Abstract
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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Acknowledgements
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.
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The measurements presented in this paper were performed with the 4-km detector at the LIGO Livingston Observatory using a novel squeezed light source. Haocun Yu performed all of the measurements. Haocun Yu and L.M. carried out the analysis of the data. M. Tse, Haocun Yu and N.K. built and commissioned the squeezed-light sources. L.B. led the squeezed-light upgrade of the LIGO detectors, involving contributions from a large number of people within the LIGO Laboratory, the Australian National University and other members of the LIGO Scientific Collaboration. N.M. led the experimental campaign to measure sub-SQL quantum noise in the Advanced LIGO detector. Haocun Yu, L.M., M. Tse, L.B. and N.M. contributed directly to the preparation of the manuscript.
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Peer review information Nature thanks Albert Schliesser, Valeria Sequino and Kentaro Somiya for their contribution to the peer review of this work.
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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.
Extended Data Fig. 2 Squeezing level of the interferometer over the full range of squeezing angles.
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
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DOI: https://doi.org/10.1038/s41586-020-2420-8
