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Optical and Quantum Sensing and Precision Metrology II

Separation estimation at the quantum limit with arbitrary Gaussian sources

Giacomo Sorelli, Ilya Karuseichyk, Clémentine Rouvière, Manuel Gessner, Mattia Walschaers, Nicolas Treps

Published Mar 9, 2022• 0 citations
Publisher

Abstract

Recent works showed that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, so far these results have been either limited to low-intensity, or thermal sources. In this talk, we will present an analytical expression for the Quantum Fisher Information for the separation between two sources in an arbitrary Gaussian states. This expression allows us to determine the ultimate resolution limit for a series of practically relevant states, e.g. correlated or displaced thermal states (corresponding to partially coherent sources) and squeezed states (exhibiting quantum correlations). Moreover, we will show how a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements can be used to saturate these limits. Finally, we will discuss the applicability of the proposed methods in present experimental setups.

DOI
10.1117/12.2618307

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Recent works showed that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, so far these results have been either limited to low-intensity, or thermal sources. In this talk, we will present an analytical expression for the Quantum Fisher Information for the separation between two sources in an arbitrary Gaussian states. This expression allows us to determine the ultimate resolution limit for a series of practically relevant states, e.g. correlated or displaced thermal states (corresponding to partially coherent sources) and squeezed states (exhibiting quantum correlations). Moreover, we will show how a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements can be used to saturate these limits. Finally, we will discuss the applicability of the proposed methods in present experimental setups.
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works, analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. However, most previous works have either consider low-intensity, or thermal sources. To broaden the applicability of this approach, it is important to extend these results to more general light sources. To this goal, we will present an analytical expression for the Quantum Fisher Information, determining the ultimate resolution limit, for the separation between two sources in an arbitrary Gaussian state. Applying this result to different quantum states, we can shine some light on some relevant questions. We can for example explore the role of partial coherence considering displaced and correlated thermal states, or investigate the importance of quantum correlations by considering squeezed light. In addition to the ultimate quantum limit, we will discuss a simple estimation technique, requiring access only to the mean value of a linear combination of demultiplexed intensity measurements, which is often sufficient to saturate these limits, and can easily be adapted to incorporate the most common noise sources. Finally, we will present our experimental setup that allows for the generation of the images of two sources with different photon statistics, as well as for spatial mode demultiplexing and we will discuss the first practical implementations if the above mentioned estimation techniques.
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. We implement this technique and provide an optimal estimator based on a linear combination of demultiplexed intensity measurements [1–3]. Our experimental setup allows for the generation of the images of two sources, with tunable mutual coherence, as well as for spatial mode demultiplexing to estimate their separation [4].
Resolving light sources below the diffraction limit is a fundamental task both for astronomy and microscopy. Several recent works analysed this problem through the lens of quantum parameter estimation theory and proved that the separation between two point sources can be estimated at the quantum limit using intensity measurements after spatial-mode demultiplexing. We implement this technique and provide an optimal estimator based on a linear combination of demultiplexed intensity measurements [1]–[3]. Our experimental setup (see Fig. 1 (left)) allows for the generation of the images of two sources, with tunable mutual coherence, as well as for spatial mode demultiplexing to estimate their separation [4].
Sensitivity limits are usually determined using the Cram\'er-Rao bound. Recently, this approach has been used to obtain the ultimate resolution limit for the estimation of the separation between two incoherent point sources. However, methods that saturate these resolution limits usually require the full measurement statistics, which can be challenging to access. In this work we introduce a simple superresolution protocol to estimate the separation between two thermal sources which relies only on the average value of a single accessible observable. We show how optimal observables for this technique may be constructed for arbitrary thermal sources and we study their sensitivities when one has access to spatially resolved intensity measurements (direct imaging) and photon counting after spatial-mode demultiplexing. For demultiplexing, our method is optimal, i.e., it saturates the quantum Cram\'er-Rao bound. We also investigate the impact of noise on the optimal observables, their measurement sensitivity, and the scaling with the number of detected photons of the smallest resolvable separation. For low signals in the image plane, we demonstrate that our method saturates the Cram\'er-Rao bound even in the presence of noise.
We analyze the problem of resolving two point-sources in the case of mutually coherent sources with arbitrary quantum statistics, mutual phase, relative and absolute intensity. We use a sensitivity measure based on the method of moments and compare direct imaging with spatial mode demultiplexing, analytically proving the advantage of the latter. We show that the sensitivity of spatial mode demultiplexing saturates the quantum Fisher information, for all known cases, even for non-Gaussian states of the sources.