- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Simultaneous cooling of the internal and external degrees of freedom of a levitated micromagnet in a cavity magnomechanical system

Lei Chen1, Yang Liu1,2, Liang Bin1, Sai-Yun Ye1,*, and Zhi-Rong Zhong1,†

  • 1Fujian Key Laboratory of Quantum Information and Quantum Optics (Fuzhou University), Fuzhou 350108, China
  • 2Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China

  • *Contact author: yesaiyun@fzu.edu.cn
  • †Contact author: zhirz@fzu.edu.cn
PDF

Phys. Rev. Research 7, 033157 – Published 14 August, 2025

DOI: https://doi.org/10.1103/8pzl-6c5l

Abstract

Cooling the internal and external degrees of freedom (DOFs) of a massive mechanical system close to the quantum ground state is a prerequisite for the quantum manipulation of macroscopic mechanical devices. In this paper, we propose a approach to simultaneously cool both the internal and external DOFs (phonon and center-of-mass modes) of a levitated micromagnet within a cavity magnomechanical (CMM) system. By driving the cavity mode and magnon mode on their respective red sidebands with microwave fields, the proposed scheme effectively suppresses Stokes scattering and significantly enhances the net cooling rate. Moreover, differing from conventional CMM systems, our proposal can achieve simultaneous cooling of the internal and external DOFs even in the unresolved-sideband regime. Our numerical simulations demonstrate the robustness and effectiveness of the scheme by analyzing average occupancies of the internal and external DOFs, as well as identifying the optimal cooling conditions. The proposed scheme establishes a foundation for probing and manipulating the internal DOFs by controlling the external DOFs, which may open additional possibilities for studying nonequilibrium quantum mesoscopic physics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (94)

  1. Y. P. Wang, J. W. Rao, Y. Yang, P. C. Xu, Y. S. Gui, B. M. Yao, J. Q. You, and C. M. Hu, Nonreciprocity and unidirectional invisibility in cavity magnonics, Phys. Rev. Lett. 123, 127202 (2019).
  2. W. Li, J. Cheng, W. J. Gong, and J. Li, Nonlinear self-sustaining dynamics in cavity magnomechanics, Phys. Rev. A 108, 033518 (2023).
  3. Y. Xu, J. Y. Liu, W. Liu, and Y. F. Xiao, Nonreciprocal phonon laser in a spinning microwave magnomechanical system, Phys. Rev. A 103, 053501 (2021).
  4. J. X. Peng, A. Kundu, Z. X. Liu, A. ur Rahman, N. Akhtar, and M. Asjad, Vector photon-magnon-phonon coherence in a polarized microwave driven cavity magnomechanical system, Phys. Rev. B 109, 064412 (2024).
  5. Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85, 623 (2013).
  6. L. Bai, M. Harder, Y. P. Chen, X. Fan, J. Q. Xiao, and C.-M. Hu, Spin pumping in electrodynamically coupled magnon-photon systems, Phys. Rev. Lett. 114, 227201 (2015).
  7. R. C. Shen, Y. P. Wang, J. Li, S. Y. Zhu, G. S. Agarwal, and J. Q. You, Long-time memory and ternary logic gate using a multistable cavity magnonic system, Phys. Rev. Lett. 127, 183202 (2021).
  8. W. Zhang, T. Wang, X. Han, S. Zhang, and H.-F. Wang, Quantum entanglement and one-way steering in a cavity magnomechanical system via a squeezed vacuum field, Opt. Express 30, 10969 (2022).
  9. Y. P. Gao, X. F. Liu, T. J. Wang, C. Cao, and C. Wang, Photon excitation and photon-blockade effects in optomagnonic microcavities, Phys. Rev. A 100, 043831 (2019).
  10. J. K. Xie, S. L. Ma, and F. L. Li, Quantum-interference-enhanced magnon blockade in an yttrium-iron-garnet sphere coupled to superconducting circuits, Phys. Rev. A 101, 042331 (2020).
  11. P. K. Gupta, S. Chakraborty, S. Kalita, and A. K. Sarma, Quantum signatures of bistability and limit cycle in Kerr-modified cavity magnomechanics, Phys. Rev. A 110, 063504 (2024).
  12. C. Gonzalez-Ballestero, D. Hümmer, J. Gieseler, and O. Romero-Isart, Theory of quantum acoustomagnonics and acoustomechanics with a micromagnet, Phys. Rev. B 101, 125404 (2020).
  13. S. Bayati, A. Mahdifar, and M. Bagheri Harouni, Entanglement formation between magnon and center-of-mass motion of a levitated particle in a magnomechanical system, Phys. Rev. A 110, 013710 (2024).
  14. D. Lachance-Quirion, Y. Tabuchi, S. Ishino, A. Noguchi, I. Ishikawa, R. Yamazaki, and Y. Nakamura, Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet, Sci. Adv. 3, e1603150 (2017).
  15. 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).
  16. U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuleti, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparticle to the motional quantum ground state, Science 367, 892 (2020).
  17. C. C. Rusconi and O. Romero-Isart, Magnetic rigid rotor in the quantum regime: Theoretical toolbox, Phys. Rev. B 93, 054427 (2016).
  18. B. A. Stickler, K. Hornberger, and M. S. Kim, Quantum rotations of nanoparticles, Nat. Rev. Phys. 3, 589 (2021).
  19. X. Zhang, C. L. Zou, L. Jiang, and H. X. Tang, Strongly coupled magnons and cavity microwave photons, Phys. Rev. Lett. 113, 156401 (2014).
  20. J. T. Hou and L. Liu, Strong coupling between microwave photons and nanomagnet magnons, Phys. Rev. Lett. 123, 107702 (2019).
  21. 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).
  22. C. Gonzalez-Ballestero, J. Gieseler, and O. Romero Isart, Quantum acoustomechanics with a micromagnet, Phys. Rev. Lett. 124, 093602 (2020).
  23. 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).
  24. Y. P. Wang, G. Q. Zhang, D. Zhang, T. F. Li, C. Hu, and J. Q. You, Bistability of cavity magnon polaritons, Phys. Rev. Lett. 120, 057202 (2018).
  25. T. Wang, S. Lourette, S. R. O’Kelley, M. Kayci, Y. Band, D. F. J. Kimball, A. O. Sushkov, and D. Budker, Dynamics of a ferromagnetic particle levitated over a superconductor, Phys. Rev. Appl. 11, 044041 (2019).
  26. C. C. Rusconi, V. Pöchhacker, J. I. Cirac, and O. Romero-Isart, Linear stability analysis of a levitated nanomagnet in a static magnetic field: Quantum spin stabilized magnetic levitation, Phys. Rev. B 96, 134419 (2017).
  27. T. Delord, L. Nicolas, Y. Chassagneux, and G. Hétet, Strong coupling between a single nitrogen-vacancy spin and the rotational mode of diamonds levitating in an ion trap, Phys. Rev. A 96, 063810 (2017).
  28. C. Gonzalez-Ballestero, M. Aspelmeyer, L. Novotny, R. Quidant, and O. Romero-Isart, Spin-controlled quantum interference of levitated nanorotors, Science 374, eabg3027 (2021).
  29. A. Pontin, H. Fu, M. Toroš, T. S. Monteiro, and P. F. Barker, Simultaneous cavity cooling of all six degrees of freedom of a levitated nanoparticle, Nat. Phys. 19, 1003 (2023).
  30. J. Gieseler, A. Kabcenell, E. Rosenfeld, J. D. Schaefer, A. Safira, M. J. A. Schuetz, C. Gonzalez-Ballestero, C. C. Rusconi, O. Romero-Isart, and M. D. Lukin, Single-spin magnetomechanics with levitated micromagnets, Phys. Rev. Lett. 124, 163604 (2020).
  31. M. Fuwa, R. Sakagami, and T. Tamegai, Ferromagnetic levitation and harmonic trapping of a milligram-scale yttrium iron garnet sphere, Phys. Rev. A 108, 063511 (2023).
  32. M. Fuwa, Stable magnetic levitation of soft ferromagnets for macroscopic quantum mechanics, Phys. Rev. A 108, 023523 (2023).
  33. Z. Zhang, M. O. Scully, and G. S. Agarwal, Quantum entanglement between two magnon modes via Kerr nonlinearity driven far from equilibrium, Phys. Rev. Res. 1, 023021 (2019).
  34. J. Hofer, R. Gross, G. Higgins, H. Huebl, O. F. Kieler, R. Kleiner, D. Koelle, P. Schmidt, J. A. Slater, M. Trupke, K. Uhl, T. Weimann, W. Wieczorek, and M. Aspelmeyer, High-q magnetic levitation and control of superconducting microspheres at millikelvin temperatures, Phys. Rev. Lett. 131, 043603 (2023).
  35. J. Prat-Camps, C. Teo, C. C. Rusconi, W. Wieczorek, and O. Romero-Isart, Ultrasensitive inertial and force sensors with diamagnetically levitated magnets, Phys. Rev. Appl. 8, 034002 (2017).
  36. S. P. Wolski, D. Lachance Quirion, Y. Tabuchi, S. Kono, A. Noguchi, K. Usami, and Y. Nakamura, Dissipation-based quantum sensing of magnons with a superconducting qubit, Phys. Rev. Lett. 125, 117701 (2020).
  37. A. Vinante, C. Timberlake, D. Budker, D. F. J. Kimball, A. O. Sushkov, and H. Ulbricht, Surpassing the energy resolution limit with ferromagnetic torque sensors, Phys. Rev. Lett. 127, 070801 (2021).
  38. C. Timberlake, A. Vinante, F. Shankar, A. Lapi, and H. Ulbricht, Probing modified gravity with magnetically levitated resonators, Phys. Rev. D 104, L101101 (2021).
  39. S. Kalia, D. Budker, D. F. J. Kimball, W. Ji, Z. Liu, A. O. Sushkov, C. Timberlake, H. Ulbricht, A. Vinante, and T. Wang, Ultralight dark matter detection with levitated ferromagnets, Phys. Rev. D 110, 115029 (2024).
  40. D. C. Moore and A. A. Geraci, Searching for new physics using optically levitated sensors, Quantum Sci. Technol. 6, 014008 (2021).
  41. F. Monteiro, G. Afek, D. Carney, G. Krnjaic, J. Wang, and D. C. Moore, Search for composite dark matter with optically levitated sensors, Phys. Rev. Lett. 125, 181102 (2020).
  42. B. A. Stickler, B. Papendell, S. Kuhn, J. Millen, M. Arndt, and K. Hornberger, Probing macroscopic quantum superpositions with nanorotors, New J. Phys. 20, 122001 (2008).
  43. A. Kani, B. Sarma, and J. Twamley, Intensive cavity-magnomechanical cooling of a levitated macromagnet, Phys. Rev. Lett. 128, 013602 (2022).
  44. C. Wan, M. Scala, G. W. Morley, A. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, Free nano-object Ramsey interferometry for large quantum superpositions, Phys. Rev. Lett. 117, 143003 (2016).
  45. C. C. Rusconi, M. Perdriat, G. Hétet, O. Romero-Isart, and B. A. Stickler, Spin-controlled quantum interference of levitated nanorotors, Phys. Rev. Lett. 129, 093605 (2022).
  46. O. Romero-Isart, A. C. Pflanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, Large quantum superpositions and interference of massive nanometer-sized objects, Phys. Rev. Lett. 107, 020405 (2011).
  47. M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys. Rev. Lett. 132, 023601 (2024).
  48. J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Near-field interferometry of a free-falling nanoparticle from a point-like source, Nat. Commun. 5, 4788 (2014).
  49. K. Streltsov, J. S. Pedernales, and M. B. Plenio, Ground-state cooling of levitated magnets in low-frequency traps, Phys. Rev. Lett. 126, 193602 (2021).
  50. T. Delord, P. Huillery, L. Nicolas, and G. Hetet, Spin-cooling of the motion of a trapped diamond, Nature (London) 580, 56 (2020).
  51. J. Piotrowski, D. Windey, and J. Vijayan, Spin-cooling of the motion of a trapped diamond, Nature (London) 19, 1038 (2023).
  52. D. Windey, C. Gonzalez Ballestero, P. Maurer, L. Novotny, O. Romero Isart, and R. Reimann, Cavity-based 3D cooling of a levitated nanoparticle via coherent scattering, Phys. Rev. Lett. 122, 123601 (2019).
  53. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, and A. N. Cleland, Quantum ground state and single-phonon control of a mechanical resonator, Nature (London) 464, 697 (2010).
  54. R. Dum, P. Zoller, and H. Ritsch, Monte Carlo simulation of the atomic master equation for spontaneous emission, Phys. Rev. A 45, 4879 (1992).
  55. C. Timberlake, E. Simcox, and H. Ulbricht, Linear cooling of a levitated micromagnetic cylinder by vibration, Phys. Rev. Res. 6, 033345 (2024).
  56. M. Kamba, H. Kiuchi, T. Yotsuya, and K. Aikawa, Recoil-limited feedback cooling of single nanoparticles near the ground state in an optical lattice, Phys. Rev. A 103, L051701 (2021).
  57. L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature (London) 595, 373 (2021).
  58. F. Tebbenjohanns, M. Luisa Mattana, M. Rossi, M. Frimmer, and L. Novotny, Quantum control of a nanoparticle optically levitated in cryogenic free space, Nature (London) 595, 378 (2021).
  59. Y. C. Liu, Y. F. Xiao, X. Luan, and C. W. Wong, Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics, Phys. Rev. Lett. 110, 153606 (2013).
  60. N. Meyer, A. de los Rios Sommer, P. Mestres, J. Gieseler, V. Jain, L. Novotny, and R. Quidant, Resolved-sideband cooling of a levitated nanoparticle in the presence of laser phase noise, Phys. Rev. Lett. 123, 153601 (2019).
  61. P. Z. G. Fonseca, E. B. Aranas, J. Millen, T. S. Monteiro, and P. F. Barker, Nonlinear dynamics and strong cavity cooling of levitated nanoparticles, Phys. Rev. Lett. 117, 173602 (2016).
  62. J. Li, S. Y. Zhu, and G. S. Agarwal, Magnon-photon-phonon entanglement in cavity magnomechanics, Phys. Rev. Lett. 121, 203601 (2018).
  63. J. Li, S. Y. Zhu, and G. S. Agarwal, Squeezed states of magnons and phonons in cavity magnomechanics, Phys. Rev. A 99, 021801 (2019).
  64. 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).
  65. X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, Cavity magnomechanics, Sci. Adv. 2, e1501286 (2016).
  66. M. Frimmer, J. Gieseler, and L. Novotny, Cooling mechanical oscillators by coherent control, Phys. Rev. Lett. 117, 163601 (2016).
  67. A. Xuereb, T. Freegarde, P. Horak, and P. Domokos, Optomechanical cooling with generalized interferometers, Phys. Rev. Lett. 105, 013602 (2010).
  68. Y. Li, L. A. Wu, and Z. D. Wang, Fast ground-state cooling of mechanical resonators with time-dependent optical cavities, Phys. Rev. A 83, 043804 (2011).
  69. J. Q. Liao and C. K. Law, Cooling of a mirror in cavity optomechanics with a chirped pulse, Phys. Rev. A 84, 053838 (2011).
  70. S. Machnes, J. Cerrillo, M. Aspelmeyer, W. Wieczorek, M. B. Plenio, and A. Retzker, Pulsed laser cooling for cavity optomechanical resonators, Phys. Rev. Lett. 108, 153601 (2012).
  71. F. Elste, S. M. Girvin, and A. A. Clerk, Quantum noise interference and backaction cooling in cavity nanomechanics, Phys. Rev. Lett. 102, 207209 (2009).
  72. A. Xuereb, R. Schnabel, and K. Hammerer, Dissipative optomechanics in a Michelson-Sagnac interferometer, Phys. Rev. Lett. 107, 213604 (2011).
  73. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes, Phys. Rev. A 77, 033804 (2008).
  74. X. Wang, S. Vinjanampathy, F. W. Strauch, and K. Jacobs, Ultraefficient cooling of resonators: Beating sideband cooling with quantum control, Phys. Rev. Lett. 107, 177204 (2011).
  75. Y.-P. Wang, G.-Q. Zhang, D. Zhang, X.-Q. Luo, W. Xiong, S.-P. Wang, T.-F. Li, C.-M. Hu, and J. Q. You, Magnon Kerr effect in a strongly coupled cavity-magnon system, Phys. Rev. B 94, 224410 (2016).
  76. Z. Y. Fan, R. C. Shen, Y. P. Wang, J. Li, and J. Q. You, Optical sensing of magnons via the magnetoelastic displacement, Phys. Rev. A 105, 033507 (2022).
  77. R. A. Norte, J. P. Moura, and S. Gröblacher, Mechanical resonators for quantum optomechanics experiments at room temperature, Phys. Rev. Lett. 116, 147202 (2016).
  78. C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, Ultralow-noise SiN trampoline resonators for sensing and optomechanics, Phys. Rev. X 6, 021001 (2016).
  79. J. Gieseler, L. Novotny, and R. Quidant, Thermal nonlinearities in a nanomechanical oscillator, Nat. Phys. 9, 806 (2013).
  80. D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, Cavity opto-mechanics using an optically levitated nanosphere, Proc. Natl. Acad. Sci. USA 107, 1005 (2009).
  81. M. Imboden and P. Mohanty, Dissipation in nanoelectromechanical systems, Phys. Rep. 534, 89 (2014).
  82. R. C. LeCraw, E. G. Spencer, and E. I. Gordon, Extremely low loss acoustic resonance in single-crystal garnet spheres, Phys. Rev. Lett. 6, 620 (1961).
  83. D. Wurm et al., The Panedm neutron electric dipole moment experiment at the ILL, EPJ Web Conf. 219, 02006 (2019).
  84. M. Bao, H. Yang, H. Yin, and Y. Sun, Energy transfer model for squeeze-film air damping in low vacuum, J. Micromech. Microeng. 12, 341 (2002).
  85. R. P. James Millen, T. S. Monteiro, and A. N. Vamivakas, Optomechanics with levitated particles, Rep. Prog. Phys. 83, 1361 (2013).
  86. P. Asenbaum, S. Kuhn, S. Nimmrichter, U. Sezer, and M. Arndt, Cavity cooling of free silicon nanoparticles in high vacuum, Nat. Commun. 4, 2743 (2013).
  87. L. Magrini, R. A. Norte, R. Riedinger, I. Marinković, D. Grass, U. Delić, S. Gröblacher, S. Hong, and M. Aspelmeyer, Near-field coupling of a levitated nanoparticle to a photonic crystal cavity, Optica 5, 1597 (2018).
  88. J. Verdú, H. Zoubi, C. Koller, J. Majer, H. Ritsch, and J. Schmiedmayer, Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity, Phys. Rev. Lett. 103, 043603 (2009).
  89. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, Theory of ground state cooling of a mechanical oscillator using dynamical backaction, Phys. Rev. Lett. 99, 093901 (2007).
  90. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  91. M. Asjad, J. Li, S. Y. Zhu, and J. Q. You, Magnon squeezing enhanced ground-state cooling in cavity magnomechanics, Fundam. Res. 3, 3 (2023).
  92. S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U. B. Hoff, S. Deleglise, S. Osnaghi, M. Brune, J. M. Raimond, S. Haroche, E. Jacques, P. Bosland, and B. Visentin, Ultrahigh finesse Fabry-Perot superconducting resonator, Appl. Phys. Lett. 90, 697 (2010).
  93. S. M. Fleischer, M. P. Ross, K. Venkateswara, C. A. Hagedorn, E. A. Shaw, E. Swanson, B. R. Heckel, and J. H. Gundlach, A cryogenic torsion balance using a liquid-cryogen free, ultra-low vibration cryostat, Rev. Sci. Instrum. 595, 064505 (2021).
  94. A. Buikema, C. Cahillane, G. L. Mansell, and Blair, Sensitivity and performance of the advanced LIGO detectors in the third observing run, Phys. Rev. D 102, 062003 (2020).

Outline

Information

Phys. Rev. Research 7, 033157– Published 14 August, 2025
  • Received 28 February 2025
  • Accepted 23 July 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation