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Conference on Lasers and Electro-Optics

Phase measurements exhibiting super sensitivity and super resolution features

Clemens Schäfermeier, Miroslav Ježek, Tobias Gehring, Ulrik L. Andersen

Published Jan 1, 2016• 0 citations
Publisher

Abstract

By using an optical squeezed state and a post-processed homodyne detection scheme we show that phase measurements can overcome Rayleigh’s resolution criterion and beat the quantum shot noise limit simultaneously.
DOI
10.1364/cleo_qels.2016.ff1c.4

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Phase super-sensitivity is obtained when the sensitivity in a phase measurement goes beyond the quantum shot noise limit, whereas super-resolution is obtained when the interference fringes in an interferometer are narrower than half the input wavelength. Here we show experimentally that these two features can be simultaneously achieved using a relatively simple setup based on Gaussian states and homodyne measurement. Using 430 photons shared between a coherent- and a squeezed vacuum state, we demonstrate a 22-fold improvement in the phase resolution while we observe a 1.7-fold improvement in the sensitivity. In contrast to previous demonstrations of super-resolution and super-sensitivity, this approach is fully deterministic.
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.
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.
Measurement, whilst being physically fundamental, is also fundamentally physical. Classical interferometric measurements suffer from physical limitations where the shot noise limit forms an upper bound of √n on a phase shift Δφ that can be resolved, with n being the average number of photons detected, making their applicability in modern nanoscale experiments quite restricted. Exotic quantum states such as maximally entangled NOON states (|N0〉A;B+|0N〉A;B)/√2, where N is the number of entangled photons are of particular importance as they have repeatedly been shown to exhibit phase super-resolution. Interesting post selection schemes and time-reversed detection schemes have been investigated for phase estimation using NOON states. These methods are inherently non-deterministic at the preparation or measurement stage and thus do not optimise resources, for instance the number of photons passing through the sample greatly exceeds those used in the measurement.