Unconditional violation of the shot-noise limit in photonic quantum metrology

Abstract

Interferometric phase measurement is widely used to precisely determine quantities such as length, speed and material properties1,2,3. Without quantum correlations, the best phase sensitivity \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}\) achievable using n photons is the shot-noise limit, \({\boldsymbol{\Delta }}{\boldsymbol{\phi }}=1\,/\sqrt{{n}}\). Quantum-enhanced metrology promises better sensitivity, but, despite theoretical proposals stretching back decades3,4, no measurement using photonic (that is, definite photon number) quantum states has truly surpassed the shot-noise limit. Instead, all such demonstrations, by discounting photon loss, detector inefficiency or other imperfections, have considered only a subset of the photons used. Here, we use an ultrahigh-efficiency photon source and detectors to perform unconditional entanglement-enhanced photonic interferometry. Sampling a birefringent phase shift, we demonstrate precision beyond the shot-noise limit without artificially correcting our results for loss and imperfections. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances.

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Fig. 1: Experimental set-up for the N = 2 NOON state optical interferometer.
Fig. 2: Experimentally measured output detection probability and the corresponding Fisher information.
Fig. 3: Experimentally measured phase estimate and phase uncertainty.

References

  1. 1.

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

    ADS  Article  Google Scholar 

  2. 2.

    Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009).

  3. 3.

    Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).

    ADS  Article  Google Scholar 

  4. 4.

    Demkowicz-Dobrzański, R., Jarzyna, M. & Kołdyński, J. Chapter four-quantum limits in optical interferometry. Prog. Opt. 60, 345–435 (2015).

    Article  Google Scholar 

  5. 5.

    Dowling, J. P. Quantum optical metrology—the lowdown on high-NOON states. Contemp. Phys. 49, 125–143 (2008).

    ADS  Article  Google Scholar 

  6. 6.

    Wolfgramm, F., Vitelli, C., Beduini, F. A., Godbout, N. & Mitchell, M. W. Entanglement-enhanced probing of a delicate material system. Nat. Photon. 7, 28–32 (2013).

    ADS  Article  Google Scholar 

  7. 7.

    Yonezawa, H. et al. Quantum-enhanced optical-phase tracking. Science 337, 1514–1517 (2012).

    ADS  Article  MATH  MathSciNet  Google Scholar 

  8. 8.

    Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).

    ADS  Article  Google Scholar 

  9. 9.

    Xiang, G., Hofmann, H. & Pryde, G. J. Optimal multi-photon phase sensing with a single interference fringe. Sci. Rep. 3, 2684 (2013).

    ADS  Article  Google Scholar 

  10. 10.

    Resch, K. J. et al. Time-reversal and super-resolving phase measurements. Phys. Rev. Lett. 98, 223601 (2007).

    ADS  Article  Google Scholar 

  11. 11.

    Ou, Z. Y., Zou, X. Y., Wang, L. J. & Mandel, L. Experiment on nonclassical fourth-order interference. Phys. Rev. A 42, 2957–2965 (1990).

    ADS  Article  Google Scholar 

  12. 12.

    Rarity, J. G. et al. Two-photon interference in a Mach–Zehnder interferometer. Phys. Rev. Lett. 65, 1348–1351 (1990).

    ADS  Article  Google Scholar 

  13. 13.

    Fonseca, E. J. S., Monken, C. H. & Pádua, S. Measurement of the de Broglie wavelength of a multiphoton wave packet. Phys. Rev. Lett. 82, 2868–2871 (1999).

    ADS  Article  Google Scholar 

  14. 14.

    Eisenberg, H. S., Hodelin, J. F., Khoury, G. & Bouwmeester, D. Multiphoton path entanglement by nonlocal bunching. Phys. Rev. Lett. 94, 090502 (2005).

    ADS  Article  Google Scholar 

  15. 15.

    Mitchell, M. W., Lundeen, J. S. & Steinberg, A. M. Super-resolving phase measurements with a multiphoton entangled state. Nature 429, 161–164 (2004).

    ADS  Article  Google Scholar 

  16. 16.

    Walther, P. et al. De Broglie wavelength of a non-local four-photon state. Nature 429, 158–161 (2004).

    ADS  Article  Google Scholar 

  17. 17.

    Nagata, T., Okamoto, R., O’Brien, J. L., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007).

    ADS  Article  Google Scholar 

  18. 18.

    Gao, W.-B. et al. Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state. Nat. Phys. 6, 331–335 (2010).

    Article  Google Scholar 

  19. 19.

    Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).

    ADS  Article  Google Scholar 

  20. 20.

    Okamoto, R. et al. Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers. New J. Phys. 10, 073033 (2008).

    ADS  Article  Google Scholar 

  21. 21.

    Datta, A. et al. Quantum metrology with imperfect states and detectors. Phys. Rev. A 83, 063836 (2011).

    ADS  Article  Google Scholar 

  22. 22.

    Weston, M. M. et al. Efficient and pure femtosecond-pulse-length source of polarization-entangled photons. Opt. Express 24, 10869–10879 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).

    ADS  Article  Google Scholar 

  24. 24.

    Klyshko, D. N. Use of two-photon light for absolute calibration of photoelectric detectors. Sov. J. Quantum Electron. 10, 1112–1116 (1980).

    ADS  Article  Google Scholar 

  25. 25.

    Lita, A. E., Miller, A. J. & Nam, S. W. Counting near-infrared single-photons with 95% efficiency. Opt. Express 16, 3032–3040 (2008).

    ADS  Article  Google Scholar 

  26. 26.

    Matthews, J. C. F. et al. Towards practical quantum metrology with photon counting. NPJ Quantum Inf. 2, 16023 (2016).

    ADS  Article  Google Scholar 

  27. 27.

    Harder, G. et al. Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics. Phys. Rev. Lett. 116, 143601 (2016).

    ADS  Article  Google Scholar 

  28. 28.

    Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M. & Pryde, G. J. Entanglement-free Heisenberg-limited phase estimation. Nature 450, 393–396 (2007).

    ADS  Article  Google Scholar 

  29. 29.

    Davison, A. C. & Hinkley, D. V. Bootstrap Methods and Their Application, Vol. 1 (Cambridge Univ. Press, 1997).

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Acknowledgements

This work was supported by the Australian Research Council (grant DP140100648). The authors thank J. Ho for help with SNSPDs.

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G.J.P. conceived the idea and supervised the project. S.S. and M.M.W. constructed and carried out the experiment with help from H.M.C. L.K.S., V.B.V. and S.W.N. developed the high-efficiency SNSPDs. All authors discussed the results and contributed to writing the manuscript.

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Correspondence to Geoff J. Pryde.

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The authors declare no competing financial interests.

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Slussarenko, S., Weston, M.M., Chrzanowski, H.M. et al. Unconditional violation of the shot-noise limit in photonic quantum metrology. Nature Photon 11, 700–703 (2017). https://doi.org/10.1038/s41566-017-0011-5

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