Unconditional violation of shot-noise limit with two-photon NOON states

Interferometric phase measurement techniques are a vital toolset used to precisely determine quantities including distance, acceleration and materials properties. Without quantum enhancement, the minimum uncertainty in optical... [ view full abstract ]

Interferometric phase measurement techniques are a vital toolset used to precisely determine quantities including distance, acceleration and materials properties. Without quantum enhancement, the minimum uncertainty in optical phase sensing with N resources (e.g. photons) is the shot-noise limit (SNL): Δφ=N^-1/2. It has been known for several decades that probing with quantum states can achieve measurement with an uncertainty below the SNL [1].

Despite theoretical proposals stretching back decades [2], no measurement using photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit. Previous demonstrations employed postselection to discount photon loss and imperfections of the setup. Here, we use the state of art single photon generation [5] and detection [6] technology to respectively make and measure a maximally phase-sensitive two-photon NOON state [3] and use it to perform unconditional phase sensing beyond the shot noise limit. Unlike previous experiments, our apparatus (Fig. 1) does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer [4]. We observed an interference fringe visibility of (98.9 ± 0.02)% and interferometer arm efficiencies around 80% (including detectors efficiency), which was sufficient for beating the SNL with two-photon NOON states [7,8].

Our results (Fig. 2) show a clear violation, for a range of phases, of the SNL bound, F=2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms. In a direct phase sensing measurement, we observed uncertainties more than 10 standard deviations below the SNL [4]. 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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[2] R. Demkowicz-Dobrzanski et al., Prog. Opt. 60, 345 (2015).

[3] J. P. Dowling, Contemp. Phys. 49, 125 (2008).

[4] S.Slussarenko et al., Nat. Photon. 11, 700 (2017).

[5] M. M. Weston et al., Opt. Express 24, 10869 (2016).

[6] F. Marsili et al., Nat. Photon. 7, 210 (2013).

[7] K. J. Resch et al., Phys. Rev. Lett. 98, 223601 (2007).

[8] A. Datta et al., Phys. Rev. A 83, 063836 (2011).