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

Nature Photonics volume 11, pages 700–703 (2017)Cite this article

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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.

It has been known for several decades that probing with various optical quantum states can achieve phase super-sensitivity, that is, measurement of the phase with an uncertainty below the shot-noise limit (SNL)3,4. It has been shown theoretically that multi-photon entangled states, such as NOON states, may achieve super-sensitivity and can, in principle, saturate the Heisenberg limit, the ultimate bound on sensitivity3,4,5. For this reason, they are of great interest for maximizing the information that can be collected per photon, which is useful for investigating sensitive samples6. NOON states are superpositions of N photons across two arms of an interferometer, each of which is a single optical mode: \(\left|{\Psi }_{NOON}\right\rangle =1/\sqrt{2}\left(\left|N\right\rangle \left|0\right\rangle +\left|0\right\rangle \left|N\right\rangle \right)\). We use the term ‘photonic’ to refer to states like this because they possess a definite photon number, and these photons are counted in detection. By contrast, we exclude from the term ‘photonic’ those schemes using states of indefinite photon number and continuous-wave-like measurement, such as squeezed states and homodyne detection. Such techniques have genuinely beaten the SNL (see, for example, refs. 7,8), but they work over narrow bandwidths and cannot directly achieve the theoretical maximal sensitivity per resource. The key feature of NOON and similar photonic states9 is that they produce interference fringes that oscillate faster than any classical interference pattern, a feature called phase super-resolution10. Super-resolution interference experiments have been reported using two-11,12,13,14, three-15, four-16,17, six-9,10 and eight-18,19 photon states.

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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.

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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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Authors and Affiliations

  1. Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland, 4111, Australia

    Sergei Slussarenko, Morgan M. Weston, Helen M. Chrzanowski & Geoff J. Pryde

  2. Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

    Helen M. Chrzanowski

  3. National Institute of Standards and Technology, 325 Broadway, Boulder, CO, 80305, USA

    Lynden K. Shalm, Varun B. Verma & Sae Woo Nam

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  1. Sergei Slussarenko
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Contributions

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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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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