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

Gyroscopically Stabilized Quantum Spin Rotors

Vanessa Wachter1,2, Silvia Viola Kusminskiy2,3, Gabriel Hétet4, and Benjamin A. Stickler1

Phys. Rev. Lett. 136, 073604 – Published 18 February, 2026

DOI: https://doi.org/10.1103/zjpt-whpf

Abstract

Recent experiments demonstrate all-electric spinning of levitated nanodiamonds with embedded nitrogen-vacancy spins. Here, we argue that such gyroscopically stabilized spin rotors offer a promising platform for probing and exploiting quantum spin-rotation coupling of particles hosting a single spin degree of freedom. Specifically, we derive the effective Hamiltonian describing how an embedded spin affects the rotation of rapidly revolving quantum rotors due to the Einstein-de Haas and Barnett effects, which we use to devise experimental protocols for observing this coupling in state-of-the-art experiments. This will open the door for future exploitations of quantum spin rotors for superposition experiments with massive objects.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (94)

  1. J. H. Van Vleck, The coupling of angular momentum vectors in molecules, Rev. Mod. Phys. 23, 213 (1951).
  2. P. R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy (NRC Research Press, Ottawa, Canada, 2006).
  3. A. Einstein and W. De Haas, Experimental proof of the existence of Ampère’s molecular currents, Proc. KNAW, 181, 696 (1915).
  4. S. J. Barnett, Magnetization by rotation, Phys. Rev. 6, 239 (1915).
  5. V. Y. Frenkel, On the history of the Einstein–de Haas effect, Sov. Phys. Usp. 22, 580 (1979).
  6. M. Ganzhorn, S. Klyatskaya, M. Ruben, and W. Wernsdorfer, Quantum Einstein-de Haas effect, Nat. Commun. 7, 11443 (2016).
  7. C. Dornes, Y. Acremann, M. Savoini, M. Kubli, M. J. Neugebauer, E. Abreu, L. Huber, G. Lantz, C. A. Vaz, H. Lemke et al., The ultrafast Einstein–de Haas effect, Nature (London) 565, 209 (2019).
  8. E. M. Chudnovsky, Conservation of angular momentum in the problem of tunneling of the magnetic moment, Phys. Rev. Lett. 72, 3433 (1994).
  9. D. F. Jackson Kimball, A. O. Sushkov, and D. Budker, Precessing ferromagnetic needle magnetometer, Phys. Rev. Lett. 116, 190801 (2016).
  10. C. C. Rusconi, V. Pöchhacker, K. Kustura, J. I. Cirac, and O. Romero-Isart, Quantum spin stabilized magnetic levitation, Phys. Rev. Lett. 119, 167202 (2017).
  11. Y. Ma, M. Kim, and B. A. Stickler, Torque-free manipulation of nanoparticle rotations via embedded spins, Phys. Rev. B 104, 134310 (2021).
  12. 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).
  13. K. Kustura, V. Wachter, A. E. Rubio López, and C. C. Rusconi, Stability of a magnetically levitated nanomagnet in vacuum: Effects of gas and magnetization damping, Phys. Rev. B 105, 174439 (2022).
  14. C. Gonzalez-Ballestero, M. Aspelmeyer, L. Novotny, R. Quidant, and O. Romero-Isart, Levitodynamics: Levitation and control of microscopic objects in vacuum, Science 374, eabg3027 (2021).
  15. D. C. Moore and A. A. Geraci, Searching for new physics using optically levitated sensors, Quantum Sci. Technol. 6, 014008 (2021).
  16. B. A. Stickler, K. Hornberger, and M. Kim, Quantum rotations of nanoparticles, Nat. Rev. Phys. 3, 589 (2021).
  17. U. Delić, M. Reisenbauer, K. Dare, D. Grass, V. Vuletić, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparticle to the motional quantum ground state, Science 367, 892 (2020).
  18. F. Tebbenjohanns, M. L. Mattana, M. Rossi, M. Frimmer, and L. Novotny, Quantum control of a nanoparticle optically levitated in cryogenic free space, Nature (London) 595, 378 (2021).
  19. 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).
  20. 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).
  21. 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).
  22. L. Dania, O. S. Kremer, J. Piotrowski, D. Candoli, J. Vijayan, O. Romero-Isart, C. Gonzalez-Ballestero, L. Novotny, and M. Frimmer, High-purity quantum optomechanics at room temperature, Nat. Phys. 21, 1603 (2025).
  23. S. Troyer, F. Fechtel, L. Hummer, H. Rudolph, B. A. Stickler, U. Delić, and M. Arndt, Quantum ground-state cooling of two librational modes of a nanorotor, arXiv:2509.13398.
  24. 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).
  25. 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).
  26. B. A. Stickler, B. Papendell, S. Kuhn, B. Schrinski, J. Millen, M. Arndt, and K. Hornberger, Probing macroscopic quantum superpositions with nanorotors, New J. Phys. 20, 122001 (2018).
  27. C. Wan, M. Scala, G. Morley, A. A. Rahman, H. Ulbricht, J. Bateman, P. Barker, S. Bose, and M. Kim, Free nano-object Ramsey interferometry for large quantum superpositions, Phys. Rev. Lett. 117, 143003 (2016).
  28. C. Wan, M. Scala, S. Bose, A. Frangeskou, A. A. Rahman, G. Morley, P. Barker, and M. Kim, Tolerance in the Ramsey interference of a trapped nanodiamond, Phys. Rev. A 93, 043852 (2016).
  29. O. Romero-Isart, M. L. Juan, R. Quidant, and J. I. Cirac, Toward quantum superposition of living organisms, New J. Phys. 12, 033015 (2010).
  30. M. Perdriat, C. Pellet-Mary, P. Huillery, L. Rondin, and G. Hétet, Spin-mechanics with nitrogen-vacancy centers and trapped particles, Micromachines 12, 651 (2021).
  31. 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).
  32. Y. Jin, K. Shen, P. Ju, X. Gao, C. Zu, A. J. Grine, and T. Li, Quantum control and Berry phase of electron spins in rotating levitated diamonds in high vacuum, Nat. Commun. 15, 5063 (2024).
  33. M. Gutierrez Latorre, G. Higgins, A. Paradkar, T. Bauch, and W. Wieczorek, Superconducting microsphere magnetically levitated in an anharmonic potential with integrated magnetic readout, Phys. Rev. Appl. 19, 054047 (2023).
  34. J. Hofer, R. Gross, G. Higgins, H. Huebl, O. F. Kieler, R. Kleiner, D. Koelle, P. Schmidt, J. A. Slater, M. Trupke et al., High-Q magnetic levitation and control of superconducting microspheres at millikelvin temperatures, Phys. Rev. Lett. 131, 043603 (2023).
  35. 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).
  36. T. Seberson, J. Ahn, J. Bang, T. Li, and F. Robicheaux, Optical levitation of a YIG nanoparticle and simulation of sympathetic cooling via coupling to a cold atomic gas, arXiv:1910.05371.
  37. S. Chakraborty, G. K. Wong, F. Oda, V. Wachter, S. V. Kusminskiy, T. Yokosawa, S. Hübner, B. A. Zubiri, E. Spiecker, M. Distaso, P. S. J. Russell, and N. Joly, Optomagnetic forces on YIG/YFeO3 microspheres levitated in chiral hollow-core photonic crystal fibre, arXiv:2404.16182.
  38. J. Gieseler, A. Kabcenell, E. Rosenfeld, J. Schaefer, A. Safira, M. J. 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).
  39. F. Ahrens, W. Ji, D. Budker, C. Timberlake, H. Ulbricht, and A. Vinante, Levitated ferromagnetic magnetometer with energy resolution well below ℏ, Phys. Rev. Lett. 134, 110801 (2025).
  40. J. K. Jose, A. Marchese, M. Cromb, H. Ulbricht, A. Cebers, P. K. Lam, T. Wang, and A. Vinante, Cryogenic pressure sensing with an ultrafast Meissner-levitated microrotor, arXiv:2509.24964.
  41. C. Gonzalez-Ballestero, J. Gieseler, and O. Romero-Isart, Quantum acoustomechanics with a micromagnet, Phys. Rev. Lett. 124, 093602 (2020).
  42. V. Wachter, V. A. Bittencourt, S. Xie, S. Sharma, N. Joly, P. S. J. Russell, F. Marquardt, and S. Viola Kusminskiy, Optical signatures of the coupled spin-mechanics of a levitated magnetic microparticle, J. Opt. Soc. Am. B 38, 3858 (2021).
  43. A. Kani, F. Quijandría, and J. Twamley, Magnonic Einstein–de Haas effect: Ultrafast rotation of magnonic microspheres, Phys. Rev. Lett. 129, 257201 (2022).
  44. 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).
  45. M. O. Steiner, J. S. Pedernales, and M. B. Plenio, Pentacene-doped naphthalene for levitated optomechanics, Quantum 9, 1928 (2025).
  46. F. Ahrens and A. Vinante, Observation of gyroscopic coupling in a non-spinning levitated ferromagnet, arXiv:2504.13744.
  47. T. Delord, P. Huillery, L. Schwab, L. Nicolas, L. Lecordier, and G. Hétet, Ramsey interferences and spin echoes from electron spins inside a levitating macroscopic particle, Phys. Rev. Lett. 121, 053602 (2018).
  48. T. Delord, P. Huillery, L. Nicolas, and G. Hétet, Spin-cooling of the motion of a trapped diamond, Nature (London) 580, 56 (2020).
  49. M. Geiselmann, M. L. Juan, J. Renger, J. M. Say, L. J. Brown, F. J. G. De Abajo, F. Koppens, and R. Quidant, Three-dimensional optical manipulation of a single electron spin, Nat. Nanotechnol. 8, 175 (2013).
  50. G. P. Conangla, A. W. Schell, R. A. Rica, and R. Quidant, Motion control and optical interrogation of a levitating single nitrogen vacancy in vacuum, Nano Lett. 18, 3956 (2018).
  51. O. Feldman, B. B. Shultz, M. Muretova, O. Dobkowski, Y. Japha, D. Grosswasser, and R. Folman, Trapping and cooling of nanodiamonds in a Paul trap under ultra-high vacuum: Towards matter-wave interferometry with massive objects, arXiv:2508.14687.
  52. M. Muretova, Y. Japha, M. Toros, and R. Folman, Parametric feedback cooling of librations of a nanodiamond in a Paul trap: Towards matter-wave interferometry with massive objects, arXiv:2508.13723.
  53. W.-L. Li and D.-L. Zhou, Preparing highly entangled states of nanodiamond rotation and NV center spin, Chin. Phys. B 33, 020305 (2024).
  54. H. Espinós, C. Munuera-Javaloy, I. Panadero, P. Acedo, R. Puebla, J. Casanova, and E. Torrontegui, Enhancing polarization transfer from nitrogen-vacancy centers to external nuclear spins via dangling bond mediators, Commun. Phys. 7, 42 (2024).
  55. P. Kumar and M. Bhattacharya, Magnetometry via spin-mechanical coupling in levitated optomechanics, Opt. Express 25, 19568 (2017).
  56. X. Ni, Z. Zou, R. Lecamwasam, A. Vinante, D. Budker, P. K. Lam, T. Wang, and J. Gong, Microscopic theory of a precessing ferromagnet for ultrasensitive magnetometry, Phys. Rev. Res. 7, 043120 (2025).
  57. 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).
  58. Z.-q. Yin, T. Li, X. Zhang, and L. Duan, Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling, Phys. Rev. A 88, 033614 (2013).
  59. J. S. Pedernales, G. W. Morley, and M. B. Plenio, Motional dynamical decoupling for interferometry with macroscopic particles, Phys. Rev. Lett. 125, 023602 (2020).
  60. Y. Japha and R. Folman, Quantum uncertainty limit for Stern-Gerlach interferometry with massive objects, Phys. Rev. Lett. 130, 113602 (2023).
  61. T. Zhou, S. Bose, and A. Mazumdar, Gyroscopic stability for nanoparticles in Stern-Gerlach interferometry and spin contrast, Phys. Rev. A 112, 013315 (2025).
  62. R. Rizaldy, T. Zhou, S. Bose, and A. Mazumdar, Rotational stability in nanorotor and spin contrast in one-loop interferometry in the Stern-Gerlach setup, Phys. Rev. Res. 7, 043095 (2025).
  63. S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. Kim, and G. Milburn, Spin entanglement witness for quantum gravity, Phys. Rev. Lett. 119, 240401 (2017).
  64. M. Perdriat, C. C. Rusconi, T. Delord, P. Huillery, C. Pellet-Mary, A. Durand, B. A. Stickler, and G. Hétet, Rotational locking of charged microparticles in quadrupole ion traps, Phys. Rev. Lett. 133, 253602 (2024).
  65. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zjpt-whpf for derivations and supporting information, which includes Refs. [66–82].
  66. C. C. Rusconi and O. Romero-Isart, Magnetic rigid rotor in the quantum regime: Theoretical toolbox, Phys. Rev. B 93, 054427 (2016).
  67. M. Ban, SU(1,1) Lie algebraic approach to linear dissipative processes in quantum optics, J. Math. Phys. (N.Y.) 33, 3213 (1992).
  68. J. Achard, V. Jacques, and A. Tallaire, Chemical vapour deposition diamond single crystals with nitrogen-vacancy centres: A review of material synthesis and technology for quantum sensing applications, J. Phys. D 53, 313001 (2020).
  69. Y.-C. Chen, P. S. Salter, S. Knauer, L. Weng, A. C. Frangeskou, C. J. Stephen, S. N. Ishmael, P. R. Dolan, S. Johnson, B. L. Green et al., Laser writing of coherent colour centres in diamond, Nat. Photonics 11, 77 (2017).
  70. K. Kinouchi, Y. Shimotsuma, M. Uemoto, M. Fujiwara, N. Mizuochi, M. Shimizu, and K. Miura, Laser writing of preferentially orientated nitrogen-vacancy centers in diamond, Carbon Trends 13, 100318 (2023).
  71. F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, Optical rotation of levitated spheres in high vacuum, Phys. Rev. A 97, 051802 (2018).
  72. T. Seberson and F. Robicheaux, Parametric feedback cooling of rigid body nanodumbbells in levitated optomechanics, Phys. Rev. A 99, 013821 (2019).
  73. D. Kim, S. Tian, B. Calderoni, C. S. Jachimska, J. Downes, and J. Twamley, A magnetically levitated conducting rotor with ultra-low rotational damping circumventing eddy loss, Commun. Phys. 8, 381 (2025).
  74. L. Martinetz, K. Hornberger, and B. A. Stickler, Gas-induced friction and diffusion of rigid rotors, Phys. Rev. E 97, 052112 (2018).
  75. L. Martinetz, Quantum electromechanics with levitated charged particles, Ph.D. thesis, Dissertation, Duisburg, Essen, Universität Duisburg-Essen, 2023, https://duepublico2.uni-due.de/receive/duepublico_mods_00078558.
  76. L. Martinetz, K. Hornberger, and B. A. Stickler, Surface-induced decoherence and heating of charged particles, PRX Quantum 3, 030327 (2022).
  77. N. Glikin, B. A. Stickler, R. Tollefsen, S. Mouradian, N. Yadav, E. Urban, K. Hornberger, and H. Häffner, Probing rotational decoherence with a trapped-ion planar rotor, Phys. Rev. Lett. 134, 033601 (2025).
  78. M. W. Mitchell and S. Palacios Alvarez, Colloquium: Quantum limits to the energy resolution of magnetic field sensors, Rev. Mod. Phys. 92, 021001 (2020).
  79. B. Papendell, B. A. Stickler, and K. Hornberger, Quantum angular momentum diffusion of rigid bodies, New J. Phys. 19, 122001 (2017).
  80. J. Schäfer, B. A. Stickler, and K. Hornberger, Decoherence of dielectric particles by thermal emission, Phys. Rev. Res. 6, 043307 (2024).
  81. M. W. Doherty, F. Dolde, H. Fedder, F. Jelezko, J. Wrachtrup, N. B. Manson, and L. C. L. Hollenberg, Theory of the ground-state spin of the NV− center in diamond, Phys. Rev. B 85, 205203 (2012).
  82. F. Dolde, H. Fedder, M. W. Doherty, T. Nöbauer, F. Rempp, G. Balasubramanian, T. Wolf, F. Reinhard, L. C. Hollenberg, F. Jelezko et al., Electric-field sensing using single diamond spins, Nat. Phys. 7, 459 (2011).
  83. L. Martinetz, K. Hornberger, and B. A. Stickler, Electric trapping and circuit cooling of charged nanorotors, New J. Phys. 23, 093001 (2021).
  84. H. Chudo, K. Harii, M. Matsuo, J. Ieda, M. Ono, S. Maekawa, and E. Saitoh, Rotational Doppler effect and Barnett field in spinning NMR, J. Phys. Soc. Jpn. 84, 043601 (2015).
  85. A. A. Wood, E. Lilette, Y. Y. Fein, N. Tomek, L. P. McGuinness, L. C. Hollenberg, R. E. Scholten, and A. M. Martin, Quantum measurement of a rapidly rotating spin qubit in diamond, Sci. Adv. 4, eaar7691 (2018).
  86. A. A. Wood, L. C. Hollenberg, R. E. Scholten, and A. M. Martin, Observation of a quantum phase from classical rotation of a single spin, Phys. Rev. Lett. 124, 020401 (2020).
  87. J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for NV-diamond magnetometry, Rev. Mod. Phys. 92, 015004 (2020).
  88. X.-Y. Chen, C.-D. Qiu, Y.-N. Lu, G.-Q. Liu, D. Ruan, F. Zhang, and G. Long, Extending dephasing time of nitrogen-vacancy center in diamond by suppressing nuclear spin noise, Phys. Rev. B 108, 174111 (2023).
  89. J. Du, F. Shi, X. Kong, F. Jelezko, and J. Wrachtrup, Single-molecule scale magnetic resonance spectroscopy using quantum diamond sensors, Rev. Mod. Phys. 96, 025001 (2024).
  90. T. F. Segawa and R. Igarashi, Nanoscale quantum sensing with nitrogen-vacancy centers in nanodiamonds–a magnetic resonance perspective, Prog. Nucl. Magn. Reson. Spectrosc. 134, 20 (2023).
  91. T. M. Hoang, J. Ahn, J. Bang, and T. Li, Electron spin control of optically levitated nanodiamonds in vacuum, Nat. Commun. 7, 12250 (2016).
  92. R. Reimann, M. Doderer, E. Hebestreit, R. Diehl, M. Frimmer, D. Windey, F. Tebbenjohanns, and L. Novotny, GHz rotation of an optically trapped nanoparticle in vacuum, Phys. Rev. Lett. 121, 033602 (2018).
  93. J. Ahn, Z. Xu, J. Bang, Y.-H. Deng, T. M. Hoang, Q. Han, R.-M. Ma, and T. Li, Optically levitated nanodumbbell torsion balance and GHz nanomechanical rotor, Phys. Rev. Lett. 121, 033603 (2018).
  94. Y. Jin, J. Yan, S. J. Rahman, J. Li, X. Yu, and J. Zhang, 6 GHz hyperfast rotation of an optically levitated nanoparticle in vacuum, Photonics Res. 9, 1344 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation