The measurement of minuscule forces and displacements with ever greater precision is inhibited by the Heisenberg uncertainty principle, which imposes a limit to the precision with which the position of an object can be measured continuously, known as the standard quantum limit1,2,3,4. When light is used as the probe, the standard quantum limit arises from the balance between the uncertainties of the photon radiation pressure applied to the object and of the photon number in the photoelectric detection. The only way to surpass the standard quantum limit is by introducing correlations between the position/momentum uncertainty of the object and the photon number/phase uncertainty of the light that it reflects5. Here we confirm experimentally the theoretical prediction5 that this type of quantum correlation is naturally produced in the Laser Interferometer Gravitational-wave Observatory (LIGO). We characterize and compare noise spectra taken without squeezing and with squeezed vacuum states injected at varying quadrature angles. After subtracting classical noise, our measurements show that the quantum mechanical uncertainties in the phases of the 200-kilowatt laser beams and in the positions of the 40-kilogram mirrors of the Advanced LIGO detectors yield a joint quantum uncertainty that is a factor of 1.4 (3 decibels) below the standard quantum limit. We anticipate that the use of quantum correlations will improve not only the observation of gravitational waves, but also more broadly future quantum noise-limited measurements.
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Caves, C. M. Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693–1708 (1981).
Braginsky, V. B. & Khalili, F. Y. Quantum nondemolition measurements: the route from toys to tools. Rev. Mod. Phys. 68, 1–11 (1996).
Braginsky, V. B., Khalili, F. Y. & Thorne, K. S. Quantum Measurement (Cambridge University Press, 1992).
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).
Unruh, W. G. Quantum Optics, Experimental Gravitation, and Measurement Theory (Plenum, 1982).
Buonanno, A. & Chen, Y. Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors. Phys. Rev. D 64, 042006 (2001).
Kwee, P., Miller, J., Isogai, T., Barsotti, L. & Evans, M. Decoherence and degradation of squeezed states in quantum filter cavities. Phys. Rev. D 90, 062006 (2014).
Danilishin, S. et al. Creation of a quantum oscillator by classical control. Preprint at https://arxiv.org/abs/0809.2024 (2008).
Purdue, P. & Chen, Y. Practical speed meter designs for quantum nondemolition gravitational-wave interferometers. Phys. Rev. D 66, 122004 (2002).
Møller, C. B. et al. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 547, 191–195 (2017).
Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).
Suh, J. et al. Mechanically detecting and avoiding the quantum fluctuations of a microwave field. Science 344, 1262–1265 (2014).
Wilson, D. J. et al. Measurement-based control of a mechanical oscillator at its thermal decoherence rate. Nature 524, 325–329 (2015).
Teufel, J., Lecocq, F. & Simmonds, R. Overwhelming thermomechanical motion with microwave radiation pressure shot noise. Phys. Rev. Lett. 116, 013602 (2016).
Cripe, J. et al. Measurement of quantum back action in the audio band at room temperature. Nature 568, 364–367 (2019).
Sudhir, V. et al. Quantum correlations of light from a room-temperature mechanical oscillator. Phys. Rev. X 7, 031055 (2017).
Purdy, T. P., Grutter, K. E., Srinivasan, K. & Taylor, J. M. Quantum correlations from a room-temperature optomechanical cavity. Science 356, 1265–1268 (2017).
Mason, D., Chen, J., Rossi, M., Tsaturyan, Y. & Schliesser, A. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).
Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).
Abbott, B. P. et al. Gw150914: the advanced LIGO detectors in the era of first discoveries. Phys. Rev. Lett. 116, 131103 (2016).
Sun, L. et al. Characterization of systematic error in advanced LIGO calibration. Preprint at https://arxiv.org/abs/2005.02531 (2020).
Kiwamu, I. Time domain implementation of dcpd cross correlation. Technical Note T1700131 (LIGO Virgo, 2017); https://dcc.ligo.org/LIGO-T1700131/public.
LIGO was constructed by the California Institute of Technology and the Massachusetts Institute of Technology with funding from the National Science Foundation, and operates under Cooperative Agreement number PHY-1764464. Advanced LIGO was built under grant number PHY-0823459. The authors gratefully acknowledge the support of the Australian Research Council under the ARC Centre of Excellence for Gravitational Wave Discovery grant number CE170100004, Linkage Infrastructure, Equipment and Facilities grant number LE170100217 and Discovery Early Career Award number DE190100437; the National Science Foundation Graduate Research Fellowship under grant number 1122374; the Science and Technology Facilities Council of the United Kingdom; and the LIGO Scientific Collaboration Fellows programme.
The authors declare no competing interests.
Peer review information Nature thanks Albert Schliesser, Valeria Sequino and Kentaro Somiya for their contribution to the peer review of this work.
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 Spectral density measurements revealing sub-SQL quantum noise of the interferometer with uncertainties.
The black and brown traces show the measured total noise level of the interferometer with the unsqueezed vacuum state (the reference) and injected squeezing at 35°, respectively. The grey curve shows the classical noise contribution to the total noise of the interferometer, which is independent of the squeezer state. The solid blue curve shows the quantum noise model and includes the 5% uncertainty in the arm power, compensated by the output optical loss to maintain the calibrated sensing function. The inferred quantum noise (green curve) and error bars include all uncertainty terms present in equation (12), as estimated in Methods, including the frequency dependence. The quantum noise model with 35° squeezing (purple line) is shown with the 5% arm power uncertainty (purple shading) and the 0.5-dB uncertainty of the squeezing generated by the squeezer (pink shading). The free-mass SQL is shown by the dashed red line, and the pure QRPN contribution of the interferometer with the unsqueezed vacuum state is shown by the dashed blue line and includes the uncertainty in the arm power.
Contour plot of squeezing level S*(ϕ, θ, ψ) detected in the interferometer as a function of the frequency and squeezing angle ϕ (top) and the corresponding theoretical model (bottom). The dashed lines indicate cross-sections in other figures. The green dashed line shows ϕ = 35° in Fig. 2, and the magenta, navy and orange lines correspond to the angles shown in Fig. 3.
Extended Data Fig. 3 Individual and combined estimates of non-stationary noise between measurement segments.
The two upper plots show the relative time variation of noise between each pair of reference and squeezing measurement segments, respectively. The black lines show 2σ or a 95% confidence level. The bottom plot shows the combined non-stationary power defined by equation (14).
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Yu, H., McCuller, L., Tse, M. et al. Quantum correlations between light and the kilogram-mass mirrors of LIGO. Nature 583, 43–47 (2020). https://doi.org/10.1038/s41586-020-2420-8