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arXiv:0802.2168 · Journal of Modern Optics

Constrained MaxLik reconstruction of multimode photon distributions

G. Brida, Marco Genovese, Alice Meda, Stefano Olivares, M.G.A. Paris, Fabrizio Piacentini

Published Jan 14, 2009• 7 citations
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Abstract

We address the reconstruction of the full photon distribution of multimode fields generated by seeded parametric down-conversion. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood (MaxLik) estimation and does not involve photon counting. We present a novel constrained MaxLik method that incorporates the request of finite energy to improve the rate of convergence and, in turn, the overall accuracy of the reconstruction.

DOI
10.1080/09500340802389805

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We address the reconstruction of the full photon distribution of multimode fields generated by seeded parametric down-conversion. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood (MaxLik) estimation and does not involve photon counting. We present a novel constrained MaxLik method that incorporates the request of finite energy to improve the rate of convergence and, in turn, the overall accuracy of the reconstruction.
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.
We give a detailed analysis of an indirect method used to obtain the photon distribution of a single-mode field using only on/off avalanche photodetectors. The method is based on measuring the field at different quantum efficiencies and then inferring the photon distribution by maximum-likelihood estimation. We address the case when only a limited range of quantum efficiency is available and when these values are not precisely known. The convergence of the method and its robustness against fluctuations are illustrated by means of numerically simulated experiments.