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Physical Review A

Mode reconstruction of a light field by multiphoton statistics

Elizabeth A. Goldschmidt, Fabrizio Piacentini, Ivano Ruo Berchera, Sergey V. Polyakov, Silke Peters, S. Kück, G. Brida, Ivo Pietro Degiovanni, Alan L. Migdall, Marco Genovese

Published Jul 15, 2013• 52 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.88.013822

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•Jan 1, 2013•1 citation
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.
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.
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).
Non-classical light is both easily encoded with quantum information and robust against decoherence, making it a key resource that enables many quantum information applications including quantum computing, quantum communication, and quantum metrology. We present a wide range of experimental and theoretical research toward the generation, detection, characterization, and storage of non-classical states of light with an eye toward quantum information applications. To provide a basis for the rest of the work, we begin by discussing theoretically the role of photon number statistics in optical quantum information and the use of second-order optical coherence to characterize non-classical light. Building on that, we present an original tool for the difficult problem of reconstructing the underlying mode distribution of multi-mode optical fields using simple measurements of higher-order optical coherence. We then move on to the problem of generating and storing single photons. We do this in a solid-state medium, a rare-earth ion-doped crystal, with a long-lived spin transition ideal for storing quantum information. We experimentally demonstrate the feasibility of this concept by showing correlations between the optical fields that herald storage and retrieval of collective excitations. This scheme can be used for the two important and distinct applications of generating single photons on-demand and storing quantum information and entanglement. The detection of non-classical light is a task as important as its generation. To this end, we study detectors with near unity detection efficiency and photon number resolution for use in quantum-enabled metrology. We use such a detector to experimentally demonstrate compression of spatial fringes and investigate the possibility of improving measurement resolution with classical and non-classical light. Finally, we report a set of experiments using photon number statistics to characterize classical and non-classical light. We measure suppression of unwanted multi-photon emission in a heralded single photon source based on four-wave mixing in microstructure optical fiber. And we, for the first time, experimentally demonstrate reconstruction of multi-mode classical and non-classical light from measured photon number statistics.