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Stabilized entanglement of massive mechanical oscillators

Naturevolume 556pages478482 (2018) | Download Citation

Abstract

Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance1. Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons2,3,4,5, ions6 and electron spins7, and more recently in microwave and electromechanical devices8,9,10. For macroscopic-scale objects8,9,10,11,12,13,14, however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 1012 atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion15,16,17. We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.

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References

  1. 1.

    Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935).

  2. 2.

    Aspect, A., Dalibard, J. & Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982).

  3. 3.

    Heidmann, A. et al. Observation of quantum noise reduction on twin laser beams. Phys. Rev. Lett. 59, 2555–2557 (1987).

  4. 4.

    Ou, Z. Y., Pereira, S. F., Kimble, H. J. & Peng, K. C. Realization of the Einstein–Podolsky–Rosen paradox for continuous variables. Phys. Rev. Lett. 68, 3663–3666 (1992).

  5. 5.

    Bowen, W. P., Treps, N., Schnabel, R. & Lam, P. K. Experimental demonstration of continuous variable polarization entanglement. Phys. Rev. Lett. 89, 253601 (2002).

  6. 6.

    Jost, J. D. et al. Entangled mechanical oscillators. Nature 459, 683–685 (2009).

  7. 7.

    Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

  8. 8.

    Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006).

  9. 9.

    DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010).

  10. 10.

    Palomaki, T. A., Teufel, J. D., Simmonds, R. W. & Lehnert, K. W. Entangling mechanical motion with microwave fields. Science 342, 710–713 (2013).

  11. 11.

    Leggett, A. J. Macroscopic quantum systems and the quantum theory of measurement. Prog. Theor. Phys. Suppl. 69, 80–100 (1980).

  12. 12.

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

  13. 13.

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

  14. 14.

    Klimov, P. V., Falk, A. L., Christle, D. J., Dobrovitski, V. V. & Awschalom, D. D. Quantum entanglement at ambient conditions in a macroscopic solid-state spin ensemble. Sci. Adv. 1, e1501015 (2015).

  15. 15.

    Woolley, M. J. & Clerk, A. A. Two-mode squeezed states in cavity optomechanics via engineering of a single reservoir. Phys. Rev. A 89, 063805 (2014).

  16. 16.

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

  17. 17.

    Ockeloen-Korppi, C. F. et al. Quantum backaction evading measurement of collective mechanical modes. Phys. Rev. Lett. 117, 140401 (2016).

  18. 18.

    Mancini, S., Giovannetti, V., Vitali, D. & Tombesi, P. Entangling macroscopic oscillators exploiting radiation pressure. Phys. Rev. Lett. 88, 120401 (2002).

  19. 19.

    Pinard, M. et al. Entangling movable mirrors in a double-cavity system. Europhys. Lett. 72, 747–753 (2005).

  20. 20.

    Tan, H., Li, G. & Meystre, P. Dissipation-driven two-mode mechanical squeezed states in optomechanical systems. Phys. Rev. A 87, 033829 (2013).

  21. 21.

    Wang, Y.-D. & Clerk, A. A. Reservoir-engineered entanglement in optomechanical systems. Phys. Rev. Lett. 110, 253601 (2013).

  22. 22.

    Li, J., Haghighi, I. M., Malossi, N., Zippilli, S. & Vitali, D. Generation and detection of large and robust entanglement between two different mechanical resonators in cavity optomechanics. New J. Phys. 17, 103037 (2015).

  23. 23.

    Mahboob, I., Okamoto, H., Onomitsu, K. & Yamaguchi, H. Two-mode thermal-noise squeezing in an electromechanical resonator. Phys. Rev. Lett. 113, 167203 (2014).

  24. 24.

    Pontin, A. et al. Dynamical two-mode squeezing of thermal fluctuations in a cavity optomechanical system. Phys. Rev. Lett. 116, 103601 (2016).

  25. 25.

    Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).

  26. 26.

    Pirkkalainen, J.-M., Damskägg, E., Brandt, M., Massel, F. & Sillanpää, M. A. Squeezing of quantum noise of motion in a micromechanical resonator. Phys. Rev. Lett. 115, 243601 (2015).

  27. 27.

    Lecocq, F., Clark, J. B., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Quantum nondemolition measurement of a nonclassical state of a massive object. Phys. Rev. X 5, 041037 (2015).

  28. 28.

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

  29. 29.

    Banaszek, K. & Wódkiewicz, K. Nonlocality of the Einstein–Podolsky–Rosen state in the Wigner representation. Phys. Rev. A 58, 4345–4347 (1998).

  30. 30.

    Weedbrook, C. et al. Gaussian quantum information. Rev. Mod. Phys. 84, 621–669 (2012).

  31. 31.

    Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).

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Acknowledgements

We thank S. Paraoanu and I. Petersen for discussions. This work was supported by the Academy of Finland (contracts 250280, 308290 and 307757) and by the European Research Council (615755-CAVITYQPD). We acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 732894 (FETPRO HOT). For this work, we used the facilities of the Micronova Nanofabrication Center and the Low Temperature Laboratory.

Author information

Affiliations

  1. Department of Applied Physics, Aalto University, Aalto, Finland

    • C. F. Ockeloen-Korppi
    • , E. Damskägg
    • , J.-M. Pirkkalainen
    •  & M. A. Sillanpää
  2. Department of Physics and Nanoscience Center, University of Jyväskylä, Jyväskylä, Finland

    • M. Asjad
    •  & F. Massel
  3. Institute for Molecular Engineering, University of Chicago, Chicago, IL, USA

    • A. A. Clerk
  4. School of Engineering and Information Technology, UNSW Canberra, Canberra, Australian Capital Territory, Australia

    • M. J. Woolley

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Contributions

M.A.S. initiated the project and was involved in all subsequent stages. C.F.O.-K. carried out the measurements. C.F.O.-K. and E.D. analysed the data. E.D. and J.-M.P. designed and fabricated the devices. M.J.W., A.A.C., F.M. and M.A. developed the theory. All authors participated in the writing of the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to M. A. Sillanpää.

Supplementary information

  1. Supplementary Information

    This file contains Supplementary Discussion, Supplementary Figures 1-10, Supplementary Tables 1-3, and additional references.

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DOI

https://doi.org/10.1038/s41586-018-0038-x

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