Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Measurement of quantum back action in the audio band at room temperature


Quantum mechanics places a fundamental limit on the precision of continuous measurements. The Heisenberg uncertainty principle dictates that as the precision of a measurement of an observable (for example, position) increases, back action creates increased uncertainty in the conjugate variable (for example, momentum). In interferometric gravitational-wave detectors, higher laser powers reduce the position uncertainty created by shot noise (the photon-counting error caused by the quantum nature of the laser) but necessarily do so at the expense of back action in the form of quantum radiation pressure noise (QRPN)1. Once at design sensitivity, the gravitational-wave detectors Advanced LIGO2, VIRGO3 and KAGRA4 will be limited by QRPN at frequencies between 10 hertz and 100 hertz. There exist several proposals to improve the sensitivity of gravitational-wave detectors by mitigating QRPN5,6,7,8,9,10, but until now no platform has allowed for experimental tests of these ideas. Here we present a broadband measurement of QRPN at room temperature at frequencies relevant to gravitational-wave detectors. The noise spectrum obtained shows effects due to QRPN between about 2 kilohertz and 100 kilohertz, and the measured magnitude of QRPN agrees with our model. We now have a testbed for studying techniques with which to mitigate quantum back action, such as variational readout and squeezed light injection7, with the aim of improving the sensitivity of future gravitational-wave detectors.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Experimental set-up.
Fig. 2: Measured and budgeted noise.
Fig. 3: Power scaling.

Data availability

The data pertaining to this study are available from the corresponding authors upon reasonable request.


  1. Caves, C. M. Quantum-mechanical radiation-pressure fluctuations in an interferometer. Phys. Rev. Lett. 45, 75–79 (1980).

    Article  ADS  Google Scholar 

  2. The LIGO Scientific Collaboration. Advanced LIGO. Class. Quantum Gravity 32, 074001 (2015).

    Article  ADS  Google Scholar 

  3. Acernese, F. et al. Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quantum Gravity 32, 024001 (2015).

    Article  ADS  Google Scholar 

  4. Somiya, K. Detector configuration of KAGRA–the Japanese cryogenic gravitational-wave detector. Class. Quantum Gravity 29, 124007 (2012).

    Article  ADS  Google Scholar 

  5. Braginsky, V. B., Vorontsov, Y. I. & Thorne, K. S. Quantum nondemolition measurements. Science 209, 547–557 (1980).

    Article  CAS  ADS  Google Scholar 

  6. Braginsky, V. B., Gorodetsky, M. L., Khalili, F. Y. & Thorne, K. S. Dual-resonator speed meter for a free test mass. Phys. Rev. D 61, 044002 (2000).

    Article  ADS  Google Scholar 

  7. 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).

    Article  ADS  Google Scholar 

  8. Harms, J. et al. Squeezed-input, optical-spring, signal-recycled gravitational-wave detectors. Phys. Rev. D 68, 042001 (2003).

    Article  ADS  Google Scholar 

  9. Oelker, E. et al. Audio-band frequency-dependent squeezing for gravitational-wave detectors. Phys. Rev. Lett. 116, 041102 (2016).

    Article  ADS  Google Scholar 

  10. Gräf, C. et al. Design of a speed meter interferometer proof-of-principle experiment. Class. Quantum Gravity 31, 215009 (2014).

    Article  ADS  Google Scholar 

  11. Braginsky, V. B. & Manukin, A. B. Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, Chicago, 1977).

    Google Scholar 

  12. Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).

    Article  ADS  Google Scholar 

  13. Saulson, P. R. Thermal noise in mechanical experiments. Phys. Rev. D 42, 2437–2445 (1990).

    Article  CAS  ADS  Google Scholar 

  14. Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).

    Article  CAS  ADS  Google Scholar 

  15. Teufel, J. D., Lecocq, F. & Simmonds, R. W. Overwhelming thermomechanical motion with microwave radiation pressure shot noise. Phys. Rev. Lett. 116, 013602 (2016).

    Article  CAS  ADS  Google Scholar 

  16. Purdy, T. P., Grutter, K. E., Srinivasan, K. & Taylor, J. M. Quantum correlations from a room-temperature optomechanical cavity. Science 356, 1265–1268 (2017).

    Article  CAS  ADS  MathSciNet  Google Scholar 

  17. Sudhir, V. et al. Quantum correlations of light from a room-temperature mechanical oscillator. Phys. Rev. X 7, 031055 (2017).

    Google Scholar 

  18. Cole, G. D., Gröblacher, S., Gugler, K., Gigan, S. & Aspelmeyer, M. Monocrystalline AlxGa1-xAs heterostructures for high-reflectivity high-Q micromechanical resonators in the megahertz regime. Appl. Phys. Lett. 92, 261108 (2008).

    Article  ADS  Google Scholar 

  19. Cole, G. D. Cavity optomechanics with low-noise crystalline mirrors. Proc. SPIE 8458, 845807 (2012).

    Article  Google Scholar 

  20. Cole, G. D. et al. High-performance near- and mid-infrared crystalline coatings. Optica 3, 647–656 (2016).

    Article  CAS  ADS  Google Scholar 

  21. Singh, R., Cole, G. D., Cripe, J. & Corbitt, T. Stable optical trap from a single optical field utilizing birefringence. Phys. Rev. Lett. 117, 213604 (2016).

    Article  ADS  Google Scholar 

  22. Cripe, J. et al. Radiation-pressure-mediated control of an optomechanical cavity. Phys. Rev. A 97, 013827 (2018).

    Article  CAS  ADS  Google Scholar 

  23. Nyquist, H. Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110–113 (1928).

    Article  CAS  ADS  Google Scholar 

  24. Fedorov, S. et al. Evidence for structural damping in a high-stress silicon nitride nanobeam and its implications for quantum optomechanics. Phys. Lett. A 382, 2251–2255 (2018).

    Article  CAS  ADS  Google Scholar 

  25. Corbitt, T., Chen, Y. & Mavalvala, N. Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formalism. Phys. Rev. A 72, 013818 (2005).

    Article  ADS  Google Scholar 

  26. Corbitt, T. et al. Squeezed-state source using radiation-pressure-induced rigidity. Phys. Rev. A 73, 023801 (2006).

    Article  ADS  Google Scholar 

  27. Willke, B., Brozek, S., Danzmann, K., Quetschke, V. & Gossler, S. Frequency stabilization of a monolithic Nd:YAG ring laser by controlling the power of the laser-diode pump source. Opt. Lett. 25, 1019–1021 (2000).

    Article  CAS  ADS  Google Scholar 

  28. Braginsky, V., Gorodetsky, M. & Vyatchanin, S. Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae. Phys. Lett. A 264, 1–10 (1999).

    Article  CAS  ADS  Google Scholar 

  29. Aggarwal, N. et al. Room temperature optomechanical squeezing. Preprint at (2018).

  30. Cripe, J. et al. Quantum back action cancellation in the audio band. Preprint at (2018).

  31. Yap, M. J. et al. Broadband reduction of quantum radiation pressure noise via squeezed light injection. Preprint at (2018).

  32. Corbitt, T. et al. An all-optical trap for a gram-scale mirror. Phys. Rev. Lett. 98, 150802 (2007).

    Article  ADS  Google Scholar 

  33. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    Article  ADS  Google Scholar 

Download references


J.C. and T.C. are supported by National Science Foundation grants PHY-1150531 and PHY-1806634. N.A., A.L. and N.M. are supported by National Science Foundation grants PHY-1707840 and PHY-1404245. A portion of this work was performed in the UCSB Nanofabrication Facility. J.C. and T.C. thank D. McClelland, R. Ward and M. J. Yap for comments and discussion. The authors thank C. Wipf and V. Sudhir for comments during the manuscript preparation. This document has been assigned the LIGO document number LIGO-P1800033.

Reviewer information

Nature thanks Warwick Bowen, Yuta Michimura and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Authors and Affiliations



J.C. led the design, construction and data taking for the experiment, and prepared the manuscript. T.C. supervised the design and construction of the experiment, and also helped with the data taking and analysis of the results. N.A., R.L., A.L. and N.M. contributed to the design of the microresonators and the writing of the manuscript. G.D.C. provided feedback on the design of the microresonators and, together with P.H. and D.F., fabricated the devices. R.S. contributed experience from previous experiments.

Corresponding authors

Correspondence to Jonathan Cripe or Thomas Corbitt.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Full noise budget.

For the measurement with 220 mW circulating power, each noise source that contributed to the sum of subdominant noises in Fig. 2 is shown (see key). The narrow peaks in the displacement noise measurement are a result of parametric nonlinear coupling between various mechanical modes, and this coupling is negligible at low circulating powers.

Extended Data Fig. 2 Dependence of thermal noise on circulating power as caused by change in beam position.

a, The total displacement noise around the yaw mechanical mode for each of the four circulating power levels (see key). b, As a but centred on the pitch mechanical mode. In these measurements, thermal noise is the dominant noise source at frequencies near the mechanical resonances. The thermal noise around the pitch mode decreases from 73 mW to 110 mW of circulating power, and then increases at 220 mW. This change is consistent with the cavity mode passing through the nodal point of this mode at an intermediate power level. Each panel includes an image from the finite element model depicting the motion associated with the mechanical mode. In both images, the blue portion represents a positive displacement from equilibrium (thin black outline), and the red area denotes a negative displacement. The nodal line for the mechanical modes is drawn in white.

Extended Data Fig. 3 Comparison of thermal noise spectra at different alignments.

The effect of the change in beam position is seen in the change of height of the peaks in the displacement spectrum at the frequencies of the higher-order mechanical modes. The blue curve is taken with 10 mW of circulating power with a cavity mode alignment similar to the QRPN measurement with 220 mW circulating power. The green curve is for an alignment to minimize the coupling of the pitch and yaw modes at 10 mW circulating power. The red curve is based on a model that sets the modal mass of the higher-order modes so that the peaks match those in the displacement measurement shown in Fig. 2.

Extended Data Fig. 4 Effect of uncertainty in detuning and loss.

Modelled quantum displacement noise at 20 kHz and 220 mW of circulating power is shown as a function of intracavity loss and cavity detuning: the optical-spring frequency, which has been precisely measured, is held constant in the model. To be conservative, the range in values for the cavity loss and detuning in this figure are much larger than the constraints obtained by measurements of the optical spring.

Extended Data Fig. 5 QRPN as a function of frequency and power.

This contour plot shows what fraction of the total measured displacement noise power spectral density (PSD) is contributed by QRPN, as a function of measurement frequency and circulating power. The quantity shown on the colour scale at right is the ratio of the PSDs of the QRPN model to the total measured noise. Whereas in the rest of this Letter we present the data as amplitude spectral densities in order to put them in the perspective of GW measurements, we use PSDs to calculate percentage and ratios, and to make this figure, because all the noises are added in quadrature to make up the total noise. We interpolate the data between the measurements at 73 mW, 110 mW, 150 mW and 220 mW. The vertical stripe at 876 Hz is an artefact of the fundamental resonance not being perfectly resolved in the measurement. The blue vertical stripes at 3.7 kHz, 15 kHz and 28 kHz are higher-order mechanical modes of the microresonator. The contours are at a spacing of 0.05 (5%).

Extended Data Fig. 6 Projected QRPN.

Shown is the measured QRPN level obtained by multiplying the transfer function measurement TFAM by the shot noise of the effective cavity input power and applying the calibration procedure, as described in Methods. The result of this calculation agrees with the modelled QRPN.

Extended Data Table 1 Standard optomechanical parameters

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cripe, J., Aggarwal, N., Lanza, R. et al. Measurement of quantum back action in the audio band at room temperature. Nature 568, 364–367 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing