terrano, Stochastic properties of ultralight scalar field gradients, Phys. Rev. D 104, 055037 (2021).
  26. Dhong Yeon Cheong, Nicholas L. Rodd, and Lian-Tao Wang, Quantum description of wave dark matter, Phys. Rev. D 111, 015028 (2025).
  27. Joel R. Primack, David Seckel, and Bernard Sadoulet, Detection of cosmic dark matter, Annu. Rev. Nucl. Part. Sci. 38, 751 (1988).
  28. Derek F. Jackson Kimball, S. Afach, D. Aybas, J. W. Blanchard, D. Budker, G. Centers, M. Engler, N. L. Figueroa, A. Garcon, P. W. Graham, H. Luo, S. Rajendran, M. G. Sendra, A. O. Sushkov, T. Wang, A. Wickenbrock, A. Wilzewski, and T. Wu, Overview of the cosmic axion spin precession experiment (CASPEr). In Microwave Cavities and Detectors for Axion Research, edited by Gianpaolo Carosi and Gray Rybka (Springer International Publishing, Cham, 2020), pp. 105–121.
  29. N. Wyn Evans, Ciaran A. J. O’Hare, and Christopher McCabe, Refinement of the standard halo model for dark matter searches in light of the Gaia Sausage, Phys. Rev. D 99, 023012 (2019).
  30. Alexander V. Gramolin, Arne Wickenbrock, Deniz Aybas, Hendrik Bekker, Dmitry Budker, Gary P. Centers, Nataniel L. Figueroa, Derek F. Jackson Kimball, and Alexander O. Sushkov, Spectral signatures of axionlike dark matter, Phys. Rev. D 105, 035029 (2022).
  31. Schive, Hsi-Yu, Chiueh, Tzihong, and Broadhurst, Tom, Cosmic structure as the quantum interference of a coherent dark wave, Nat. Phys. 10, 496 (2014).
  32. Gary P. Centers, John W. Blanchard, Jan Conrad, Nataniel L. Figueroa, Antoine Garcon, Alexander V. Gramolin, Derek F. Jackson Kimball, Matthew Lawson, Bart Pelssers, Joseph A. Smiga, Alexander O. Sushkov, Arne Wickenbrock, Dmitry Budker, and Andrei Derevianko, Stochastic fluctuations of bosonic dark matter, Nat. Commun. 12, 7321 (2021).
  33. Jonathan L. Ouellet, Chiara P. Salemi, Joshua W. Foster, Reyco Henning, Zachary Bogorad, Janet M. Conrad, Joseph A. Formaggio, Yonatan Kahn, Joe Minervini, Alexey Radovinsky et al., First results from ABRACADABRA-10 cm: A search for sub-μeV axion dark matter, Phys. Rev. Lett. 122, 121802 (2019).
  34. Nick Du, N. Force, R. Khatiwada, E. Lentz, R. Ottens, L. J. Rosenberg, Gray Rybka, G. Carosi, N. Woollett, D. Bowring et al., Search for invisible axion dark matter with the axion dark matter experiment, Phys. Rev. Lett. 120, 151301 (2018).
  35. Alexander J. Millar et al., Searching for dark matter with plasma haloscopes, Phys. Rev. D 107, 055013 (2023).
  36. Beatriz Aja, Sergio Arguedas Cuendis, Ivan Arregui, Eduardo Artal, R. Belén Barreiro, Francisco J. Casas, Marina C. de Ory, Alejandro Díaz-Morcillo, Luisa de la Fuente, Juan Daniel Gallego et al., The canfranc axion detection experiment (CADEx): Search for axions at 90 GHz with kinetic inductance detectors, J. Cosmol. Astropart. Phys. 11 (2022) 044.
  37. Saebyeok Ahn et al., Extensive search for axion dark matter over 1 GHz with CAPP’S main axion experiment, Phys. Rev. X 14, 031023 (2024).
  38. L. Brouwer, S. Chaudhuri, H.-M. Cho, J. Corbin, W. Craddock, C. S. Dawson, A. Droster, J. W. Foster, J. T. Fry, P. W. Graham et al., Projected sensitivity of DMRadio-m 3: A search for the QCD axion below 1μeV, Phys. Rev. D 106, 103008 (2022).
  39. David Alesini, Danilo Babusci, Paolo Beltrame, Fabio Bossi, Paolo Ciambrone, Alessandro D’Elia, Daniele Di Gioacchino, Giampiero Di Pirro, Babette Döbrich, Paolo Falferi et al., The future search for low-frequency axions and new physics with the FLASH resonant cavity experiment at Frascati National Laboratories, Phys. Dark Universe 42, 101370 (2023).
  40. L. Zhong, S. A. l. Kenany, K. M. Backes, B. M. Brubaker, S. B. Cahn, G. Carosi, Y. V. Gurevich, W. F. Kindel, S. K. Lamoreaux, K. W. Lehnert et al., Results from phase 1 of the HAYSTAC microwave cavity axion experiment, Phys. Rev. D 97, 092001 (2018).
  41. B. Ary dos Santos Garcia et al. (MADMAX Collaboration), First search for axion dark matter with a MADMAX prototype, Phys. Rev. Lett. 135, 041001 (2025).
  42. Aaron P. Quiskamp, Graeme Flower, Steven Samuels, Ben T. McAllister, Paul Altin, Eugene N. Ivanov, Maxim Goryachev, and Michael E. Tobar, Near-quantum limited axion dark matter search with the ORGAN experiment around 26  μeV, Phys. Rev. D 111, 095007 (2025).
  43. A. Rettaroli et al., Search for axion dark matter with the QUAX–LNF tunable haloscope, Phys. Rev. D 110, 022008 (2024).
  44. Alexander V. Gramolin, Deniz Aybas, Dorian Johnson, Janos Adam, and Alexander O. Sushkov, Search for axion-like dark matter with ferromagnets, Nat. Phys. 17, 79 (2021).
  45. Daniel Gavilan-Martin, Grzegorz Lukasiewicz, Mikhail Padniuk, Emmanuel Klinger, Magdalena Smolis, Nataniel L. Figueroa, Derek F. Jackson Kimball, Alexander O Sushkov, Szymon Pustelny, Dmitry Budker et al., Searching for dark matter with a spin-based interferometer, Nat. Commun. 16, 4953 (2025).
  46. Itay M. Bloch, Gil Ronen, Roy Shaham, Ori Katz, Tomer Volansky, and Or Katz, New constraints on axion-like dark matter using a Floquet quantum detector, Sci. Adv. 8, eabl8919 (2022).
  47. Teng Wu, John W. Blanchard, Gary P. Centers, Nataniel L. Figueroa, Antoine Garcon, Peter W. Graham, Derek F. Jackson Kimball, Surjeet Rajendran, Yevgeny V Stadnik, Alexander O. Sushkov et al., Search for axionlike dark matter with a liquid-state nuclear spin comagnetometer, Phys. Rev. Lett. 122, 191302 (2019).
  48. C. Abel, Nicholas John Ayres, G. Ban, Georg Bison, Kazimierz Bodek, Vira Bondar, E. Chanel, C. B. Crawford, M. Daum, B. Dechenaux et al., Search for ultralight axion dark matter in a side-band analysis of a Hg199 free-spin precession signal, SciPost Phys. 15, 058 (2023).
  49. Swathi Karanth, Edward J. Stephenson, Seung Pyo Chang, Volker Hejny, Seongtae Park, Jörg Pretz, Yannis K. Semertzidis, A. Wirzba, Aleksandra Wrońska, Falastine Abusaif et al., First search for axionlike particles in a storage ring using a polarized deuteron beam, Phys. Rev. X 13, 031004 (2023).
  50. Junyi Lee, Mariangela Lisanti, William A. Terrano, and Michael Romalis, Laboratory constraints on the neutron-spin coupling of feV-scale axions, Phys. Rev. X 13, 011050 (2023).
  51. Francesco Capozzi, Bhaskar Dutta, Gajendra Gurung, Wooyoung Jang, Ian M Shoemaker, Adrian Thompson, and Jaehoon Yu, New constraints on ALP couplings to electrons and photons from ArgoNeuT and the MiniBooNE beam dump, Phys. Rev. D 108, 075019 (2023).
  52. Dmitry Budker, Peter W. Graham, Micah Ledbetter, Surjeet Rajendran, and Alexander O. Sushkov, Proposal for a cosmic axion spin precession experiment (CASPEr), Phys. Rev. X 4, 021030 (2014).
  53. Tao Wang, Derek F. Jackson Kimball, Alexander O. Sushkov, Deniz Aybas, John W Blanchard, Gary Centers, Sean R. O’Kelley, Arne Wickenbrock, Jiancheng Fang, and Dmitry Budker, Application of spin-exchange relaxation-free magnetometry to the cosmic axion spin precession experiment, Phys. Dark Universe 19, 27 (2018).
  54. Deniz Aybas, Janos Adam, Emmy Blumenthal, Alexander V. Gramolin, Dorian Johnson, Annalies Kleyheeg, Samer Afach, John W. Blanchard, Gary P. Centers, Antoine Garcon et al., Search for axionlike dark matter using solid-state nuclear magnetic resonance, Phys. Rev. Lett. 126, 141802 (2021).
  55. Antoine Garcon, John W. Blanchard, Gary P. Centers, Nataniel L. Figueroa, Peter W. Graham, Derek F. Jackson Kimball, Surjeet Rajendran, Alexander O. Sushkov, Yevgeny V. Stadnik, Arne Wickenbrock, Teng Wu, and Dmitry Budker, Constraints on bosonic dark matter from ultralow-field nuclear magnetic resonance, Sci. Adv. 5, eaax4539 (2019).
  56. Carl Beadle, Sebastian A. R. Ellis, Jacob M. Leedom, and Nicholas L. Rodd, Dark matter nuclear magnetic resonance is sensitive to dark photons and the axion-photon coupling, arXiv:2505.15897.
  57. Antoine Garcon, Deniz Aybas, John W. Blanchard, Gary Centers, Nataniel L. Figueroa, Peter W. Graham, Derek F. Jackson Kimball, Surjeet Rajendran, Marina Gil Sendra, Alexander O. Sushkov et al., The cosmic axion spin precession experiment (CASPEr): A dark-matter search with nuclear magnetic resonance, Quantum Sci. Technol. 3, 014008 (2017).
  58. Julian Walter, Hendrik Bekker, John Blanchard, Dmitry Budker, Nataniel L. Figueroa, Arne Wickenbrock, Yuzhe Zhang, and Pengyu Zhou, Fast shimming algorithm based on Bayesian optimization for magnetic resonance based dark matter search, Ann. Phys. (Berlin) 536, 2300258 (2024).
  59. Deniz Aybas, Hendrik Bekker, John W. Blanchard, Dmitry Budker, Gary P. Centers, Nataniel L. Figueroa, Alexander V. Gramolin, Derek F. Jackson Kimball, Arne Wickenbrock, and Alexander O. Sushkov, Quantum sensitivity limits of nuclear magnetic resonance experiments searching for new fundamental physics, Quantum Sci. Technol. 6, 034007 (2021).
  60. Yuzhe Zhang, Deniz Aybas Tumturk, Hendrik Bekker, Dmitry Budker, Derek F. Jackson Kimball, Alexander O. Sushkov, and Arne Wickenbrock, Frequency-scanning considerations in axionlike dark matter spin-precession experiments, Ann. Phys. (Berlin) 536, 2300223 (2024).
  61. John Clarke and Alex I. Braginski, The SQUID Handbook: Applications of SQUIDs and SQUID Systems (John Wiley & Sons, New York, 2006).
  62. H. Y. Carr and E. M. Purcell, Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev. 94, 630 (1954).
  63. B. M. Brubaker, L. Zhong, S. K. Lamoreaux, K. W. Lehnert, and K. A. van Bibber, HAYSTAC axion search analysis procedure, Phys. Rev. D 96, 123008 (2017).
  64. Alexander Gramolin, Deniz Aybas, Dorian Johnson, Janos Adam, and Alexander Sushkov, Search for axion-like dark matter with ferromagnets, Nat. Phys. 17, 79 (2021).
  65. Ariel Arza, Abaz Kryemadhi, and Konstantin Zioutas, Searching for axion streams with the echo method, Phys. Rev. D 108, 083001 (2023).
  66. Ciaran A. J. O’Hare, Giovanni Pierobon, and Javier Redondo, Axion minicluster streams in the solar neighborhood, Phys. Rev. Lett. 133, 081001 (2024).
  67. Javier De Miguel, Abaz Kryemadhi, and Konstantin Zioutas, DALI sensitivity to streaming axion dark matter, Phys. Rev. D 111, 023016 (2025).
  68. Abraham. Savitzky and M. J. E. Golay, Smoothing and differentiation of data by simplified least squares procedures, Anal. Chem. 36, 1627 (1964).
  69. David A. Freedman and Persi Diaconis, On the histogram as a density estimator:L2 theory, Z. Wahrsch. Verw. Geb. 57, 453 (1981).
  70. James Eills, Dmitry Budker, Silvia Cavagnero, Eduard Y. Chekmenev, Stuart J. Elliott, Sami Jannin, Anne Lesage, Jörg Matysik, Thomas Meersmann, Thomas Prisner, Jeffrey A. Reimer, Hanming Yang, and Igor V. Koptyug, Spin hyperpolarization in modern magnetic resonance, Chem. Rev. 123, 1417 (2023).
  71. Georg G. Raffelt, Particle physics from stars, Annu. Rev. Nucl. Part. Sci. 49, 163 (1999).
  72. Anatole Abragam, The principles of nuclear magnetism (Clarendon Press, Oxford, 1961), p. 599.

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Phys. Rev. D 112, 052008– Published 22 September, 2025
  • Received 28 April 2025
  • Accepted 20 August 2025
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