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Large-size magnon cat states through intrinsic three-magnon nonlinearity

Da-Wei Liu, Zi-Hao Li, Ying Wu, and Liu-Gang Si*

  • *Contact author: siliugang@hust.edu.cn
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Phys. Rev. Research 8, 033172 – Published 11 August, 2026

DOI: https://doi.org/10.1103/hmf4-19vq

Abstract

The cat state, as an important tool for exploring the classical-quantum boundary, not only provides important tests of macroscopic quantum effects, but also has important applications in quantum metrology and quantum computation. The three-magnon process, which originates from the magnetic dipole-dipole interaction, has been less explored in the preparation of nonclassical magnon state. Here, we develop the magnon parametric coupling process that arises from the three-magnon scattering. The magnon parametric coupling strength is analytically derived and can reach a strong coupling regime within a discretized magnon mode system. Based on this, we propose a scheme to prepare the cat state without involving external nonlinearity in a magnetic system. Through the magnon parametric coupling, the extra magnon dissipation channel provided by the magnon-photon interaction induces an effective two-magnon loss channel, thereby steering the magnon into the cat state manifold. Notably, the size of the magnon cat state is inversely proportional to the parametric coupling strength, which facilitates the preparation of large-size cat states, even under environmental decoherence. Our work opens a path for the preparation of nonclassical states in magnon spintronics systems without extra nonlinear materials and also promotes the study of fundamental nonlinear physics on the magnetic platform.

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References (92)

  1. E. Schrödinger, Die gegenwärtige situation in der quantenmechanik, Naturwissenschaften 23, 844 (1935).
  2. Y. Xia and G. Guo, Nonclassical properties of even and odd coherent states, Phys. Lett. A 136, 281 (1989).
  3. J. Janszky and A. V. Vinogradov, Squeezing via one-dimensional distribution of coherent states, Phys. Rev. Lett. 64, 2771 (1990).
  4. J. Janszky, P. Domokos, and P. Adam, Coherent states on a circle and quantum interference, Phys. Rev. A 48, 2213 (1993).
  5. J. Janszky, P. Domokos, S. Szabó, and P. Adam, Quantum-state engineering via discrete coherent-state superpositions, Phys. Rev. A 51, 4191 (1995).
  6. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
  7. M. Brune, E. Hagley, J. Dreyer, X. Maître, A. Maali, C. Wunderlich, J. M. Raimond, and S. Haroche, Observing the progressive decoherence of the “meter” in a quantum measurement, Phys. Rev. Lett. 77, 4887 (1996).
  8. C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, A “Schrödinger cat” superposition state of an atom, Science 272, 1131 (1996).
  9. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Quantum computation with optical coherent states, Phys. Rev. A 68, 042319 (2003).
  10. A. Gilchrist, K. Nemoto, W. J. Munro, T. C. Ralph, S. Glancy, S. L. Braunstein, and G. J. Milburn, Schrödinger cats and their power for quantum information processing, J. Opt. B: Quantum Semiclass. Opt. 6, S828 (2004).
  11. M. Gu, Computing with quantum cats: From Colossus to qubits, Phys. Today 68(1), 46 (2015).
  12. W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, Bosonic quantum error correction codes in superconducting quantum circuits, Fundam. Res. 1, 50 (2021).
  13. M. Kira, S. W. Koch, R. P. Smith, A. E. Hunter, and S. T. Cundiff, Quantum spectroscopy with Schrödinger-cat states, Nat. Phys. 7, 799 (2011).
  14. L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
  15. J. Clarke, A. N. Cleland, M. H. Devoret, D. Esteve, and J. M. Martinis, Quantum mechanics of a macroscopic variable: The phase difference of a Josephson junction, Science 239, 992 (1988).
  16. J. R. Friedman, V. Patel, W. Chen, S. Tolpygo, and J. E. Lukens, Quantum superposition of distinct macroscopic states, Nature (London) 406, 43 (2000).
  17. C. H. van der Wal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, Quantum superposition of macroscopic persistent-current states, Science 290, 773 (2000).
  18. J. S. Neergaard-Nielsen, B. M. Nielsen, C. Hettich, K. Mølmer, and E. S. Polzik, Generation of a superposition of odd photon number states for quantum information networks, Phys. Rev. Lett. 97, 083604 (2006).
  19. M. Arndt, O. Nairz, J. Vos-Andreae, C. Keller, G. Van der Zouw, and A. Zeilinger, Wave–particle duality of C60 molecules, Nature (London) 401, 680 (1999).
  20. Z. Leghtas, S. Touzard, I. M. Pop, A. Kou, B. Vlastakis, A. Petrenko, K. M. Sliwa, A. Narla, S. Shankar, M. J. Hatridge, M. Reagor, L. Frunzio, R. J. Schoelkopf, M. Mirrahimi, and M. H. Devoret, Confining the state of light to a quantum manifold by engineered two-photon loss, Science 347, 853 (2015).
  21. R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas, Exponential suppression of bit-flips in a qubit encoded in an oscillator, Nat. Phys. 16, 509 (2020).
  22. Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to adiabaticity for the quantum Rabi model: Efficient generation of giant entangled cat states via parametric amplification, Phys. Rev. Lett. 126, 023602 (2021).
  23. J.-Q. Liao and L. Tian, Macroscopic quantum superposition in cavity optomechanics, Phys. Rev. Lett. 116, 163602 (2016).
  24. M. Dakna, T. Anhut, T. Opatrný, L. Knöll, and D.-G. Welsch, Generating Schrödinger-cat-like states by means of conditional measurements on a beam splitter, Phys. Rev. A 55, 3184 (1997).
  25. A. Ourjoumtsev, R. Tualle-Brouri, J. Laurat, and P. Grangier, Generating optical Schrödinger kittens for quantum information processing, Science 312, 83 (2006).
  26. F.-X. Sun, S.-S. Zheng, Y. Xiao, Q. Gong, Q. He, and K. Xia, Remote generation of magnon Schrödinger cat state via magnon-photon entanglement, Phys. Rev. Lett. 127, 087203 (2021).
  27. C. C. Gerry and E. E. Hach, Generation of even and odd coherent states in a competitive two-photon process, Phys. Lett. A 174, 185 (1993).
  28. L. Gilles, B. M. Garraway, and P. L. Knight, Generation of nonclassical light by dissipative two-photon processes, Phys. Rev. A 49, 2785 (1994).
  29. W. Qin, A. Miranowicz, H. Jing, and F. Nori, Generating long-lived macroscopically distinct superposition states in atomic ensembles, Phys. Rev. Lett. 127, 093602 (2021).
  30. B. D. Hauer, J. Combes, and J. D. Teufel, Nonlinear sideband cooling to a cat state of motion, Phys. Rev. Lett. 130, 213604 (2023).
  31. A. Vrajitoarea, Z. Huang, P. Groszkowski, J. Koch, and A. A. Houck, Quantum control of an oscillator using a stimulated Josephson nonlinearity, Nat. Phys. 16, 211 (2020).
  32. G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Observation of quantum state collapse and revival due to the single-photon Kerr effect, Nature (London) 495, 205 (2013).
  33. D.-W. Liu, Y. Wu, and L.-G. Si, Magnon cat states induced by photon parametric coupling, Phys. Rev. Appl. 21, 044018 (2024).
  34. K.-i. Uchida, J. Xiao, H. Adachi, J.-I. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. Kajiwara, H. Umezawa, H. Kawai, G. E. W. Bauer, S. Maekawa, and E. Saitoh, Spin Seebeck insulator, Nat. Mater. 9, 894 (2010).
  35. Y. Kajiwara, K. Harii, S. Takahashi, J.-I. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, Transmission of electrical signals by spin-wave interconversion in a magnetic insulator, Nature (London) 464, 262 (2010).
  36. H. Huebl, C. W. Zollitsch, J. Lotze, F. Hocke, M. Greifenstein, A. Marx, R. Gross, and S. T. B. Goennenwein, High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids, Phys. Rev. Lett. 111, 127003 (2013).
  37. M. Goryachev, W. G. Farr, D. L. Creedon, Y. Fan, M. Kostylev, and M. E. Tobar, High-cooperativity cavity QED with magnons at microwave frequencies, Phys. Rev. Appl. 2, 054002 (2014).
  38. X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Strongly coupled magnons and cavity microwave photons, Phys. Rev. Lett. 113, 156401 (2014).
  39. Y. Tabuchi, S. Ishino, T. Ishikawa, R. Yamazaki, K. Usami, and Y. Nakamura, Hybridizing ferromagnetic magnons and microwave photons in the quantum limit, Phys. Rev. Lett. 113, 083603 (2014).
  40. Z. Wang, H. Y. Yuan, Y. Cao, Z.-X. Li, R. A. Duine, and P. Yan, Magnonic frequency comb through nonlinear magnon-skyrmion scattering, Phys. Rev. Lett. 127, 037202 (2021).
  41. Z. Wang, H. Y. Yuan, Y. Cao, and P. Yan, Twisted magnon frequency comb and Penrose superradiance, Phys. Rev. Lett. 129, 107203 (2022).
  42. G.-T. Xu, M. Zhang, Y. Wang, Z. Shen, G.-C. Guo, and C.-H. Dong, Magnonic frequency comb in the magnomechanical resonator, Phys. Rev. Lett. 131, 243601 (2023).
  43. X. Wang, K.-W. Huang, Q.-Y. Qiu, and H. Xiong, Nonreciprocal double-carrier frequency combs in cavity magnonics, Chaos, Solitons Fractals 176, 114137 (2023).
  44. S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, Bose–Einstein condensation of quasi-equilibrium magnons at room temperature under pumping, Nature (London) 443, 430 (2006).
  45. Z.-X. Liu and H. Xiong, Magnon laser based on Brillouin light scattering, Opt. Lett. 45, 5452 (2020).
  46. Y.-J. Xu and J. Song, Nonreciprocal magnon laser, Opt. Lett. 46, 5276 (2021).
  47. K.-W. Huang, Y. Wu, and L.-G. Si, Parametric-amplification-induced nonreciprocal magnon laser, Opt. Lett. 47, 3311 (2022).
  48. Z.-X. Liu, H. Xiong, and Y. Wu, Magnon blockade in a hybrid ferromagnet-superconductor quantum system, Phys. Rev. B 100, 134421 (2019).
  49. J. Li, S.-Y. Zhu, and G. S. Agarwal, Magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. Lett. 121, 203601 (2018).
  50. A. Kamra and W. Belzig, Super-Poissonian shot noise of squeezed-magnon mediated spin transport, Phys. Rev. Lett. 116, 146601 (2016).
  51. A. Kamra and W. Belzig, Magnon-mediated spin current noise in ferromagnet | nonmagnetic conductor hybrids, Phys. Rev. B 94, 014419 (2016).
  52. A. Kamra, U. Agrawal, and W. Belzig, Noninteger-spin magnonic excitations in untextured magnets, Phys. Rev. B 96, 020411(R) (2017).
  53. Y.-P. Wang, G.-Q. Zhang, D. Zhang, T.-F. Li, C.-M. Hu, and J. Q. You, Bistability of cavity magnon polaritons, Phys. Rev. Lett. 120, 057202 (2018).
  54. Y. Li, T. Polakovic, Y.-L. Wang, J. Xu, S. Lendinez, Z. Zhang, J. Ding, T. Khaire, H. Saglam, R. Divan, J. Pearson, W.-K. Kwok, Z. Xiao, V. Novosad, A. Hoffmann, and W. Zhang, Strong coupling between magnons and microwave photons in on-chip ferromagnet-superconductor thin-film devices, Phys. Rev. Lett. 123, 107701 (2019).
  55. F.-Y. Zhang, Q.-C. Wu, and C.-P. Yang, Non-Hermitian shortcut to adiabaticity in Floquet cavity electromagnonics, Phys. Rev. A 106, 012609 (2022).
  56. R.-C. Shen, J. Li, Z.-Y. Fan, Y.-P. Wang, and J. Q. You, Mechanical bistability in Kerr-modified cavity magnomechanics, Phys. Rev. Lett. 129, 123601 (2022).
  57. R. Hisatomi, A. Osada, Y. Tabuchi, T. Ishikawa, A. Noguchi, R. Yamazaki, K. Usami, and Y. Nakamura, Bidirectional conversion between microwave and light via ferromagnetic magnons, Phys. Rev. B 93, 174427 (2016).
  58. A. Osada, R. Hisatomi, A. Noguchi, Y. Tabuchi, R. Yamazaki, K. Usami, M. Sadgrove, R. Yalla, M. Nomura, and Y. Nakamura, Cavity optomagnonics with spin-orbit coupled photons, Phys. Rev. Lett. 116, 223601 (2016).
  59. X. Zhang, N. Zhu, C.-L. Zou, and H. X. Tang, Optomagnonic whispering gallery microresonators, Phys. Rev. Lett. 117, 123605 (2016).
  60. A. Osada, A. Gloppe, R. Hisatomi, A. Noguchi, R. Yamazaki, M. Nomura, Y. Nakamura, and K. Usami, Brillouin light scattering by magnetic quasivortices in cavity optomagnonics, Phys. Rev. Lett. 120, 133602 (2018).
  61. L. Sheng, M. Elyasi, J. Chen, W. He, Y. Wang, H. Wang, H. Feng, Y. Zhang, I. Medlej, S. Liu, W. Jiang, X. Han, D. Yu, J.-P. Ansermet, G. E. W. Bauer, and H. Yu, Nonlocal detection of interlayer three-magnon coupling, Phys. Rev. Lett. 130, 046701 (2023).
  62. V. T. Synogach, Y. K. Fetisov, C. Mathieu, and C. E. Patton, Ultrashort microwave pulses generated due to three magnon interactions, Phys. Rev. Lett. 85, 2184 (2000).
  63. T. Qu, A. Hamill, R. H. Victora, and P. A. Crowell, Oscillations and confluence in three-magnon scattering of ferromagnetic resonance, Phys. Rev. B 107, L060401 (2023).
  64. T. Makihara, K. Hayashida, G. T. Noe Ii, X. Li, N. Marquez Peraca, X. Ma, Z. Jin, W. Ren, G. Ma, I. Katayama, et al., Ultrastrong magnon–magnon coupling dominated by antiresonant interactions, Nat. Commun. 12, 3115 (2021).
  65. C. L. Ordóñez-Romero, B. A. Kalinikos, P. Krivosik, W. Tong, P. Kabos, and C. E. Patton, Three-magnon splitting and confluence processes for spin-wave excitations in yttrium iron garnet films: Wave vector selective Brillouin light scattering measurements and analysis, Phys. Rev. B 79, 144428 (2009).
  66. H. J. J. Liu, G. A. Riley, C. L. Ordóñez-Romero, B. A. Kalinikos, and K. S. Buchanan, Time-resolved study of nonlinear three-magnon processes in yttrium iron garnet films, Phys. Rev. B 99, 024429 (2019).
  67. S. Lendinez, M. T. Kaffash, O. G. Heinonen, S. Gliga, E. Iacocca, and M. B. Jungfleisch, Nonlinear multi-magnon scattering in artificial spin ice, Nat. Commun. 14, 3419 (2023).
  68. M. Elyasi, K. Yamamoto, T. Hioki, T. Makiuchi, H. Shimizu, E. Saitoh, and G. E. W. Bauer, Nonlinear enhancement of coherent magnetization dynamics, Phys. Rev. B 109, L180402 (2024).
  69. O. Lee, K. Yamamoto, M. Umeda, C. W. Zollitsch, M. Elyasi, T. Kikkawa, E. Saitoh, G. E. W. Bauer, and H. Kurebayashi, Nonlinear magnon polaritons, Phys. Rev. Lett. 130, 046703 (2023).
  70. M. Mohseni, Q. Wang, B. Heinz, M. Kewenig, M. Schneider, F. Kohl, B. Lägel, C. Dubs, A. V. Chumak, and P. Pirro, Controlling the nonlinear relaxation of quantized propagating magnons in nanodevices, Phys. Rev. Lett. 126, 097202 (2021).
  71. K. Nikolaev, S. Lake, G. Schmidt, S. Demokritov, and V. Demidov, Resonant generation of propagating second-harmonic spin waves in nano-waveguides, Nat. Commun. 15, 1827 (2024).
  72. S. Sharma, V. A. S. V. Bittencourt, A. D. Karenowska, and S. V. Kusminskiy, Spin cat states in ferromagnetic insulators, Phys. Rev. B 103, L100403 (2021).
  73. S. He, X. Xin, F.-Y. Zhang, and C. Li, Generation of a Schrödinger cat state in a hybrid ferromagnet-superconductor system, Phys. Rev. A 107, 023709 (2023).
  74. I. Barsukov, H. K. Lee, A. A. Jara, Y.-J. Chen, A. M. Gonçalves, C. Sha, J. A. Katine, R. E. Arias, B. A. Ivanov, and I. N. Krivorotov, Giant nonlinear damping in nanoscale ferromagnets, Sci. Adv. 5, eaav6943 (2019).
  75. P. Krivosik and C. E. Patton, Hamiltonian formulation of nonlinear spin-wave dynamics: Theory and applications, Phys. Rev. B 82, 184428 (2010).
  76. M. Hurben and C. Patton, Theory of magnetostatic waves for in-plane magnetized isotropic films, J. Magn. Magn. Mater. 139, 263 (1995).
  77. A. Prabhakar and D. D. Stancil, Spin Waves: Theory and Applications (Springer, New York, 2009), Vol. 5.
  78. M. Sparks, Ferromagnetic resonance in thin films. I. Theory of normal-mode frequencies, Phys. Rev. B 1, 3831 (1970).
  79. R. F. Soohoo, General exchange boundary condition and surface anisotropy energy of a ferromagnet, Phys. Rev. 131, 594 (1963).
  80. Y. S. Gui, N. Mecking, and C. M. Hu, Quantized spin excitations in a ferromagnetic microstrip from microwave photovoltage measurements, Phys. Rev. Lett. 98, 217603 (2007).
  81. R. Salikhov, I. Ilyakov, L. Körber, A. Kákay, R. A. Gallardo, A. Ponomaryov, J.-C. Deinert, T. V. de Oliveira, K. Lenz, J. Fassbender, et al., Coupling of terahertz light with nanometre-wavelength magnon modes via spin–orbit torque, Nat. Phys. 19, 529 (2023).
  82. B. Zare Rameshti, S. Viola Kusminskiy, J. A. Haigh, K. Usami, D. Lachance-Quirion, Y. Nakamura, C.-M. Hu, H. X. Tang, G. E. Bauer, and Y. M. Blanter, Cavity magnonics, Phys. Rep. 979, 1 (2022) .
  83. O. Gamel and D. F. V. James, Time-averaged quantum dynamics and the validity of the effective Hamiltonian model, Phys. Rev. A 82, 052106 (2010).
  84. W. Shao, C. Wu, and X.-L. Feng, Generalized James’ effective Hamiltonian method, Phys. Rev. A 95, 032124 (2017).
  85. B. Yurke and D. Stoler, Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion, Phys. Rev. Lett. 57, 13 (1986).
  86. G. Björk and P. G. L. Mana, A size criterion for macroscopic superposition states, J. Opt. B: Quantum Semiclass. Opt. 6, 429 (2004).
  87. Z.-H. Li, F. Yu, Z.-Y. Li, M. Al-Amri, and M. S. Zubairy, Method to deterministically generate large-amplitude optical cat states, Commun. Phys. 7, 134 (2024).
  88. P. Krivosik, N. Mo, S. Kalarickal, and C. E. Patton, Hamiltonian formalism for two magnon scattering microwave relaxation: Theory and applications, J. Appl. Phys. 101, 083901 (2007).
  89. Y.-P. Zhao, G. Palasantzas, G.-C. Wang, and J. T. M. De Hosson, Surface/interface-roughness-induced demagnetizing effect in thin magnetic films, Phys. Rev. B 60, 1216 (1999).
  90. R. Verba, V. Tiberkevich, and A. Slavin, Hamiltonian formalism for nonlinear spin wave dynamics under antisymmetric interactions: Application to Dzyaloshinskii-Moriya interaction, Phys. Rev. B 99, 174431 (2019).
  91. J. T. Hugall, A. Singh, and N. F. van Hulst, Plasmonic cavity coupling, ACS Photon. 5, 43 (2018).
  92. P. Haikka, Y. Kubo, A. Bienfait, P. Bertet, and K. Mølmer, Proposal for detecting a single electron spin in a microwave resonator, Phys. Rev. A 95, 022306 (2017).

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Phys. Rev. Research 8, 033172– Published 11 August, 2026
  • Received 2 October 2024
  • Accepted 24 July 2026
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