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Entanglement between distant macroscopic mechanical and spin systems


Entanglement is an essential property of multipartite quantum systems, characterized by the inseparability of quantum states of objects regardless of their spatial separation. Generation of entanglement between increasingly macroscopic and disparate systems is an ongoing effort in quantum science, as it enables hybrid quantum networks, quantum-enhanced sensing and probing of the fundamental limits of quantum theory. The disparity of hybrid systems and the vulnerability of quantum correlations have thus far hampered the generation of macroscopic hybrid entanglement. Here, we generate an entangled state between the motion of a macroscopic mechanical oscillator and a collective atomic spin oscillator, as witnessed by an Einstein–Podolsky–Rosen variance below the separability limit, 0.83 ± 0.02 < 1. The mechanical oscillator is a millimetre-size dielectric membrane and the spin oscillator is an ensemble of 109 atoms in a magnetic field. Light propagating through the two spatially separated systems generates entanglement because the collective spin plays the role of an effective negative-mass reference frame and provides—under ideal circumstances—a back-action-free subspace; in the experiment, quantum back-action is suppressed by 4.6 dB.

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Fig. 1: Tracking of the EPR oscillator.
Fig. 2: Experimental set-up for hybrid entanglement generation.
Fig. 3: Quantum noise spectra of the hybrid system.
Fig. 4: Entanglement tuning and optimization.

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Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.


  1. Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009).

    ADS  MathSciNet  MATH  Google Scholar 

  2. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    ADS  MathSciNet  Google Scholar 

  3. Chen, Y. Macroscopic quantum mechanics: theory and experimental concepts of optomechanics. J. Phys. B 46, 104001 (2013).

    ADS  Google Scholar 

  4. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    ADS  Google Scholar 

  5. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    ADS  Google Scholar 

  6. Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl. Acad. Sci. USA 112, 3866–3873 (2015).

    ADS  Google Scholar 

  7. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).

    ADS  Google Scholar 

  8. Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

    ADS  Google Scholar 

  9. Brown, K. R., Kim, J. & Monroe, C. Co-designing a scalable quantum computer with trapped atomic ions. npj Quant. Inf. 2, 16034 (2016).

    Google Scholar 

  10. Hammerer, K., Aspelmeyer, M., Polzik, E. S. & Zoller, P. Establishing Einstein-Poldosky-Rosen channels between nanomechanics and atomic ensembles. Phys. Rev. Lett. 102, 020501 (2009).

    ADS  Google Scholar 

  11. Manukhova, A. D., Rakhubovsky, A. A. & Filip, R. Pulsed atom-mechanical quantum non-demolition gate. npj Quant. Inf. 6, 4 (2020).

    ADS  Google Scholar 

  12. Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400–403 (2001).

    ADS  Google Scholar 

  13. Polzik, E. S. & Hammerer, K. Trajectories without quantum uncertainties. Ann. Phys. 527, A15–A20 (2015).

    ADS  MathSciNet  Google Scholar 

  14. Møller, C. B. et al. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547, 191–195 (2017).

    ADS  Google Scholar 

  15. Tsang, M. & Caves, C. M. Coherent quantum-noise cancellation for optomechanical sensors. Phys. Rev. Lett. 105, 123601 (2010).

    ADS  Google Scholar 

  16. Hammerer, K., Sørensen, A. S. & Polzik, E. S. Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041–1093 (2010).

    ADS  Google Scholar 

  17. Muschik, C. A., Polzik, E. S. & Cirac, J. I. Dissipatively driven entanglement of two macroscopic atomic ensembles. Phys. Rev. A 83, 052312 (2011).

    ADS  Google Scholar 

  18. Krauter, H. et al. Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys. Rev. Lett. 107, 080503 (2011).

    ADS  Google Scholar 

  19. Stannigel, K., Rabl, P. & Zoller, P. Driven-dissipative preparation of entangled states in cascaded quantum-optical networks. New J. Phys. 14, 063014 (2012).

    ADS  MATH  Google Scholar 

  20. Vasilyev, D. V., Muschik, C. A. & Hammerer, K. Dissipative versus conditional generation of Gaussian entanglement and spin squeezing. Phys. Rev. A 87, 053820 (2013).

    ADS  Google Scholar 

  21. Huang, X. et al. Unconditional steady-state entanglement in macroscopic hybrid systems by coherent noise cancellation. Phys. Rev. Lett. 121, 103602 (2018).

    ADS  Google Scholar 

  22. Tsang, M. & Caves, C. M. Evading quantum mechanics: engineering a classical subsystem within a quantum environment. Phys. Rev. X 2, 031016 (2012).

    Google Scholar 

  23. Kohler, J., Gerber, J. A., Dowd, E. & Stamper-Kurn, D. M. Negative-mass instability of the spin and motion of an atomic gas driven by optical cavity backaction. Phys. Rev. Lett. 120, 013601 (2018).

    ADS  Google Scholar 

  24. Karg, T. M. et al. Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart. Science 369, 174–179 (2020).

    ADS  Google Scholar 

  25. Jöckel, A. et al. Sympathetic cooling of a membrane oscillator in a hybrid mechanical–atomic system. Nat. Nanotechnol. 10, 55–59 (2015).

    ADS  Google Scholar 

  26. Christoph, P. et al. Combined feedback and sympathetic cooling of a mechanical oscillator coupled to ultracold atoms. New J. Phys. 20, 093020 (2018).

    ADS  Google Scholar 

  27. Tan, H., Buchmann, L. F., Seok, H. & Li, G. Achieving steady-state entanglement of remote micromechanical oscillators by cascaded cavity coupling. Phys. Rev. A 87, 022318 (2013).

    ADS  Google Scholar 

  28. Woolley, M. J. & Clerk, A. A. Two-mode back-action-evading measurements in cavity optomechanics. Phys. Rev. A 87, 063846 (2013).

    ADS  Google Scholar 

  29. Ockeloen-Korppi, C. F. et al. Stabilized entanglement of massive mechanical oscillators. Nature 556, 478–482 (2018).

    ADS  Google Scholar 

  30. Riedinger, R. et al. Remote quantum entanglement between two micromechanical oscillators. Nature 556, 473–477 (2018).

    ADS  Google Scholar 

  31. Lee, K. C. et al. Entangling macroscopic diamonds at room temperature. Science 334, 1253–1256 (2011).

    ADS  Google Scholar 

  32. Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotechnol. 12, 776–783 (2017).

    Google Scholar 

  33. Borregaard, J. et al. Scalable photonic network architecture based on motional averaging in room temperature gas. Nat. Commun. 7, 11356 (2016).

    ADS  Google Scholar 

  34. Holstein, T. & Primakoff, H. Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098–1113 (1940).

    ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  36. Müller-Ebhardt, H. et al. Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors. Phys. Rev. A 80, 043802 (2009).

    ADS  Google Scholar 

  37. Rossi, M., Mason, D., Chen, J. & Schliesser, A. Observing and verifying the quantum trajectory of a mechanical resonator. Phys. Rev. Lett. 123, 163601 (2019).

    ADS  Google Scholar 

  38. Wieczorek, W. et al. Optimal state estimation for cavity optomechanical systems. Phys. Rev. Lett. 114, 223601 (2015).

    ADS  Google Scholar 

  39. Wasilewski, W. et al. Quantum noise limited and entanglement-assisted magnetometry. Phys. Rev. Lett. 104, 133601 (2010).

    ADS  Google Scholar 

  40. Balabas, M. V. et al. High quality anti-relaxation coating material for alkali atom vapor cells. Opt. Express 18, 5825–5830 (2010).

    ADS  Google Scholar 

  41. Geremia, J. M., Stockton, J. K. & Mabuchi, H. Tensor polarizability and dispersive quantum measurement of multilevel atoms. Phys. Rev. A 73, 042112 (2006).

    ADS  Google Scholar 

  42. Lammers, J. State Preparation and Verification in Continuously Measured Quantum Systems. PhD thesis, Leibniz University Hannover (2018).

  43. Higginbotham, A. P. et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat. Phys. 14, 1038–1042 (2018).

    Google Scholar 

  44. Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Quantum transduction of optical photons from a superconducting qubit. Preprint at (2020).

  45. Khalili, F. Y. & Polzik, E. S. Overcoming the standard quantum limit in gravitational wave detectors using spin systems with a negative effective mass. Phys. Rev. Lett. 121, 031101 (2018).

    ADS  Google Scholar 

  46. Zeuthen, E., Polzik, E. S. & Khalili, F. Y. Gravitational wave detection beyond the standard quantum limit using a negative-mass spin system and virtual rigidity. Phys. Rev. D 100, 062004 (2019).

    ADS  Google Scholar 

  47. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: The MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

    ADS  Google Scholar 

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We acknowledge conversations with K. Hammerer and J. H. Müller. X. Huang contributed theoretical simulations in the early stages of the project. We acknowledge M. Balabas for fabricating the coated caesium cells. This project has been supported by the European Research Council Advanced grant QUANTUM-N, the Villum Foundation and John Templeton Foundation. E.Z. acknowledges funding from the Carlsberg Foundation. M.P. was partially supported by the Foundation for Polish Science (FNP). R.A.T. was partially funded by the programme Science without Borders of the Brazilian Federal Government.

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Authors and Affiliations



E.S.P. conceived and led the project. R.A.T., C.B.M., C.Ø. and M.P. built the experiment with the help of C.B. and J.A. The membrane resonator was conceived by A.S. and Y.T. designed and fabricated the device. R.A.T., M.P., C.Ø., C.B.M. and C.B. collected the data. E.Z. and M.P. developed the theory with input from J.A., E.S.P. and R.A.T. The paper was written by E.S.P., E.Z., R.A.T., M.P., C.Ø., C.B.M. and C.B., with contributions from other authors.

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Correspondence to Eugene S. Polzik.

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Supplementary information

Supplementary Information

Details of the experimental set-up and of supporting theory including Supplementary Figs. 1–8 and Table 1.

Source data

Source Data Fig. 1

A trajectory of the oscillator.

Source Data Fig. 3

Noise spectra; Wiener filter.

Source Data Fig. 4

Noise spectra and theory fits; conditional variance.

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Thomas, R.A., Parniak, M., Østfeldt, C. et al. Entanglement between distant macroscopic mechanical and spin systems. Nat. Phys. 17, 228–233 (2021).

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