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Measurement-based quantum control of mechanical motion

Naturevolume 563pages5358 (2018) | Download Citation

Abstract

Controlling a quantum system by using observations of its dynamics is complicated by the backaction of the measurement process—that is, the unavoidable quantum disturbance caused by coupling the system to a measurement apparatus. An efficient measurement is one that maximizes the amount of information gained per disturbance incurred. Real-time feedback can then be used to cancel the backaction of the measurement and to control the evolution of the quantum state. Such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, but its application to motional degrees of freedom has remained elusive. Here we demonstrate measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the resonator in a fraction of its millisecond-scale coherence time, with an overall measurement efficiency close to unity. An electronic feedback loop converts this position record to a force that cools the resonator mode to its quantum ground state (residual thermal occupation of about 0.29). This occupation is nine decibels below the quantum-backaction limit of sideband cooling and six orders of magnitude below the equilibrium occupation of the thermal environment. We thus realize a long-standing goal in the field, adding position and momentum to the degrees of freedom that are amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational-wave detectors.

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Data availability

Source Data for Figs. 15 are provided with the online version of the paper and are available in the UCPH ERDA repository (https://doi.org/10.17894/ucph.2612dd59-20ab-40d2-a33d-f53e4428c4cd).

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Acknowledgements

We acknowledge discussions with K. Hammerer, E. Zeuthen and D. Vitali, and early-stage sample fabrication by Y. Seis. This work was supported by funding from the European Union’s Horizon 2020 research and innovation programme (European Research Council (ERC) project Q-CEOM, grant agreement no. 638765 and FET proactive project HOT, grant agreement no. 732894), a starting grant from the Danish Council for Independent Research and the Carlsberg Foundation.

Reviewer information

Nature thanks D. Bouwmeester, M. Poggio and M. Vanner for their contribution to the peer review of this work.

Author information

Author notes

  1. These authors contributed equally: Massimiliano Rossi, David Mason, Junxin Chen

Affiliations

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

    • Massimiliano Rossi
    • , David Mason
    • , Junxin Chen
    • , Yeghishe Tsaturyan
    •  & Albert Schliesser
  2. Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    • Massimiliano Rossi
    • , David Mason
    • , Junxin Chen
    •  & Albert Schliesser

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Contributions

M.R., D.M. and J.C. built (with initial contributions from Y.T.) and performed the experiments, analysed the data and, together with A.S., discussed the results and wrote the paper. Y.T. designed and fabricated the membrane resonators. A.S. conceived and directed the project.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Albert Schliesser.

Extended data figures and tables

  1. Extended Data Fig. 1 Soft-clamped membrane.

    a, Photograph of the soft-clamped membrane. b, Simulated displacement pattern of defect-localized mode A. c, Mechanical spectrum of the lowest-frequency bandgap, with defect-localized modes labelled from A to E. The grey peak at 1.09 MHz is a phase-calibration tone.

  2. Extended Data Fig. 2 Mode A ringdowns.

    a, Ringdowns with continuous and stroboscopic optical monitoring. The inset shows the power spectral density (PSD) of the continuous ringdown data. b, Ringdowns at different continuous optical powers. The Q values extracted are 1.02 × 109, 1.06 × 109, 1.07 × 109 and 1.04 × 109 from high to low optical power.

  3. Extended Data Fig. 3 Experimental set-up.

    An overview of the optical and electronic scheme used in the experiments is shown. AM, amplitude modulator; PM, phase modulator; DAQ, data acquisition card; LIA, lock-in amplifier; aux, auxiliary; νPDH, Pound–Drever–Hall modulation frequency; νcal, calibration tone frequency.

  4. Extended Data Fig. 4 OMIT.

    Measured traces of the transmission |tp| are shown for different laser detunings, close to the mechanical frequency Ωm (dashed red line). Black lines are theoretical fits.

  5. Extended Data Table 1 Contribution to detection efficiency

Supplementary information

  1. Supplementary Information

    This file contains a table with a summary of symbols used throughout the manuscript and three additional sections. In the first one we discuss about the theoretical model used to describe the measurements presented in the manuscript. In the second one we give details about the methods used to analyse the data. In the third section we provide additional measurements which characterize the additional technical noise of the laser source used in the experiment.

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DOI

https://doi.org/10.1038/s41586-018-0643-8

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