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Entanglement between distant macroscopic mechanical and spin systems

Nature Physics volume 17, pages 228–233 (2021)Cite this article

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Abstract

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.

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Acknowledgements

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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Author notes

  1. Christoffer B. Møller

    Present address: ICFO - Institut De Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Spain

  2. Yeghishe Tsaturyan

    Present address: Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA

  3. Jürgen Appel

    Present address: Danish Fundamental Metrology, Hørsholm, Denmark

  4. These authors contributed equally: Rodrigo A. Thomas, Michał Parniak, Christoffer Østfeldt, Christoffer B. Møller.

Authors and Affiliations

  1. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    Rodrigo A. Thomas, Michał Parniak, Christoffer Østfeldt, Christoffer B. Møller, Christian Bærentsen, Yeghishe Tsaturyan, Albert Schliesser, Jürgen Appel, Emil Zeuthen & Eugene S. Polzik

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Contributions

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). https://doi.org/10.1038/s41567-020-1031-5

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