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Continuous force and displacement measurement below the standard quantum limit


Quantum mechanics dictates that the precision of physical measurements must always comply with certain noise constraints. In the case of interferometric displacement measurements, these restrictions impose a standard quantum limit (SQL), which optimally balances the precision of a measurement with its unwanted backaction1. To go beyond this limit, one must devise more sophisticated measurement techniques, which either ‘evade’ the backaction of the measurement2 or achieve clever cancellation of the unwanted noise at the detector3,4. In the half-century since the SQL was established, systems ranging from LIGO5 to ultracold atoms6 and nanomechanical devices7,8 have pushed displacement measurements towards this limit, and a variety of sub-SQL techniques have been tested in proof-of-principle experiments9,10,11,12,13. However, so far, no experimental system has successfully demonstrated an interferometric displacement measurement with sensitivity (including all relevant noise sources—thermal, backaction and imprecision) below the SQL. Here, we exploit strong quantum correlations in an ultracoherent optomechanical system to demonstrate off-resonant force and displacement sensitivity reaching 1.5 dB below the SQL. This achieves an outstanding goal in mechanical quantum sensing and further enhances the prospects of using such devices for state-of-the-art force sensing applications.

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Fig. 1: Measuring beyond the SQL.
Fig. 2: Measuring displacement below the SQL.
Fig. 3: Opening broadband regions of sub-SQL sensitivity.
Fig. 4: Quantum-enhanced force sensing beyond the SQL.

Data availability

Source data for Figs. 2–4 are available in the UCPH ERDA repository ( The remaining data are available from the corresponding author upon request.


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The authors acknowledge input from J. Appel regarding photodetector design. This work was supported by funding from the European Union’s Horizon 2020 research and innovation programme (European Research Council project Q-CEOM, grant agreement no. 638765 and FET proactive project HOT, grant agreement no. 732894).

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Authors and Affiliations



D.M., J.C. and M.R. built the set-up 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. supervised the project.

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Correspondence to Albert Schliesser.

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Mason, D., Chen, J., Rossi, M. et al. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).

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