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arXiv:1412.8630 · Optics Letters

Positive operator-valued measure reconstruction of a beam-splitter tree-based photon-number-resolving detector

Fabrizio Piacentini, M. P. Levi, Alessio Avella, Marco López, S. Kück, Sergey V. Polyakov, Ivo Pietro Degiovanni, G. Brida, Marco Genovese

Published Mar 29, 2015• 19 citations
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Abstract

Here we present a reconstruction of the positive operator-value measurement of a photon-number-resolving detector comprised of three 50∶50 beam-splitters in a tree configuration, terminated with four single-photon avalanche detectors. The four detectors' outputs are processed by an electronic board that discriminates detected photon number states from 0 to 4 and implements a "smart counting" routine to compensate for dead time issues at high count rates.

DOI
10.1364/ol.40.001548

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Here we present a reconstruction of the positive operator-value measurement of a photon-number-resolving detector comprised of three 50∶50 beam-splitters in a tree configuration, terminated with four single-photon avalanche detectors. The four detectors' outputs are processed by an electronic board that discriminates detected photon number states from 0 to 4 and implements a "smart counting" routine to compensate for dead time issues at high count rates.
Single-photon avalanche detectors (SPADs) are used ubiquitously in optical and quantum science, but they are not photon-number-resolving detectors. Despite this, in this work we present preliminary results that show that a single SPAD can still be used to perform number-state reconstruction. Through detector characterization and use of maximum-likelihood analysis, we perform number-state reconstruction with a single SPAD and obtain good agreement with independently measured distributions for both Poissonian and anti-bunched light. Our method works well for photon rates up to roughly one input photon per dead time as well as pulse lengths and correlation times of at least a few dead times, fitting many of today’s quantum optics experiments.
Single-photon avalanche detectors (SPADs) are crucial sensors of light for many fields and applications. However, they are not able to resolve photon number, so typically more complex and more expensive experimental setups or devices must be used to measure the number of photons in a pulse. Here, we present a methodology for performing photon number-state reconstruction with only one SPAD. The methodology, which is cost-effective and easy to implement, uses maximum-likelihood techniques with a detector model whose parameters are measurable. We achieve excellent agreement between known input pulses and their reconstructions for coherent states with up to ≈10 photons and peak input photon rates up to several Mcounts/s. When detector imperfections are small, we maintain good agreement for coherent pulses with peak input photon rates of over 40 Mcounts/s, greater than one photon per detector dead time. For anti-bunched light, the reconstructed and independently measured pulse-averaged values of g (2) (0) are also consistent with one another. Our algorithm is applicable to light pulses whose pulse width and correlation time scales are both at least a few detector dead times. These results, achieved with single commercially available SPADs, provide an inexpensive number-state reconstruction method and expand the capabilities of single-photon detectors.
We investigate the feasibility and performance of photon-number-resolved photodetection employing single-photon avalanche photodiodes (SPADs) with low dark counts. While the main idea, to split n photons into m detection modes with a vanishing probability of more than one photon per mode, is not new, we investigate here a important variant of this situation where SPADs are side-coupled to the same waveguide rather than terminally coupled to a propagation tree. This prevents the nonideal SPAD quantum efficiency from contributing to photon loss. We propose a concrete SPAD segmented waveguide detector based on a vertical directional coupler design, and characterize its performance by evaluating the purities of Positive-Operator-Valued Measures (POVMs) in terms of number of SPADs, photon loss, dark counts, and electrical cross-talk.
Photon counting is a cornerstone of quantum optics. Here, we demonstrate precisely counting from 0 to over 9000 photons, beating the Poisson noise limit by at least 4.1 dB4.1~\mathrm{dB}4.1 dB across this range. We achieve sub-single-photon precision up to 276 photons per pulse. To do so, we multiplex eight intrinsically photon-number-resolving superconducting nanowire single-photon detectors across 128 temporal modes. We use a model-informed characterization of each of the 1024 detection bins, for optimal precision. We perform quantum detector tomography to reconstruct the positive operator valued measures (POVMs) of the complete device, which consists of 1.38⋅1081.38\cdot10^81.38⋅108 matrix elements. At the repetition rate of our experiment of 80 kHz80~\mathrm{kHz}80 kHz, we can precisely count photons corresponding to an optical power of approximately 71 pW71~\mathrm{pW}71 pW, bridging the gap from single-photon measurements to high-sensitivity optical power meters. A photon-number-resolving detector of this size, and the tools used to analyze it, will become increasingly important to characterize large quantum states, as well as tasks in precision metrology and optical power standards.
We report the development of a photon-number-resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers and operates on the well-known principle by which a single-mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.