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Photonics for Quantum (PfQ)

Measurement of photon number statistics using photon-number resolving detectors

Nicola N Low, Sai Sreesh Venuturumilli, Michal Bajcsy

Published Jul 18, 2025• 0 citations
Publisher

Abstract

We investigate the use of a photon-number resolving (PNR) detector as an alternative method for measuring the second-order correlation function g2(0). Our implementation employs four spatially multiplexed single-photon detectors to reconstruct the photon number distribution P(n) from click statistics. We estimate g2(0) for both coherent and quantum dot excition emission, and compare the results to those obtained from a conventional Hanbury Brown-Twiss (HBT) setup. In the single-mode regime, we observe close agreement between both approaches. We additionally compare the acquisition times required for each method and find that PNR-based measurements enable faster estimation of g2(0), offering potential advantages for scalable characterisation of quantum light sources.

DOI
10.1117/12.3063223

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We investigate the use of a photon-number resolving (PNR) detector as an alternative method for measuring the second-order correlation function g2(0). Our implementation employs four spatially multiplexed single-photon detectors to reconstruct the photon number distribution P(n) from click statistics. We estimate g2(0) for both coherent and quantum dot excition emission, and compare the results to those obtained from a conventional Hanbury Brown-Twiss (HBT) setup. In the single-mode regime, we observe close agreement between both approaches. We additionally compare the acquisition times required for each method and find that PNR-based measurements enable faster estimation of g2(0), offering potential advantages for scalable characterisation of quantum light sources.
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Abstract We investigate the operation of a photon-number-resolving (PNR) detector consisting of a cascade of waveguide-coupled Λ-type emitters, where each waveguide-coupled emitter extracts a single photon from the input light and sends it to a single-photon detector. Using Green’s function and input-output formalisms, we derive the scattering matrices and photon–photon correlators for individual scatterers. By cascading these results, we obtain a closed-form expression for the detector’s precision in the linear regime and predict how correlations generated by nonlinear photon–photon interactions influence this precision. To evaluate the performance of this PNR detector in the nonlinear regime, we apply the quantum trajectory method to the cascaded setup, calculating the achievable precision and analyzing its dependence on key system parameters, such as the number of emitters and their coupling strength to the waveguide. We compare the performance of the proposed PNR detector with that of a conventional PNR scheme based on spatial demultiplexing via beamsplitters. Our results indicate that the proposed scheme can outperform conventional detectors under realistic conditions, making it a promising candidate for next-generation PNR detection.
We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon ``click detectors'' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.
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Quantum state tomography and the reconstruction of the photon number distribution are techniques to extract the properties of a light field from measurements of its mean and fluctuations. These techniques are particularly useful when dealing with macroscopic or mesoscopic systems, where a description limited to the second order autocorrelation soon becomes inadequate. In particular, the emission of nonclassical light is expected from mesoscopic quantum dot systems strongly coupled to a cavity or in systems with large optical nonlinearities. We analyze the emission of a quantum dot-semiconductor optical amplifier system by quantifying the modifications of a femtosecond laser pulse propagating through the device. Using a balanced detection scheme in a self-heterodyning setup, we achieve precise measurements of the quadrature components and their fluctuations at the quantum noise limit1. We resolve the photon number distribution and the thermal-to-coherent evolution in the photon statistics of the emission. The interferometric detection achieves a high sensitivity in the few photon limit. From our data, we can also reconstruct the second order autocorrelation function with higher precision and time resolution compared with classical Hanbury Brown-Twiss experiments.