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Quantum back-action-evading measurement of motion in a negative mass reference frame

Nature volume 547, pages 191195 (13 July 2017) | Download Citation

Abstract

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back-action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion1,2. As a consequence of this randomness, and in accordance with the Heisenberg uncertainty principle, the QBA3,4 puts a limitation—the so-called standard quantum limit—on the precision of sensing of position, velocity and acceleration. Here we show that QBA5 on a macroscopic mechanical oscillator can be evaded if the measurement of motion is conducted in the reference frame of an atomic spin oscillator6,7. The collective quantum measurement on this hybrid system of two distant and disparate oscillators is performed with light. The mechanical oscillator is a vibrational ‘drum’ mode of a millimetre-sized dielectric membrane8, and the spin oscillator is an atomic ensemble in a magnetic field9,10. The spin oriented along the field corresponds to an energetically inverted spin population and realizes a negative-effective-mass oscillator, while the opposite orientation corresponds to an oscillator with positive effective mass. The QBA is suppressed by −1.8 decibels in the negative-mass setting and enhanced by 2.4 decibels in the positive-mass case. This hybrid quantum system paves the way to entanglement generation and distant quantum communication between mechanical and spin systems and to sensing of force, motion and gravity beyond the standard quantum limit.

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Acknowledgements

We acknowledge discussions with F. Khalili. This work was supported by the European Union Seventh Framework Program (ERC grant INTERFACE, projects SIQS and iQUOEMS), the European Union’s Horizon 2020 research and innovation programme (ERC grant Q-CEOM, grant agreement no. 638765), a Sapere Aude starting grant from the Danish Council for Independent Research, and the DARPA project QUASAR. R.A.T. is funded by the program Science without Borders of the Brazilian Federal Government. E.Z. is supported by the Carlsberg Foundation. K.H. and E.Z. acknowledge support from DFG through SFB 1227 (DQ-mat). We acknowledge help from M. Gaudesius at the early stage of the experimental development.

Author information

Author notes

    • Christoffer B. Møller
    •  & Rodrigo A. Thomas

    These authors contributed equally to this work.

Affiliations

  1. Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark

    • Christoffer B. Møller
    • , Rodrigo A. Thomas
    • , Georgios Vasilakis
    • , Emil Zeuthen
    • , Yeghishe Tsaturyan
    • , Mikhail Balabas
    • , Kasper Jensen
    • , Albert Schliesser
    •  & Eugene S. Polzik
  2. Institute for Electronic Structure and Laser, Foundation for Research and Technology-Hellas, Heraklion 71110, Greece

    • Georgios Vasilakis
  3. Institute for Theoretical Physics and Institute for Gravitational Physics (Albert Einstein Institute), Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany

    • Emil Zeuthen
    •  & Klemens Hammerer
  4. Department of Physics, St Petersburg State University, Universitetskii prospekt 28, 198504 Staryi Peterhof, Russia

    • Mikhail Balabas

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Contributions

E.S.P. conceived and led the project. C.B.M., R.A.T. and G.V. built the experiment with the help of K.J., Y.T. and A.S. The membrane resonator was designed and fabricated by Y.T. M.B. fabricated caesium cells with spin protecting coating. C.B.M., R.A.T., G.V. and E.S.P. took the data. E.Z. and K.H. developed the theory with input from A.S. and E.S.P. The paper was written by E.S.P., K.H., E.Z., R.A.T., C.B.M. and G.V. with contributions from other authors. A.S., K.H. and E.S.P. supervised the research.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Eugene S. Polzik.

Reviewer Information Nature thanks W. Bowen and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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https://doi.org/10.1038/nature22980

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