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Intrinsically Quantum Effects of Axion Dark Matter Are Undetectable

Yunjia Bao1,2,3,4, Dhong Yeon Cheong1,2,3,4,5, Nicholas L. Rodd6,7, Joey Takach6,7, Lian-Tao Wang1,2,3,4, and Kevin Zhou6,7

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Phys. Rev. Lett. 136, 171601 – Published 29 April, 2026

DOI: https://doi.org/10.1103/9mff-p5k6

Abstract

Is the usual treatment of axion dark matter as a classical field reliable? We show that the answer is subtle: the axion field could well be in a quantum state that has no complete classical description, but realistic detectors cannot tell the difference. To see this, we solve a fully quantum model of axion detection using quantum optics techniques. We show that intrinsically quantum effects are washed out by mode averaging or small amounts of noise, and significantly suppressed by the weakness of the axion coupling. Our Letter exemplifies that there should always be a classical analog for axion dark matter effects, extends to other wave (ultralight) dark-matter candidates, and gives a general method to compute the effects of exotic dark-matter states.

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References (106)

  1. C. B. Adams et al., Axion dark matter, in Snowmass 2021 (2022), arXiv:2203.14923.
  2. D. Antypas et al., New horizons: Scalar and vector ultralight dark matter, arXiv:2203.14915.
  3. A. Berlin and Y. Kahn, New technologies for axion and dark photon searches, Annu. Rev. Nucl. Part. Sci. 75, 83 (2025).
  4. Y. Fang, C. Gao, Y.-Y. Li, J. Shu, Y. Wu, H. Xing, B. Xu, L. Xu, and C. Zhou, Quantum frontiers in high energy physics, Sci. China Phys. Mech. Astron. 68, 260301 (2025).
  5. J. Abadie et al. (LIGO Scientific Collaboration), A gravitational wave observatory operating beyond the quantum shot-noise limit: Squeezed light in application, Nat. Phys. 7, 962 (2011).
  6. J. Aasi et al. (LIGO Scientific Collaboration), Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light, Nat. Photonics 7, 613 (2013).
  7. M. Malnou, D. A. Palken, B. M. Brubaker, L. R. Vale, G. C. Hilton, and K. W. Lehnert, Squeezed vacuum used to accelerate the search for a weak classical signal, Phys. Rev. X 9, 021023 (2019); 10, 039902(E) (2020).
  8. K. M. Backes et al. (HAYSTAC Collaboration), A quantum-enhanced search for dark matter axions, Nature (London) 590, 238 (2021).
  9. M. J. Jewell et al. (HAYSTAC Collaboration), New results from HAYSTAC’s phase II operation with a squeezed state receiver, Phys. Rev. D 107, 072007 (2023).
  10. X. Bai et al. (HAYSTAC Collaboration), Dark matter axion search with HAYSTAC phase II, Phys. Rev. Lett. 134, 151006 (2025).
  11. S. K. Lamoreaux, K. A. van Bibber, K. W. Lehnert, and G. Carosi, Analysis of single-photon and linear amplifier detectors for microwave cavity dark matter axion searches, Phys. Rev. D 88, 035020 (2013).
  12. R. Lescanne, S. Deléglise, E. Albertinale, U. Réglade, T. Capelle, E. Ivanov, T. Jacqmin, Z. Leghtas, and E. Flurin, Irreversible qubit-photon coupling for the detection of itinerant microwave photons, Phys. Rev. X 10, 021038 (2020).
  13. L. Balembois, J. Travesedo, L. Pallegoix, A. May, E. Billaud, M. Villiers, D. Estève, D. Vion, P. Bertet, and E. Flurin, Cyclically operated microwave single-photon counter with sensitivity of 10−22  W/Hz, Phys. Rev. Appl. 21, 014043 (2024).
  14. C. Braggio et al., Quantum-enhanced sensing of axion dark matter with a transmon-based single microwave photon counter, Phys. Rev. X 15, 021031 (2025).
  15. A. Pankratov, L. Revin, A. Gordeeva, A. Yablokov, L. Kuzmin, and E. Il’Ichev, Towards a microwave single-photon counter for searching axions, npj Quantum Inf. 8, 61 (2022).
  16. A. L. Pankratov, A. V. Gordeeva, A. V. Chiginev, L. S. Revin, A. V. Blagodatkin, N. Crescini, and L. S. Kuzmin, Detection of single-mode thermal microwave photons using an underdamped Josephson junction, Nat. Commun. 16, 3457 (2025); 16, 5364(E) (2025).
  17. A. L. Pankratov, A. V. Gordeeva, A. V. Chiginev, L. S. Revin, A. V. Blagodatkin, N. Crescini, and L. S. Kuzmin, Detection of single-mode thermal microwave photons using an underdamped Josephson junction, Nat. Commun. 16, 3457 (2025).
  18. A. L. Pankratov et al., Search for dark-matter axions beyond the quantum limit: The cosmological axion Sarov haloscope proposal, Phys. Rev. D 112, 035003 (2025).
  19. C.-L. Kuo et al., Maximizing quantum enhancement in axion dark matter experiments, Phys. Rev. D 111, 123018 (2025).
  20. S. Chakram, A. E. Oriani, R. K. Naik, A. V. Dixit, K. He, A. Agrawal, H. Kwon, and D. I. Schuster, Seamless high-Q microwave cavities for multimode circuit quantum electrodynamics, Phys. Rev. Lett. 127, 107701 (2021).
  21. A. V. Dixit, S. Chakram, K. He, A. Agrawal, R. K. Naik, D. I. Schuster, and A. Chou, Searching for dark matter with a superconducting qubit, Phys. Rev. Lett. 126, 141302 (2021).
  22. Y. Gu (RADES Collaboration), Dark matter detection with superconducting qubit in RADES experiment, Proc. Sci. COSMICWISPers2024 (2025) 067.
  23. A. Agrawal, A. V. Dixit, T. Roy, S. Chakram, K. He, R. K. Naik, D. I. Schuster, and A. Chou, Stimulated emission of signal photons from dark matter waves, Phys. Rev. Lett. 132, 140801 (2024).
  24. P. Zheng et al., Quantum-enhanced dark matter detection using Schrödinger cat states, arXiv:2507.23538.
  25. K. Wurtz, B. M. Brubaker, Y. Jiang, E. P. Ruddy, D. A. Palken, and K. W. Lehnert, Cavity entanglement and state swapping to accelerate the search for axion dark matter, PRX Quantum 2, 040350 (2021).
  26. Y. Jiang, E. P. Ruddy, K. O. Quinlan, M. Malnou, N. E. Frattini, and K. W. Lehnert, Accelerated weak signal search using mode entanglement and state swapping, PRX Quantum 4, 020302 (2023).
  27. H. Shi and Q. Zhuang, Ultimate precision limit of noise sensing and dark matter search, npj Quantum Inf. 9, 27 (2023).
  28. H. Shi, A. J. Brady, W. Górecki, L. Maccone, R. Di Candia, and Q. Zhuang, Quantum-enhanced dark matter detection with in-cavity control: Mitigating the Rayleigh curse, npj Quantum Inf. 11, 48 (2025).
  29. A. J. Brady, C. Gao, R. Harnik, Z. Liu, Z. Zhang, and Q. Zhuang, Entangled sensor-networks for dark-matter searches, PRX Quantum 3, 030333 (2022).
  30. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Detecting hidden photon dark matter using the direct excitation of transmon qubits, Phys. Rev. Lett. 131, 211001 (2023).
  31. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Quantum enhancement in dark matter detection with quantum computation, Phys. Rev. Lett. 133, 021801 (2024).
  32. A. Ito, R. Kitano, W. Nakano, and R. Takai, Quantum entanglement of ions for light dark matter detection, J. High Energy Phys. 02 (2024) 124.
  33. S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichanugrist, Search for QCD axion dark matter with transmon qubits and quantum circuit, Phys. Rev. D 110, 115021 (2024).
  34. J. Shu, B. Xu, and Y. Xu, Eliminating incoherent noise: A coherent quantum approach in multi-sensor dark matter detection, arXiv:2410.22413.
  35. H. Fukuda, Y. Matsuzaki, and T. Sichanugrist, Directional search for light dark matter with quantum sensors, Phys. Rev. Lett. 135, 241802 (2025).
  36. D. Y. Cheong, N. L. Rodd, and L.-T. Wang, Quantum description of wave dark matter, Phys. Rev. D 111, 015028 (2025).
  37. P. Sikivie, Experimental tests of the invisible axion, Phys. Rev. Lett. 51, 1415 (1983); 52, 695(E) (1984).
  38. Y. Bao, D. Y. Cheong, N. L. Rodd, J. Takach, L.-T. Wang, and K. Zhou, A fully quantum description of axion dark matter detection (to be published).
  39. R. J. Glauber, Coherent and incoherent states of the radiation field, Phys. Rev. 131, 2766 (1963).
  40. E. C. G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams, Phys. Rev. Lett. 10, 277 (1963).
  41. J. L. J. Kuß and D. J. E. Marsh, Squeezing the axion, Open J. Astrophys. 4, 6 (2021).
  42. S. Kalia, Stamps of state on structure: Probing the state of ultralight dark matter via its density fluctuations, Phys. Rev. D 113, 043534 (2026).
  43. M. Gorghetto, E. Hardy, and G. Villadoro, More axion stars from strings, J. High Energy Phys. 08 (2024) 126.
  44. K. Saikawa, J. Redondo, A. Vaquero, and M. Kaltschmidt, Spectrum of global string networks and the axion dark matter mass, J. Cosmol. Astropart. Phys. 10 (2024) 043.
  45. H. Kim, J. Park, and M. Son, Axion dark matter from cosmic string network, J. High Energy Phys. 07 (2024) 150.
  46. J. N. Benabou, M. Buschmann, J. W. Foster, and B. R. Safdi, Axion mass prediction from adaptive mesh refinement cosmological lattice simulations, Phys. Rev. Lett. 134, 241003 (2025).
  47. A. Eberhardt, M. Kopp, and T. Abel, When quantum corrections alter the predictions of classical field theory for scalar field dark matter, Phys. Rev. D 106, 103002 (2022).
  48. A. Eberhardt, A. Zamora, M. Kopp, and T. Abel, Classical field approximation of ultralight dark matter: Quantum break times, corrections, and decoherence, Phys. Rev. D 109, 083527 (2024).
  49. I. Allali and M. P. Hertzberg, Gravitational decoherence of dark matter, J. Cosmol. Astropart. Phys. 07 (2020) 056.
  50. I. J. Allali and M. P. Hertzberg, Decoherence from general relativity, Phys. Rev. D 103, 104053 (2021).
  51. I. J. Allali and M. P. Hertzberg, General relativistic decoherence with applications to dark matter detection, Phys. Rev. Lett. 127, 031301 (2021).
  52. D. V. Semikoz and I. I. Tkachev, Condensation of bosons in kinetic regime, Phys. Rev. D 55, 489 (1997).
  53. P. Sikivie and Q. Yang, Bose-Einstein condensation of dark matter axions, Phys. Rev. Lett. 103, 111301 (2009).
  54. A. H. Guth, M. P. Hertzberg, and C. Prescod-Weinstein, Do dark matter axions form a condensate with long-range correlation?, Phys. Rev. D 92, 103513 (2015).
  55. D. J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
  56. D. Budker, J. Eby, M. Gorghetto, M. Jiang, and G. Perez, A generic formation mechanism of ultralight dark matter solar halos, J. Cosmol. Astropart. Phys. 12 (2023) 021.
  57. J. A. Dror, H. Murayama, and N. L. Rodd, Cosmic axion background, Phys. Rev. D 103, 115004 (2021); 106, 119902(E) (2022).
  58. M. Ley and R. L. and, Theory of single-photon interference experiments, Opt. Acta 33, 371 (1986).
  59. P. Hariharan, N. Brown, and B. S. and, Interference of independent laser beams at the single-photon level, J. Mod. Opt. 40, 113 (1993).
  60. D. F. Walls, A simple field theoretic description of photon interference, Am. J. Phys. 45, 952 (1977).
  61. C. J. Villas-Boas, C. E. Máximo, P. J. Paulino, R. P. Bachelard, and G. Rempe, Bright and dark states of light: The quantum origin of classical interference, Phys. Rev. Lett. 134, 133603 (2025).
  62. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys. 82, 1155 (2010).
  63. J. Beckey, D. Carney, and G. Marocco, Quantum measurements in fundamental physics: A user’s manual, arXiv:2311.07270.
  64. J.-D. Bernal, R. B. Petery, K. J. Joven, and S. Singh, Characterizing the quantum properties of ultralight dark matter: An open quantum systems approach, Phys. Rev. D 111, 032003 (2025).
  65. J. W. Foster, N. L. Rodd, and B. R. Safdi, Revealing the dark matter halo with axion direct detection, Phys. Rev. D 97, 123006 (2018).
  66. H. J. Carmichael, Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations (Springer, Berlin, Heidelberg, 1999).
  67. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, England, 1995).
  68. C. K. Hong, S. Friberg, and L. Mandel, Conditions for nonclassical behavior in the light amplifier, J. Opt. Soc. Am. B 2, 494 (1985).
  69. D. Klyshko, Nonunitary transformations in quantum optics, Phys. Lett. 137A, 334 (1989).
  70. G. S. Agarwal and K. Tara, Transformations of the nonclassical states by an optical amplifier, Phys. Rev. A 47, 3160 (1993).
  71. M. Bohmann and E. Agudelo, Phase-space inequalities beyond negativities, Phys. Rev. Lett. 124, 133601 (2020).
  72. J. Park, J. Lee, and H. Nha, Verifying single-mode nonclassicality beyond negativity in phase space, Phys. Rev. Res. 3, 043116 (2021).
  73. M. Hillery, Conservation laws and nonclassical states in nonlinear optical systems, Phys. Rev. A 31, 338 (1985).
  74. C. T. Lee, Higher-order criteria for nonclassical effects in photon statistics, Phys. Rev. A 41, 1721 (1990).
  75. C. T. Lee, Many-photon antibunching in generalized pair coherent states, Phys. Rev. A 41, 1569 (1990).
  76. D. Klyshko, Observable signs of nonclassical light, Phys. Lett. A 213, 7 (1996).
  77. G. S. Agarwal and K. Tara, Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics, Phys. Rev. A 46, 485 (1992).
  78. G. Agarwal, Nonclassical characteristics of the marginals for the radiation field, Opt. Commun. 95, 109 (1993).
  79. T. Richter and W. Vogel, Nonclassicality of quantum states: A hierarchy of observable conditions, Phys. Rev. Lett. 89, 283601 (2002).
  80. E. Shchukin, T. Richter, and W. Vogel, Nonclassicality criteria in terms of moments, Phys. Rev. A 71, 011802 (2005).
  81. E. V. Shchukin and W. Vogel, Nonclassical moments and their measurement, Phys. Rev. A 72, 043808 (2005).
  82. S. Ryl, J. Sperling, E. Agudelo, M. Mraz, S. Köhnke, B. Hage, and W. Vogel, Unified nonclassicality criteria, Phys. Rev. A 92, 011801 (2015).
  83. C. J. Riedel, Direct detection of classically undetectable dark matter through quantum decoherence, Phys. Rev. D 88, 116005 (2013).
  84. C. J. Riedel and I. Yavin, Decoherence as a way to measure extremely soft collisions with dark matter, Phys. Rev. D 96, 023007 (2017).
  85. P. G. C. Rufo, A. Kumar, C. Sabín, and A. Mazumdar, Entanglement witnesses mediated via axionlike particles, Phys. Rev. D 111, 115005 (2025).
  86. L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. 120B, 133 (1983).
  87. J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. 120B, 127 (1983).
  88. J. Jaeckel and A. Ringwald, The low-energy frontier of particle physics, Annu. Rev. Nucl. Part. Sci. 60, 405 (2010).
  89. M. Battaglieri et al., US cosmic visions: New ideas in dark matter 2017: Community report, in U.S. Cosmic Visions: New Ideas in Dark Matter (2017), arXiv:1707.04591.
  90. I. G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102, 89 (2018).
  91. D. J. E. Marsh, Measuring the quantum state of dark matter, Ann. Phys. (Berlin) 536, 2200609 (2024).
  92. E. W. Lentz, Signatures from non-classical features of axion dark matter in cavity haloscopes, arXiv:2509.03877.
  93. J. L. Evans, Effect of ultralight dark matter on g−2 of the electron, Phys. Rev. Lett. 132, 091801 (2024).
  94. K. Zhou, Ponderomotive effects of ultralight dark matter, J. High Energy Phys. 05 (2025) 134.
  95. F. Dyson, Is a graviton detectable?, Int. J. Mod. Phys. A 28, 1330041 (2013).
  96. T. Rothman and S. Boughn, Can gravitons be detected?, Found. Phys. 36, 1801 (2006).
  97. S. Boughn and T. Rothman, Aspects of graviton detection: Graviton emission and absorption by atomic hydrogen, Classical Quantum Gravity 23, 5839 (2006).
  98. D. Carney, V. Domcke, and N. L. Rodd, Graviton detection and the quantization of gravity, Phys. Rev. D 109, 044009 (2024).
  99. D. Carney, Comments on graviton detection, arXiv:2408.00094.
  100. S. K. Manikandan and F. Wilczek, Testing the coherent state description of radiation fields, Phys. Rev. A 111, 033705 (2025).
  101. E. Boyers, G. Goldstein, and A. O. Sushkov, Spin squeezing of macroscopic nuclear spin ensembles, Phys. Rev. D 111, 052004 (2025).
  102. Y. G. del Castillo, G. Pierobon, D. Sengupta, and Y. Y. Y. Wong, Prospects for relic neutrino detection using nuclear spin experiments, Phys. Rev. D 113, 043061 (2026).
  103. M. Galanis, O. Hosten, A. Arvanitaki, and S. Dimopoulos, Toward 48 dB spin squeezing and 96 db signal magnification for cosmic relic searches with nuclear spins, arXiv:2508.20520.
  104. L. Mandel, Non-classical states of the electromagnetic field, Phys. Scr. 1986, 34 (1986).
  105. L. Brouwer et al. (DMRadio Collaboration), Projected sensitivity of DMRadio-m3: A search for the QCD axion below 1  μeV, Phys. Rev. D 106, 103008 (2022).
  106. Z. Li, K. Zhou, M. Oriunno, A. Berlin, S. Calatroni, R. Tito D’Agnolo, S. A. R. Ellis, P. Schuster, S. G. Tantawi, and N. Toro, A prototype hybrid mode cavity for heterodyne axion detection, Nucl. Instrum. Methods Phys. Res., Sect. A 1088, 171474 (2026).

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Phys. Rev. Lett. 136, 171601– Published 29 April, 2026
  • Received 16 October 2025
  • Accepted 31 March 2026
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