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.
This is a preview of subscription content
Subscribe to Nature+
Get immediate online access to the entire Nature family of 50+ journals
Subscribe to Journal
Get full journal access for 1 year
only $8.25 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Source data for Figs. 2–4 are available in the UCPH ERDA repository (https://doi.org/10.17894/ucph.8f3edcdf-d030-49e0-93de-8b7fdccdfd8e). The remaining data are available from the corresponding author upon request.
Braginsky, V. B. Classical and quantum restrictions on the detection of weak disturbances of a macroscopic oscillator. J. Exp. Theor. Phys. 26, 831–834 (1968).
Braginsky, V., Vorontsov, Y. & Thorne, K. Quantum nondemolition measurements. Science 209, 547–557 (1980).
Unruh, W. In Quantum Optics, Experimental Gravitation, and Measurement Theory (eds Meystre, P. & Scully, M. O.) 647 (Plenum, 1982).
Vyatchanin, S. P. & Zubova, E. A. Quantum variation measurement of a force. Phys. Lett. A 201, 269–274 (1995).
The LIGO Scientific Collaboration. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 201, 962–965 (2011).
Schreppler, S. et al. Optically measuring force near the standard quantum limit. Science 344, 1486–1489 (2014).
LaHaye, M. D., Buu, O., Camarota, B. & Schwab, K. C. Approaching the quantum limit of a nanomechanical resonator. Science 304, 74–77 (2004).
Rossi, M., Mason, D., Chen, J., Tsaturyan, Y. & Schliesser, A. Measurement-based quantum control of mechanical motion. Nature 563, 53–58 (2018).
Kampel, N. S. et al. Improving broadband displacement detection with quantum correlations. Phys. Rev. X 7, 021008 (2017).
Suh, J. et al. Mechanically detecting and avoiding the quantum fluctuations of a microwave field. Science 344, 1262–1265 (2014).
Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).
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).
Sudhir, V. et al. Quantum correlations of light from a room-temperature mechanical oscillator. Phys. Rev. X 7, 031055 (2017).
Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).
Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).
Braginsky, V. B., Khalili, F. Y. & Thorne, K. S. Quantum Measurement (Cambridge University Press, 1992).
Bowen, W. P. & Milburn, G. J. Quantum Optomechanics (CRC Press, 2016).
Kimble, H. J., Levin, Y., Matsko, A. B., Thorne, K. S. & Vyatchanin, S. P. Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics. Phys. Rev. D 65, 022002 (2001).
Corbitt, T. & Mavalvala, N. Quantum noise in gravitational-wave interferometers. J. Opt. B 6, S675 (2004).
Purdue, P. & Chen, Y. Practical speed meter designs for quantum nondemolition gravitational-wave interferometers. Phys. Rev. D 66, 122004 (2002).
Thorne, K. S., Drever, R. W., Caves, C. M., Zimmermann, M. & Sandberg, V. D. Quantum nondemolition measurements of harmonic oscillators. Phys. Rev. Lett. 40, 667–671 (1978).
Braginskiĭ, V. B., Vorontsov, Y. I. & Khalili, F. Y. Optimal quantum measurements in detectors of gravitation radiation. Sov. J. Exp. Theor. Phys. Lett. 27, 276 (1978).
Ockeloen-Korppi, C. F. et al. Quantum backaction evading measurement of collective mechanical modes. Phys. Rev. Lett. 117, 140401 (2016).
Møller, C. B. et al. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547, 191–195 (2017).
Arcizet, O., Briant, T., Heidmann, A. & Pinard, M. Beating quantum limits in an optomechanical sensor by cavity detuning. Phys. Rev. A 73, 033819 (2006).
Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).
Brooks, D. W. C. et al. Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012).
Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013).
Purdy, T. P., Yu, P.-L., Peterson, R. W., Kampel, N. S. & Regal, C. A. Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013).
Giovannetti, V., Lloyd, S. & Maccone, L. Quantum enhanced measurement: beating the standard quantum limit. Science 306, 1330–1336 (2004).
Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotechnol. 12, 776–783 (2017).
Clerk, A. A. Quantum-limited position detection and amplification: a linear response perspective. Phys. Rev. B 70, 1–9 (2004).
Buchmann, L. F., Schreppler, S., Kohler, J., Spethmann, N. & Stamper-Kurn, D. M. Complex squeezing and force measurement beyond the standard quantum limit. Phys. Rev. Lett. 117, 030801 (2016).
Habibi, H., Zeuthen, E., Ghanaatshoar, M. & Hammerer, K. Quantum feedback cooling of a mechanical oscillator using variational measurements: tweaking Heisenberg’s microscope. J. Opt. 18, 084004 (2016).
Poggio, M. & Degen, C. L. Force-detected nuclear magnetic resonance: recent advances and future challenges. Nanotechnology 21, 342001 (2010).
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).
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Mason, D., Chen, J., Rossi, M. et al. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019). https://doi.org/10.1038/s41567-019-0533-5
Communications Physics (2022)
Nature Physics (2022)
Ultrasensitive detection of local acoustic vibrations at room temperature by plasmon-enhanced single-molecule fluorescence
Nature Communications (2022)
Nature Nanotechnology (2021)