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

Abstract

Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and various materials properties [1][2][3].Without quantum enhancement, the precision limit in determining an unknown optical phase ϕ-i.e. the minimum uncertainty ∆ϕ-is the shot noise limit (SNL): ∆ϕ SN L = 1/ √ n, where n is the number of resources (e.g. photons) used. Entangled photons promise measurement sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is a path-entangled state of definite number of photons N . Despite theoretical proposals stretching back decades [3,4], no measurement using such photonic (definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all demonstrations have employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use an ultra-high efficiency source and high efficiency superconducting photon detectors to respectively make and measure a two-photon instance of the maximally-phase-sensitive NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit-that is, without artificially correcting for loss or any other source of imperfection. Our results enable quantum-enahanced 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, i.e measurement of the phase with an uncertainty below the 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 (HL), the ultimate bound on sensitivity [3,4,7]. For this reason, they are of great interest for maximising the information that can be collected per photon, which is useful for investigating sensitive samples [8]. NOON states are superpositions of N photons across two arms of an interferometer, each of which is a single optical mode:We use the term photonic to refer to states like this, because they possess definite photon number, and these photons are counted in detection. By contrast, we exclude from term "photonic" 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, e.g. refs [5,6], but work over narrow bandwidths and cannot directly achieve the theoretical maximal sensitivity per resource. Super-resolution, however, is not enough by itself to surpass the SNL [9,20]: a high interference fringe visibility, and high transmission and detection efficiency are also required-they must exceed the t...

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