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arXiv:2212.13873 · Advanced Quantum Technologies

Photon Statistics Modal Reconstruction by Detected and Undetected Light

Laura T. Knoll, Giulia Petrini, Fabrizio Piacentini, P. Traina, Sergey V. Polyakov, Ekaterina V. Moreva, Ivo Pietro Degiovanni, Marco Genovese

Published Jun 17, 2023• 4 citations
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Abstract

Abstract A novel technique is introduced for the reconstruction of multimode optical fields, based on simultaneously exploiting both the generalized Glauber's K th ‐order correlation function and a recently proposed anti‐correlation function (dubbed ) which is resilient to Poissonian noise. It is experimentally demonstrated that this method yields mode reconstructions with higher fidelity with respect to those obtained with reconstruction methods based only on 's, even requiring less “a priori” information. The reliability and versatility of this technique make it suitable for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially when one needs to characterize ensembles of single‐photon emitters in the presence of background noise (due, for example, to residual excitation laser, stray light or unwanted fluorescence).

DOI
10.1002/qute.202300062

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Abstract A novel technique is introduced for the reconstruction of multimode optical fields, based on simultaneously exploiting both the generalized Glauber's K th ‐order correlation function and a recently proposed anti‐correlation function (dubbed ) which is resilient to Poissonian noise. It is experimentally demonstrated that this method yields mode reconstructions with higher fidelity with respect to those obtained with reconstruction methods based only on 's, even requiring less “a priori” information. The reliability and versatility of this technique make it suitable for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially when one needs to characterize ensembles of single‐photon emitters in the presence of background noise (due, for example, to residual excitation laser, stray light or unwanted fluorescence).
The rapid growth of single-photon metrology [1] and (optical) quantum technologies [2-5] in the last years has made the development of simple, versatile and robust methods for characterizing complex optical states a task of the utmost relevance. Here we introduce and experimentally test a novel technique [6] for the reconstruction of multimode optical fields, based on the simultaneously exploiting both the generalized Glauber’s K^th-order correlation function g^((K)) and a recently-proposed anti-correlation function dubbed θ^((K)) [7], proven to be resilient to Poissonian noise. Our experimental results show how this method, although requiring less “a priori” information than other mode reconstruction techniques based only on g^((K))’s [8], steadily outperforms them. This is particularly advantageous for measurements in Hanbury-Brown & Twiss interferometric arrangements hosting non-photon-number-resolving detectors, since the insensitivity of θ^((K))’s to Poissonian fields forbids a reconstruction method relying only on these functions from delivering reliable results. Given its versatility and robustness, this new mode reconstruction technique is suited for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially for characterizing ensembles of single-photon emitters in the presence of background noise (caused by, e.g., residual excitation laser light, stray light or unwanted fluorescence). References A. Migdall, S. V. Polyakov, J. Fan, J. C. Bienfang, in Single-Photon Generation and Detection: Physics and Applications, Academic Press, Cambridge, MA, USA 2013. S. Pirandola et al., Adv. Opt. Photon. 12, 1012 (2020). M. Genovese, AVS Quantum Sci. 3, 044702 (2021). J. Wang, F. Sciarrino, A. Laing, M. G. Thompson, Nat. Photon. 14, 273 (2020). G. Petrini et al., Adv. Quantum Technol. 3, 2000066 (2020). L. T. Knoll et al., Adv. Quantum Technol. 6, 2300062 (2023). L. Lachman, L. Slodička, R. Filip, Sci. Rep. 6, 19760 (2016). E. Goldschmidt et al., Phys. Rev. A 88, 013822 (2013).
We report on a robust method for reconstructing multi-mode optical fields. In particular, our method correctly identifies the number and types of modes as well as each mode’s energy, which we demonstrated experimentally. Our method uses multidetector trees and both high-order autocorrelation functions of detected photons (the Glauber function) and high-order autocorrelation functions of no-photon detection. Here we show successful reconstruction for classical and nonclassical multimode fields that contain up to 4 modes whose types are not disclosed to the reconstruction algorithm. This method is significantly more successful than the previously reported one, based on high-order Glauber functions only.
We present a simple method to reconstruct the mode distribution of multimode classical and nonclassical optical fields using a single measurement of higher-order photon number correlation functions. Knowing the underlying number and structure of occupied modes of a light field plays a crucial role in minimizing loss and decoherence of quantum information. Typically, full characterization of the mode structure involves a series of several separate measurements in spatial, temporal, frequency, and polarization domains. We experimentally demonstrate reconstruction of up to three modes with excellent agreement and study the robustness of our method in experimentally realizable regimes.
We present a method to reconstruct the complete statistical mode structure and optical losses of multimode conjugated optical fields using an experimentally measured joint photon-number probability distribution. We demonstrate that this method evaluates classical and nonclassical properties using a single measurement technique and is well suited for quantum mesoscopic state characterization. We obtain a nearly perfect reconstruction of a field comprised of up to ten modes based on a minimal set of assumptions. To show the utility of this method, we use it to reconstruct the mode structure of an unknown bright parametric down-conversion source.
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our approach accounts for losses and photon indistinguishability, making it robust to experimental imperfections. By minimizing the requirements for the input states, the method simplifies the experimental implementation. We demonstrate the effectiveness of our technique through theoretical modeling and experimental validation in a 4-mode programmable integrated optical interferometer. The results show high fidelity in matrix reconstruction and successful application in boson sampling experiments. In addition, we provide a comprehensive formalism for correlation functions and discuss the robustness of the method to measurement errors. This work offers a practical and efficient solution for characterizing linear-optical networks, paving the way for scaling up photonic quantum technologies.