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arXiv:0810.4026 · Advanced Science Letters

Light Statistics by Non-Calibrated Linear Photodetectors

Maria Bondani, Alessia Allevi, Alessandra Andreoni

Published Dec 1, 2009• 49 citations
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Abstract

We theoretically demonstrate that detectors endowed with internal gain and operated in regimes in which they do not necessarily behave as photon-counters, but still ensure linear input/output responses, can allow a self-consistent characterization of the statistics of the number of detected photons without need of knowing their gain. We present experiments performed with a photo-emissive hybrid detector on a number of classical fields endowed with non-trivial statistics and show that the method works for both microscopic and mesoscopic photon numbers. The obtained detected-photon probability distributions agree with those expected for the photon numbers, which are also reconstructed by an independent method.

DOI
10.1166/asl.2009.1052

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We theoretically demonstrate that detectors endowed with internal gain and operated in regimes in which they do not necessarily behave as photon-counters, but still ensure linear input/output responses, can allow a self-consistent characterization of the statistics of the number of detected photons without need of knowing their gain. We present experiments performed with a photo-emissive hybrid detector on a number of classical fields endowed with non-trivial statistics and show that the method works for both microscopic and mesoscopic photon numbers. The obtained detected-photon probability distributions agree with those expected for the photon numbers, which are also reconstructed by an independent method.
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We demonstrate that by using pairs of photodetectors endowed with internal gain we are able to quantify the photon-number correlation coefficient between the two components of a pulsed bipartite state in the "mesoscopic" intensity regime (less than 100 mean photons). We compare the performances of hybrid photoemissive detectors to those of multipixel silicon photon counters and demonstrate that the absence of significant noise allows the evaluation of the variance of the distribution of the differences in photon numbers, and hence of the shot-noise level, without any correction.
We investigate the possibility of using linear detectors that exhibit a response to dark just resolved from that corresponding to a single detected photon to reconstruct the photon-number statistics of pulsed fields containing sizeable numbers of photons per pulse. We demonstrate that by applying a self-consistent procedure to analyze the output pulses of such detectors, we can properly measure statistical distributions of the number of detected photons and photon number correlations. The lack of fulfillment of such minimal requirements impairs the possibility of reliable shot-by-shot determinations of photon numbers.
The output of a photodetector consists of a current pulse whose charge has the statistical distribution of the actual photon numbers convolved with a Bernoulli distribution. Photodetectors are characterized by a nonunit quantum efficiency, i.e., not all the photons lead to a charge, and by a finite resolution, i.e., a different number of detected photons leads to a discriminable values of the charge only up to a maximum value. We present a detailed comparison, based on Monte Carlo simulated experiments and real data, among the performances of detectors with different upper limits of counting capability. In our scheme the inversion of Bernoulli convolution is performed by maximum-likelihood methods assisted by measurements taken at different quantum efficiencies. We show that detectors that are only able to discriminate between zero, one and more than one detected photons are generally enough to provide a reliable reconstruction of the photon number distribution for single-peaked distributions, while detectors with higher resolution limits do not lead to further improvements. In addition, we demonstrate that, for semiclassical states, even on/off detectors are enough to provide a good reconstruction. Finally, we show that a reliable reconstruction of multipeaked distributions requires either higher quantum efficiency or higher resolution.
We present the reconstruction of the Wigner function of some classical pulsed optical states obtained by direct measurement of the detected-photon probability distributions of the state displaced by a coherent field. We use a photodetector endowed with internal gain, which is operated in the non-photon-resolving regime. The measurements are performed up to mesoscopic intensities (up to more than 30 photons per pulse). The method can be applied to characterize nonclassical continuous-variable states.