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arXiv:1202.1437 · Physical Review A

Photon-number distributions of twin beams generated in spontaneous parametric down-conversion and measured by an intensified CCD camera

Jan Peřina, Martin Hamar, Václav Michálek, Ondřej Haderka

Published Feb 14, 2012• 70 citations
arXivHTMLPDF

Abstract

The measurement of photon-number statistics of fields composed of photon pairs, generated in spontaneous parametric down-conversion and detected by an intensified charge-coupled device (iCCD) camera, is described. Final quantum detection efficiencies, electronic noises, finite numbers of detector pixels, transverse intensity spatial profiles of the detected beams, as well as losses of single photons from a pair are taken into account in a developed general theory of photon-number detection. The measured data provided by an iCCD camera with single-photon detection sensitivity are analyzed along the developed theory. Joint signal-idler photon-number distributions are recovered using the reconstruction method based on the principle of maximum likelihood. The range of applicability of the method is discussed. The reconstructed joint signal-idler photon-number distribution is compared with that obtained by a method that uses superposition of signal and noise and minimizes photoelectron entropy. Statistics of the reconstructed fields are identified to be multimode Gaussian. Elements of the measured as well as the reconstructed joint signal-idler photon-number distributions violate classical inequalities. Sub-shot-noise correlations in the difference of the signal and idler photon numbers as well as partial suppression of odd elements in the distribution of the sum of signal and idler photon numbers are observed.

DOI
10.1103/physreva.85.023816

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The measurement of photon-number statistics of fields composed of photon pairs, generated in spontaneous parametric down-conversion and detected by an intensified charge-coupled device (iCCD) camera, is described. Final quantum detection efficiencies, electronic noises, finite numbers of detector pixels, transverse intensity spatial profiles of the detected beams, as well as losses of single photons from a pair are taken into account in a developed general theory of photon-number detection. The measured data provided by an iCCD camera with single-photon detection sensitivity are analyzed along the developed theory. Joint signal-idler photon-number distributions are recovered using the reconstruction method based on the principle of maximum likelihood. The range of applicability of the method is discussed. The reconstructed joint signal-idler photon-number distribution is compared with that obtained by a method that uses superposition of signal and noise and minimizes photoelectron entropy. Statistics of the reconstructed fields are identified to be multimode Gaussian. Elements of the measured as well as the reconstructed joint signal-idler photon-number distributions violate classical inequalities. Sub-shot-noise correlations in the difference of the signal and idler photon numbers as well as partial suppression of odd elements in the distribution of the sum of signal and idler photon numbers are observed.
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Measurement of photon-number statistics of fields composed of photon pairs generated in spontaneous parametric down-conversion pumped by strong ultrashort pulses is described. Finite detection quantum efficiencies, noises as well as possible loss of one or both photons from a pair are taken into account. Measured data provided by an intensified CCD camera are analyzed along the developed model. The joint signal-idler photon-number distribution is obtained using the expectation maximization algorithm. Covariance of the signal and idler photon-numbers exceeds 98%. Entanglement area of the correlated photon pairs is determined.
Joint signal-idler photoelectron distributions of twin beams have been measured recently in two distinct regimes: either the mean number of photon pairs per one pump pulse is lower that the number of independent modes or vice versa. Exploiting a microscopic quantum theory for joint quasi-distributions in parametric down-conversion based on the model of superposition of signal and noise we characterize properties of twin beams in terms of quasidistributions using experimental data. In parallel to the microscopic model, joint signal-idler photon-number distribution is reconstructed using the method of maximum likelihood. Negative values as well as oscillating behavior in quantum region are characteristic for the joint signal-idler quasi-distributions of integrated intensities. The larger the mean number of photon pairs per mode the weaker the quantum features are. However, they survive even in the mesoscopic regime, i.e. when tens of photon pairs per mode are present on average. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively. Violation of classical inequalities for photon-number distributions is discussed.