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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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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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.
The authors declare no competing interests.
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Details of the experimental set-up and of supporting theory including Supplementary Figs. 1–8 and Table 1.
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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