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arXiv:1311.2721

Experimental super-resolved phase measurements with shot-noise sensitivity

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

Published Nov 12, 2013• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.1311.2721

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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.
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.
Sub-shot-noise performance in transmission measurements can be achieved in optical quantum metrology owing to significantly lower uncertainty in light intensity of quantum beams compared to their classical counterparts. In this work, we simulate the outcome of an experiment that uses a multiplexed single-photon source, considering several types of experimental losses, where we show that the sub-Poissonian statistics of the output is key for achieving sub-shot-noise performance. We compare the numerical results with the shot-noise limit attained using coherent sources and the quantum limit, obtained with an ideal photon-number Fock state. We also investigate conditions in which threshold detectors can be used, as well as the effect of input light fluctuations. Our results show that sub-shot-noise performance can be achieved with improvement factors ranging from 1.5 to 2, even without using number-resolving detectors.
Quantum metrology enables us to estimate optical phase shifts beyond the shot noise limit. Applications include quantum-enhanced biological measurement [1], microscopy [2] and gravitational wave detection[3]. For two-mode N-photon system, the NOON state can achieve the highest possible phase sensitivity where multi-photon coherence between two states significantly contributes to improving the phase sensitivity. Another alternative approach to improve the phase sensitivity by use of squeezed states. Squeezing is usually characterized by reducing the quantum noise of desired observable at the expense of increasing the quantum noise for its non-commute partner. Because shot-noise limits the phase sensitivity of any classical states, the reduced quantum noise can be used for improving the phase sensitivity. Here we experimentally study the phase sensitivity of an optical spin-squeezed state by using linear optics. We generated the optical spin-squeezed state using one photon subtraction from a down converted photon source. To implement the sub-shot noise measurement, we used multiplexed photon number resolving detectors so that we can reconstruct the photon number statistics of the state. In the talk, we will analyse the generated state in terms of both squeezing and phase sensitivity by using Fisher information.