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International Journal of Quantum Information

CHOOSING A PHOTOEMISSIVE DETECTOR SUITABLE FOR PHOTON-NUMBER STATISTICS OF PULSED FIELDS

Maria Bondani, Alessia Allevi, Alessandra Andreoni

Published Jan 1, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749911007113

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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.
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 characterization of a multi-pixel detector (SiPM, Hamamatsu) in the presence of dark-count and cross-talk effects. Our description yields a self-consistent calibration of the device, based on the light under investigation, which is used to evaluate shot-by-shot detected-photon numbers including dark-counts and cross-talk. The analysis allows us to reliably reconstruct the detected-photons statistics of different light states by taking into account the modifications introduced by detector features. Finally we quantify photon-number correlations in bipartite states and use the data to produce conditional states: only if dark-count and cross-talk effects can be neglected, the experimental results match theory.
We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.
Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and helps with various relevant applications. Nevertheless, no detector that can reliably discriminate the number of incident photons is available. On the other hand, the alternative of reconstructing the density matrix by quantum tomography leads to various technical difficulties that are particularly severe in the pulsed regime (where mode matching between a signal and local oscillator is very challenging). Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photo-counters, it was recently shown how reconstruction of photon statistics is possible by considering a variable quantum efficiency. Here we present experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams in a scheme based on on/off avalanche photodetection assisted by maximum-likelihood estimation. Reconstructions of the distribution for both semiclassical and quantum states of light (as single photon, coherent, pseudothermal, and multithermal states) are reported for single-mode and multimode beams. The stability and good accuracy obtained in the reconstruction of these states clearly demonstrate the interesting potentialities of this simple technique.