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Experimental super resolved phase measurements at the shot noise limit

Lior Cohen, Liat Dovrat, D. Istrati, H. S. Eisenberg

Published Jan 1, 2013• 0 citations
Publisher

Abstract

Using photon-number resolving detectors, we directly measure the parity of coherent states in a Mach-Zehnder interferometer. Phases are super resolved by a factor of 150 and shot noise limited measurements are demonstrated with 200 photons.
DOI
10.1364/cleo_qels.2013.qth1e.7

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Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the shot noise limit and reach the Heisenberg limit. Nevertheless, many of those experiments fail to break even the classical shot-noise limit. Following a recent proposal, we present here the results of optical phase measurements with a photon-number resolving detector using coherent states of up to 4200 photons on average. An additional scheme that can be implemented using standard single-photon detectors is also presented, and the results of the two schemes are compared. These measurements present deterministic single-shot sub-wavelength super-resolution up to 288 better than the optical wavelength. The results follow the classically limited sensitivity, up to 86 times better than the wavelength.
Previous studies [J. Opt. Soc. Am. B27, A170 (2010)JOBPDE0740-322410.1364/JOSAB.27.00A170; J. Appl. Phys.114, 193102 (2013)JAPIAU0021-897910.1063/1.4829016] have asserted that a coherent-state Mach–Zehnder interferometer (MZI) with parity-based phase estimation can achieve superresolution at the shot-noise limit (SNL). We show that these studies have ignored the need for repeated measurements in order to achieve root-mean-square accuracy at the SNL. Consequently, their superresolution claims need major revision. For comparison, we present the performance of a coherent-state MZI that uses dual-homodyne detection and show that it can achieve SNL scaling in a single measurement, albeit without superresolution.
There has been much recent interest in quantum optical interferometry for applications to metrology, subwavelength imaging, and remote sensing such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the Beer law for classical optical attenuation, and which provides sensitivity at the shot-noise limit. We show that coherent light coupled with photon-number-resolving detectors can provide a super-resolution much below the Rayleigh diffraction limit, with sensitivity no worse than shot noise in terms of the detected photon power.