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Single- and two-mode magnon thermal squeezing

Nature Physics (2026) Cite this article

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Abstract

Squeezed states play a central role in modern precision measurement and information processing, reducing the noise through manipulating its distributions in phase space. Although squeezing has been explored in various physical systems, realization and characterization in magnetic media remain largely unexplored. Here we demonstrate the single-mode thermal squeezing of the magnetization dynamics in an yttrium iron garnet film using microwave parametric excitation. We also demonstrate two-mode thermal squeezing in the form of correlated fluctuations of magnons concentrated on the top and bottom surfaces of the film. Establishing the control of thermal squeezing in magnetic systems provides insights into the fluctuation dynamics of the magnetic order, and represents a key advance in the quest to observe quantum effects in magnetic films.

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Fig. 1: Squeezing of magnetization fluctuations.
The alternative text for this image may have been generated using AI.
Fig. 2: Observation of single-mode thermal squeezing of magnetization fluctuations.
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Fig. 3: Observation of two-mode squeezing of the magnetization fluctuations.
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Fig. 4: Localization of magnons under non-degenerate parametric excitation.
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Fig. 5: Numerical simulation of magnon modes.
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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request. Due to the size of the datasets and the specialized analysis procedures required, they are not publicly available. Source data are provided with this paper.

Code availability

The codes used in theoretical simulations and calculations are available from the corresponding author upon reasonable request.

References

  1. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer Nature, 2008).

  2. Slusher, R. E., Hollberg, L. W., Yurke, B., Mertz, J. C. & Valley, J. F. Observation of squeezed states generated by four-wave mixing in an optical cavity. Phys. Rev. Lett. 55, 2409–2412 (1985).

    Article  ADS  Google Scholar 

  3. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).

    Article  ADS  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. McKenzie, K., Shaddock, D. A., McClelland, D. E., Buchler, B. C. & Lam, P. K. Experimental demonstration of a squeezing-enhanced power-recycled michelson interferometer for gravitational wave detection. Phys. Rev. Lett. 88, 231102 (2002).

    Article  ADS  Google Scholar 

  6. Goda, K. et al. A quantum-enhanced prototype gravitational-wave detector. Nat. Phys. 4, 472–476 (2008).

    Article  Google Scholar 

  7. Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  8. Jennewein, T., Simon, C., Weihs, G., Weinfurter, H. & Zeilinger, A. Quantum cryptography with entangled photons. Phys. Rev. Lett. 84, 4729 (2000).

    Article  ADS  Google Scholar 

  9. Naik, D. S., Peterson, C. G., White, A. G., Berglund, A. J. & Kwiat, P. G. Entangled state quantum cryptography: eavesdropping on the Ekert protocol. Phys. Rev. Lett. 84, 4733 (2000).

    Article  ADS  Google Scholar 

  10. Tittel, W., Brendel, J., Zbinden, H. & Gisin, N. Quantum cryptography using entangled photons in energy-time Bell states. Phys. Rev. Lett. 84, 4737 (2000).

    Article  ADS  Google Scholar 

  11. Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575–579 (1997).

    Article  ADS  Google Scholar 

  12. Furusawa, A. et al. Unconditional quantum teleportation. Science 282, 706–709 (1998).

    Article  ADS  Google Scholar 

  13. Kim, M. S., de Oliveira, F. A. M. & Knight, P. L. Properties of squeezed number states and squeezed thermal states. Phys. Rev. A 40, 2494 (1989).

    Article  ADS  Google Scholar 

  14. Roßnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K. & Lutz, E. Nanoscale heat engine beyond the Carnot limit. Phys. Rev. Lett. 112, 030602 (2014).

    Article  ADS  Google Scholar 

  15. Niedenzu, W., Mukherjee, V., Ghosh, A., Kofman, A. G. & Kurizki, G. Quantum engine efficiency bound beyond the second law of thermodynamics. Nat. Commun. 9, 165 (2018).

    Article  ADS  Google Scholar 

  16. Scully, M. O., Zubairy, M. S., Agarwal, G. S. & Walther, H. Extracting work from a single heat bath via vanishing quantum coherence. Science 299, 862–864 (2003).

    Article  ADS  Google Scholar 

  17. Wang, Y.-C. et al. Magnon squeezing in the quantum regime. Nat. Commun. 17, 2679 (2026).

    Article  ADS  Google Scholar 

  18. L’vov, V. S. Wave Turbulence Under Parametric Excitation (Springer-Verlag, 1994).

  19. Rezende, S. M. Fundamentals of Magnonics (Springer Nature, 2020).

  20. Che, P., Baumgaertl, K., Kúkol’ová, A., Dubs, C. & Grundler, D. Efficient wavelength conversion of exchange magnons below 100 nm by magnetic coplanar waveguides. Nat. Commun. 11, 1445 (2020).

    Article  ADS  Google Scholar 

  21. Wang, Q. et al. Deeply nonlinear excitation of self-normalized short spin waves. Sci. Adv. 9, eadg4609 (2023).

    Article  Google Scholar 

  22. Kamra, A., Belzig, W. & Brataas, A. Magnon-squeezing as a niche of quantum magnonics. Appl. Phys. Lett. 117, 090501 (2020).

    Article  ADS  Google Scholar 

  23. Elyasi, M., Blanter, Y. M. & Bauer, G. E. W. Resources of nonlinear cavity magnonics for quantum information. Phys. Rev. B 101, 054402 (2020).

    Article  ADS  Google Scholar 

  24. Tabuchi, Y. et al. Hybridizing ferromagnetic magnons and microwave photons in the quantum limit. Phys. Rev. Lett 113, 083603 (2014).

    Article  ADS  Google Scholar 

  25. Huebl, H. et al. High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids. Phys. Rev. Lett. 111, 127003 (2013).

    Article  ADS  Google Scholar 

  26. Hisatomi, R. et al. Bidirectional conversion between microwave and light via ferromagnetic magnons. Phys. Rev. B 93, 174427 (2016).

    Article  ADS  Google Scholar 

  27. Berk, C. et al. Strongly coupled magnon–phonon dynamics in a single nanomagnet. Nat. Commun. 10, 2652 (2019).

    Article  ADS  Google Scholar 

  28. An, K. et al. Coherent long-range transfer of angular momentum between magnon Kittel modes by phonons. Phys. Rev. B 101, 060407 (2020).

    Article  ADS  Google Scholar 

  29. Tabuchi, Y. et al. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405–408 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  30. Lachance-Quirion, D. et al. Entanglement-based single-shot detection of a single magnon with a superconducting qubit. Science 367, 425–428 (2020). 6476.

    Article  ADS  Google Scholar 

  31. Wu, L. A., Kimble, H. J., Hall, J. L. & Wu, H. Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 57, 2520 (1986).

    Article  ADS  Google Scholar 

  32. Polzik, E. S., Carri, J. & Kimble, H. J. Spectroscopy with squeezed light. Phys. Rev. Lett. 68, 3020 (1992).

    Article  ADS  Google Scholar 

  33. Breitenbach, G., Schiller, S. & Mlynek, J. Measurement of the quantum states of squeezed light. Nature 387, 471–475 (1997).

    Article  ADS  Google Scholar 

  34. Makiuchi, T. et al. Persistent magnetic coherence in magnets. Nat. Mater. 23, 627–632 (2024).

    Article  Google Scholar 

  35. Hioki, T., Shimizu, H., Makiuchi, T. & Saitoh, E. State tomography for magnetization dynamics. Phys. Rev. B 104, L100419 (2021).

    Article  ADS  Google Scholar 

  36. Jiao, H. J. & Bauer, G. E. W. Spin backflow and a.c. voltage generation by spin pumping and the inverse spin Hall effect. Phys. Rev. Lett. 110, 217602 (2013).

    Article  ADS  Google Scholar 

  37. Hahn, C. et al. Detection of microwave spin pumping using the inverse spin Hall effect. Phys. Rev. Lett. 111, 217204 (2013).

    Article  ADS  Google Scholar 

  38. Wei, D., Obstbaum, M., Ribow, M., Back, C. H. & Woltersdorf, G. Spin Hall voltages from a.c. and d.c. spin currents. Nat. Commun. 5, 3768 (2014).

    Article  ADS  Google Scholar 

  39. Tserkovnyak, Y., Brataas, A. & Bauer, G. E. W. Enhanced Gilbert damping in thin ferromagnetic films. Phys. Rev. Lett. 88, 117601 (2002).

    Article  ADS  Google Scholar 

  40. Mizukami, S., Ando, Y. & Miyazaki, T. Effect of spin diffusion on Gilbert damping for a very thin permalloy layer in Cu/permalloy/Cu/Pt films. Phys. Rev. B 66, 104413 (2002).

    Article  ADS  Google Scholar 

  41. Saitoh, E., Ueda, M., Miyajima, H. & Tatara, G. Conversion of spin current into charge current at room temperature: inverse spin-Hall effect. Appl. Phys. Lett. 88, 182509 (2006).

    Article  ADS  Google Scholar 

  42. Costache, M. V., Sladkov, M., Watts, S. M., van der Wal, C. H. & van Wees, B. J. Electrical detection of spin pumping due to the precessing magnetization of a single ferromagnet. Phys. Rev. Lett. 97, 216603 (2006).

    Article  ADS  Google Scholar 

  43. Valenzuela, S. O. & Tinkham, M. Direct electronic measurement of the spin Hall effect. Nature 442, 176–179 (2006).

    Article  ADS  Google Scholar 

  44. Macklin, C. A near–quantum-limited Josephson traveling-wave parametric amplifier. Science 350, 307–310 (2015). 6258.

    Article  ADS  Google Scholar 

  45. Kosen, S., van Loo, A. F., Bozhko, D. A., Mihalceanu, L. & Karenowska, A. D. Microwave magnon damping in YIG films at millikelvin temperatures. APL Mater. 7, 101120 (2019).

    Article  ADS  Google Scholar 

  46. Seiden, P. E. Ferrimagnetic resonance relaxation in rare-earth iron garnets. Phys. Rev. 133, A728 (1964).

    Article  ADS  Google Scholar 

  47. Mahboob, I., Okamoto, H., Onomitsu, K. & Yamaguchi, H. Two-mode thermal-noise squeezing in an electromechanical resonator. Phys. Rev. Lett. 113, 167203 (2014).

    Article  ADS  Google Scholar 

  48. Hurben, M. J. & Patton, C. E. Theory of magnetostatic waves for in-plane magnetized isotropic films. J. Magn. Magn. Mat. 139, 263–291 (1995).

    Article  ADS  Google Scholar 

  49. Melkov, G. A., Vasyuchka, V. I., Lazovskiy, V. V., Tiberkevich, V. S. & Slavin, A. N. Wave front reversal with frequency conversion in a nonreciprocal medium. Appl. Phys. Lett. 89, 252510 (2006).

    Article  ADS  Google Scholar 

  50. Roy, A., Jahani, S., Langrock, C., Fejer, M. & Marandi, A. Spectral phase transitions in optical parametric oscillators. Nat. Commun. 12, 835 (2021).

    Article  ADS  Google Scholar 

  51. Duan, L.-M., Giedke, G., Cirac, J. I. & Zoller, P. Inseparability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2722–2725 (2000).

    Article  ADS  Google Scholar 

  52. Simon, R. Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726–2729 (2000).

    Article  ADS  Google Scholar 

  53. An, T. et al. Unidirectional spin-wave heat conveyer. Nat. Mater. 12, 549–553 (2013).

    Article  Google Scholar 

  54. Vansteenkiste, A. et al. The design and verification of MuMax3. AIP Adv. 4, 107133 (2014).

    Article  ADS  Google Scholar 

  55. Kapelrud, A. & Brataas, A. Spin pumping and enhanced Gilbert damping in thin magnetic insulator films. Phys. Rev.Lett. 111, 097602 (2013).

    Article  ADS  Google Scholar 

  56. Jia, X., Liu, K., Xia, K. & Bauer, G. E. W. B. Spin transfer torque on magnetic insulators. Europhys. Lett. 96, 17005 (2011).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank B. Hillebrands, A. Serga, V. I. Vasyuchka, K. Kobayashi and T. Kikkawa for fruitful discussions. This work was partially supported by JST CREST (JPMJCR20C1 and JPMJCR20T2), JST PRESTO (JPMJPR24F9), JSPS KAKENHI (JP21K13847, JP22K14584, JP22H04965, JP22H04965, JP23KJ0607, JP24H02231, JP24KJ0927, JP24H02231 and JP25K17943), Advanced Technology Institute Research Grants, Support Center for Advanced Telecommunications Technology Research Grants, SCAT Research Grant, Institute for AI and Beyond of the University of Tokyo, and IBM–UTokyo lab.

Author information

Author notes

  1. These authors contributed equally: Tomosato Hioki, Kaito Tojo.

Authors and Affiliations

  1. Department of Applied Physics, The University of Tokyo, Tokyo, Japan

    Tomosato Hioki, Kaito Tojo, Sohei Horibe, Hiroki Shimizu, Koujiro Hoshi & Eiji Saitoh

  2. RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan

    Tomosato Hioki, Takahiko Makiuchi & Eiji Saitoh

  3. WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan

    Tomosato Hioki, Mehrdad Elyasi, Gerrit E. W. Bauer & Eiji Saitoh

  4. Institute for AI and Beyond, The University of Tokyo, Tokyo, Japan

    Koujiro Hoshi & Eiji Saitoh

  5. Institute for Materials Research and CSIS, Tohoku University, Sendai, Japan

    Gerrit E. W. Bauer

  6. Kavli Institute for Theoretical Sciences, University of the Chinese Academy of Sciences, Beijing, China

    Gerrit E. W. Bauer

  7. Quantum-Phase Electronics Centre, The University of Tokyo, Tokyo, Japan

    Eiji Saitoh

Authors
  1. Tomosato Hioki
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Contributions

T.H. designed the experiments. T.H., S.H. and H.S. prepared the sample. T.H and K.T. performed the experiments and T.H. analysed the data. M.E., and G.E.W.B. developed the theory. K.H. and T.M. supported numerical calculation. T.H., M.E., G.E.W.B. and E.S. discussed the interpretation. T.H. wrote the manuscript with input from all authors. E.S. supervised the research. All the authors discussed the results and contents of the manuscript.

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Correspondence to Tomosato Hioki.

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Nature Physics thanks Hossein Taghinejad for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Correlation measurement procedure.

The input microwave is generated by combining two channels (Ch.1 and Ch.2) into the pump channel (Ch.3) at the pump frequency \({f}_{{\rm{p}}}\) using a multichannel signal generator (Holtzworth 8990B). Ch.1 is used to finely tune the input microwave power with small increments, while Ch.2 is used for harmonic locking at frequency \(2{f}_{2}\). The signals from Ch.2 and Ch.3 are amplified ( + 35 dB) and combined with the output from Ch.1. The resulting microwave signal is delivered to the sample via the main coplanar waveguide (CPW; orange antenna). The AC signal generated from the YIG/Pt disc (orange circle) is detected by a secondary CPW (blue antenna) and routed, via an RF switch, to either the lock-in amplifier circuit or a spectrum analyser (SA). Before entering the lock-in amplifier, the signal is filtered (providing −80 dB attenuation at \(2f\)) to suppress crosstalk, amplified ( + 35 dB), and mixed with a local oscillator signal from Ch.4 of the signal generator. The mixed signal is then fed into a lock-in amplifier (Zurich UHFLI). FMR absorption spectra and spectra during the non-degenerate process are measured by routing the microwave signal to a vector network analyser (VNA) or spectrum analyser (SA) using an additional RF switch.

Extended Data Fig. 2 Evaluation of temperature increase by microwave pumping.

a, Temperature dependence of the resistance of the Pt film. b, Microwave power dependence of the resistance of the Pt film. c, Detuning frequency dependence of variance of \(I(f)\) and \(Q(f)\) plotted with theoretical curve of amplified noise due to non-degenerate parametric amplification.

Source data

Extended Data Fig. 3 Temperature dependence of S parameters and damping.

a, Temperature dependence of the microwave absorption spectrum (S11). b, Numerically calculated magnon intensity at 31.93 mT at T = 300 K. The calculation was performed for a magnetic disc with a diameter of 100 μm and a thickness of 1.6 μm, using the same material parameters as those used to obtain Fig. 5a–c. c, Magnetic field dependence of microwave absorption spectrum, d, Frequency dependence of microwave absorption spectrum up to 5 GHz, e, Temperature dependence of intrinsic Gilbert damping constant. All data were obtained from repeated measurements (n = 10) of the same sample under identical conditions. These measurements correspond to technical replicates. Error bars represent standard deviation (SD) of the data. Data are presented as mean ± SD.

Source data

Extended Data Fig. 4 Schematics of magnetization dynamics under parametric pumping.

a,b, Schematics of magnetization precession component and AC magnetic field when phase-matching conditions are satisfied. c, Snapshots of the elliptical magnetization (M) precession under an ac magnetic field (bac, pink arrows) and its torque (light blue arrows) that enforce or suppress the torques by the dc magnetic field \(-\gamma {\bf{M}}\times {\bf{B}}\) (black arrows). d, Top view of magnetization precession without AC magnetic field. e, Top view of magnetization precession under parametric pumping as in c. The torque arrow due to AC magnetic field (light blue) directs the same direction as \({\dot{M}}_{Y}\) when \({M}_{Y}\) takes maximum or minimum, while it directs the opposite when \({M}_{Y}=0\), leading to smaller noise along\({M}_{Y}\) and larger noise in \({M}_{X}\).

Extended Data Fig. 5 Two-mode Wigner function below and above threshold.

a,b, Single-mode Wigner functions measured at frequencies \({f}_{1}\) and \({f}_{2}\) at a pump power P = 28.6 mW below the parametric pumping threshold at 220 K under B = 30.14 mT. c,d, Two-mode Wigner functions of the I and Q quadratures measured at the same power as in a,b. e,f, Single-mode Wigner functions measured at \({f}_{1}\) and \({f}_{2}\) for P = 29.1 mW above the threshold. g,h, Two-mode Wigner functions of the I and Q quadratures measured at P = 29.1 mW.

Extended Data Fig. 6 Temperature dependence of two-mode thermal squeezing.

a,d,g, Power dependence of noise intensity (bandwidth = 19 kHz) measured at 300 K at B = 29.84 mT (a), 260 K at B = 30.00 mT (d) and 220 K at B = 30.15 mT, (g). b,e,h, Wigner functions representing correlations between the I (in-phase) components near the nondegenerate parametric excitation threshold at 300 K (b), 260 K (e), and 220 K (h). c,f,i, Wigner functions representing correlations between the Q (quadrature) components near the nondegenerate parametric excitation threshold at 300 K (c), 260 K (f), and 220 K (i).

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Hioki, T., Tojo, K., Elyasi, M. et al. Single- and two-mode magnon thermal squeezing. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03294-4

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