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arXiv:1802.00489 · Physical Review A

Optimizing the signal-to-noise ratio of biphoton distribution measurements

Matthew C. Reichert, Hugo Defienne, Jason W. Fleischer

Published Jul 26, 2018• 20 citations
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Abstract

Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in high-dimensional joint Hilbert spaces.

DOI
10.1103/physreva.98.013841

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Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in high-dimensional joint Hilbert spaces.
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Intensity correlation measurements form the basis of many experiments based on spontaneous parametric down-conversion. In the most common situation, two single-photon avalanche diodes and coincidence electronics are used in the detection of the photon pairs, and the coincidence count distributions are measured by making use of some scanning procedure. Here we analyze the measurement of intensity correlations using multielement detector arrays. By considering the detector parameters such as the detection and noise probabilities, we found that the mean number of detected photons that maximizes the visibility of the two-photon correlations is approximately equal to the mean number of noise events in the detector array. We provide expressions predicting the strength of the measured intensity correlations as a function of the detector parameters and on the mean number of detected photons. We experimentally test our predictions by measuring far-field intensity correlations of spontaneous parametric down-conversion with an electron multiplying charge-coupled device camera, finding excellent agreement with the theoretical analysis.
Abstract Entangled states of light are essential for quantum technologies and fundamental tests of physics. Current systems rely on entanglement in 2D degrees of freedom, e.g., polarization states. Increasing the dimensionality provides exponential speed-up of quantum computation, enhances the channel capacity and security of quantum communication protocols, and enables quantum imaging; unfortunately, characterizing high-dimensional entanglement of even bipartite quantum states remains prohibitively time-consuming. Here, we develop and experimentally demonstrate a new theory of camera detection that leverages the massive parallelization inherent in an array of pixels. We show that a megapixel array, for example, can measure a joint Hilbert space of 1012 dimensions, with a speed-up of nearly four orders-of-magnitude over traditional methods. The technique uses standard geometry with existing technology, thus removing barriers of entry to quantum imaging experiments, generalizes readily to arbitrary numbers of entangled photons, and opens previously inaccessible regimes of high-dimensional quantum optics.
To evidence multimode spatial entanglement of spontaneous down-conversion, detector arrays allow a full-field measurement, without any a priori selection of the paired photons. We show by comparing results of the recent literature that electron-multiplying CCD cameras allow, in the present state of technology, the detection of quantum correlations with the best signal-to-noise ratio (SNR), while intensified CCD cameras allow at best the identification of pairs. The SNR appears to be proportional to the square root of the number of coherence cells in each image, or Schmidt number. Then corrected estimates are derived for extended coherence cells and not-very-low and non-space-stationary photon fluxes. Finally, experimental measurements of the SNR confirm our model.