Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement

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In continuously monitored systems the standard quantum limit is given by the trade-off between shot noise and back-action noise. In gravitational-wave detectors, such as Advanced LIGO, both contributions can be simultaneously squeezed in a broad frequency band by injecting a spectrum of squeezed vacuum states with a frequency-dependent squeeze angle. This approach requires setting up an additional long baseline, low-loss filter cavity in a vacuum system at the detector’s site. Here, we show that the need for such a filter cavity can be eliminated, by exploiting Einstein–Podolsky–Rosen (EPR)-entangled signals and idler beams. By harnessing their mutual quantum correlations and the difference in the way each beam propagates in the interferometer, we can engineer the input signal beam to have the appropriate frequency-dependent conditional squeezing once the out-going idler beam is detected. Our proposal is appropriate for all future gravitational-wave detectors for achieving sensitivities beyond the standard quantum limit.

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Figure 1: Sensitivity of an Advanced LIGO-type gravitational-wave detector driven by squeezed vacuum (6 dB squeeze degree is chosen for comparing the 5% input/output loss case in Fig. 4) with a fixed squeezing angle.
Figure 2: Optical configuration for noise suppression via EPR entanglement.
Figure 3: The differential mode of the interferometer as seen by the signal (upper panel) and idler (lower panel) beams.
Figure 4: Sensitivity enhancement.
Figure 5: Spectral decomposition of EPR-entangled beams (upper panel) and the quantum statics of the signal and idler beams (lower panel).


  1. 1

    Abbott, B. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016).

  2. 2

    Punturo, M. et al. The Einstein telescope: a third-generation gravitational wave observatory. Class. Quant. Gravity 27, 194002 (2010).

  3. 3

    Danilishin, S. & Khalili, F. Y. Quantum measurement theory in gravitational-wave detectors. Living Rev. Relativ. 15, 5 (2012).

  4. 4

    Miao, H., Yang, H., Adhikari, R. X. & Chen, Y. Quantum limits of interferometer topologies for gravitational radiation detection. Class. Quant. Gravity 31, 165010 (2014).

  5. 5

    Dwyer, S. et al. Gravitational wave detector with cosmological reach. Phys. Rev. D 91, 082001 (2015).

  6. 6

    Abbott, B. et al. Exploring the sensitivity of next generation gravitational wave detectors. Class. Quant. Gravity 34, 044001 (2017).

  7. 7

    Sathyaprakash, B. et al. Scientific objectives of Einstein telescope. Class. Quant. Gravity 29, 124013 (2012).

  8. 8

    Tso, R., Isi, M., Chen, Y. & Stein, L. Modeling the dispersion and polarization content of gravitational waves for tests of general relativity. In Seventh Meeting on CPT and Lorentz Symmetry. Preprint at (2016).

  9. 9

    Kostelecky, A. & Mewes, M. Testing local Lorentz invariance with gravitational waves. Phys. Lett. B 757, 510–514 (2016).

  10. 10

    Lasky, P., Thrane, E., Levin, Y., Blackman, J. & Chen, Y. Detecting gravitational-wave memory with LIGO: implications of GW150914. Phys. Rev. Lett. 117, 061102 (2016).

  11. 11

    Berti, E. Astrophysical black holes as natural laboratories for fundamental physics and strong-field gravity. Braz. J. Phys. 43, 341 (2013).

  12. 12

    Chu, Q. et al. Capturing the electromagnetic counterparts of binary neutron star mergers through low-latency gravitational wave triggers. Mon. Not. R. Astron. Soc. 459, 121–139 (2016).

  13. 13

    Metzger, B. D. & Berger, E. What is the most promising electromagnetic counterpart of a neutron star binary merger? Astrophys. J. 746, 48 (2012).

  14. 14

    Aasi, J. et al. Constraints on cosmic strings from the LIGO-Virgo gravitational-wave detectors. Phys. Rev. Lett. 112, 131101 (2014).

  15. 15

    Drever, R. W. P., Hough, J., Edelstein, W. A., Pugh, J. R. & Martin, W. in Experimental Gravitation 365 (ed. Bertotii, B.) (Accademia Nazionale dei Lincei., 1976).

  16. 16

    Braginsky, V. B. & Vorontsov, Y. I. Quantum-mechanical restrictions in macroscopic measurements and modern experimental devices. Sov. Phys. Usp. 17, 644–650 (1975).

  17. 17

    Weiss, R. Sources of Gravitational Radiation (Cambridge Univ. Press, 1979).

  18. 18

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

  19. 19

    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).

  20. 20

    Buonanno, A. & Chen, Y. Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors. Phys. Rev. D 64, 042006 (2001).

  21. 21

    Buonanno, A. & Chen, Y. Scaling law in signal recycled laser-interferometer gravitational-wave detectors. Phys. Rev. D 67, 062002 (2003).

  22. 22

    Unruh, W. G. Quantum Noise in the Interferometer Detector 647 (Plenum Press, 1983).

  23. 23

    Schnabel, R., Mavalvala, N., McClelland, D. E. & Lam, P. K. Quantum metrology for gravitational wave astronomy. Nat. Commun. 1, 121 (2010).

  24. 24

    LIGO Instrument Science White Paper Technical report (2015).

  25. 25

    Vahlbruch, H. et al. Observation of squeezed light with 10-dB quantum-noise reduction. Phys. Rev. Lett. 100, 033602 (2009).

  26. 26

    Mehmet, M. et al. Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB. Opt. Express 19, 25763 (2011).

  27. 27

    Chua, S. S. Y. et al. Backscatter tolerant squeezed light source for advanced gravitational-wave detectors. Opt. Lett. 36, 4680–4682 (2011).

  28. 28

    Stefszky, M. S. et al. Balanced homodyne detection of optical quantum states at audio-band frequencies and below. Class. Quant. Gravity 29, 145015 (2012).

  29. 29

    McKenzie, K. et al. Squeezing in the audio gravitational-wave detection band. Phys. Rev. Lett. 93, 161105 (2004).

  30. 30

    Vahlbruch, H., Mehmet, M., Danzmann, K. & Schnabel, R. Detection of 15 dB squeezed states of light and their application for the absolute calibration of photo-electric quantum efficiency. Phys. Rev. Lett. 117, 110801 (2016).

  31. 31

    Abbott, B. et al. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962 (2011).

  32. 32

    Abbott, B. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613 (2013).

  33. 33

    Jaekel, M. T. & Reynaud, S. Quantum limits in interferometer measurement. Europhys. Lett. 13, 301 (1990).

  34. 34

    Chelkowski, S. et al. Experimental characterization of frequency-dependent squeezed light. Phys. Rev. A 71, 013806 (2005).

  35. 35

    Evans, M., Barsotti, L., Kwee, P., Harms, J. & Miao, H. Realistic filter cavities for advanced gravitational wave detectors. Phys. Rev. D 88, 022002 (2013).

  36. 36

    Khalili, F. Y. Quantum variational measurement in the next generation gravitational-wave detectors. Phys. Rev. D 76, 102002 (2007).

  37. 37

    Khalili, F. Y. Optimal configurations of filter cavity in future gravitational-wave detectors. Phys. Rev. D 81, 122002 (2010).

  38. 38

    Isogai, T., Miller, J., Kwee, P., Barsotti, L. & Evans, M. Loss in long-storage-time optical cavities. Opt. Express 21, 30114–30125 (2013).

  39. 39

    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).

  40. 40

    Caposcasa, E. et al. Estimation of losses in a 300 m filter cavity and quantum noise reduction in the kagra gravitational-wave detector. Phys. Rev. D 93, 082004 (2016).

  41. 41

    ET Science Team. Einstein gravitative wave telescope conceptual design study. ET-0106C-10 (2011).

  42. 42

    Mikhailov, E. E., Goda, K., Corbitt, T. & Mavalvala, N. Frequency-dependent squeeze-amplitude attenuation and squeeze-angle rotation by electromagnetically induced transparency for gravitational-wave interferometers. Phys. Rev. A 73, 053810 (2006).

  43. 43

    Ma, Y. et al. Narrowing the filter-cavity bandwidth in gravitational-wave detectors via optomechanical interaction. Phys. Rev. Lett. 113, 151102 (2014).

  44. 44

    Qin, J. et al. Classical demonstration of frequency-dependent noise ellipse rotation using optomechanically induced transparency. Phys. Rev. A 89, 041802(R) (2014).

  45. 45

    Zhang, J. Einstein–Podolsky–Rosen sideband entanglement in broadband squeezed light. Phys. Rev. A 67, 054302 (2003).

  46. 46

    Marino, A. M., Stroud, C. R., Wong, V., Bennink, R. S. & Boyd, R. W. Bichromatic local oscillator for detection of two-mode squeezed states of light. J. Opt. Soc. Am. B 24, 335–339 (2007).

  47. 47

    Hage, B., Samblowski, A. & Schnabel, R. Towards Einstein–Podolsky–Rosen quantum channel multiplexing. Phys. Rev. A 81, 062301 (2010).

  48. 48

    Barsotti, L. LIGO: The A+ Upgrade LIGO Doc. G1601199-v2 (2016).

  49. 49

    Barsotti, L. Squeezing for Advanced LIGO LIGO Doc. G1401092-v1 (2014).

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Research of Y.M., B.H.P. and Y.C. is supported by NSF grant PHY-1404569 and PHY-1506453, as well as the Institute for Quantum Information and Matter, a Physics Frontier Center. H.M. is supported by the Marie-Curie Fellowship and UK STFC Ernest Rutherford Fellowship. C.Z. would like to thank the support of Australian Research Council Discovery Project DP120104676 and DP120100898. R.S. is supported by DFG grant SCHN757/6 and by ERC grant 339897 (‘Mass Q’).

Author information

Y.M., H.M. and Y.C. formulated the idea; Y.M. performed the analysis of the idea and wrote the initial draft, which was later revised by Y.C.; B.H.P. checked Y.M.’s calculation; M.E., J.H., R.S. and C.Z. provided important experimental parameters for doing theoretical analysis and gave valuable comments on Y.M.’s calculations and initial/revised draft.

Correspondence to Yiqiu Ma.

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Ma, Y., Miao, H., Pang, B. et al. Proposal for gravitational-wave detection beyond the standard quantum limit through EPR entanglement. Nature Phys 13, 776–780 (2017) doi:10.1038/nphys4118

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