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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Photocount measurements as a tool for investigation of non-classical properties of twin beams

Jan Peřina, Jan Peřina, Ondřej Haderka, J. Křepelka, Martin Hamar, Václav Michálek, Maria Bondani, Alessia Allevi, Alessandra Andreoni

Published Nov 20, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.822349

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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.
Joint signal-idler photoelectron distributions of twin beams containing several tens of photons per mode have been measured recently. Exploiting a microscopic quantum theory for joint quasidistributions in parametric down-conversion developed earlier we characterize properties of twin beams in terms of quasidistributions using experimental data. Negative values as well as oscillating behavior in the quantum region are characteristic for the subsequently determined joint signal-idler quasidistributions of integrated intensities. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively.
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.
Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation of the postselection process are applied to arrive at the corresponding photon-number distributions. Their nonclassical properties are analyzed by suitable nonclassicality criteria and quantified by the corresponding nonclassicality depths. Determining the appropriate quasidistributions of integrated intensities with negative values, the performance of different non-classicality criteria is judged. Properties of the postselected fields reached both by the used and ideal photon-number-resolved detectors are mutually compared.
We demonstrate, by direct measurement of the number of photons in signal and idler, that the twin-beam of light produced by ps-pulsed spontaneous parametric downconversion is endowed with sub-shot-noise photon-number correlations in a mesoscopic intensity regime (more than 1000 detected photons). The noise reduction, calculated from the variance of the difference in the numbers of detected-photons, resulted to be 3.25 dB below the shot-noise level. From experimental data we can recover joint photon-number distribution and a negative-valued joint signal-idler quasi-distributions of integrated intensities, which demonstrates the nonclassical character of the generated field.
We demonstrate sub-shot-noise photon-number correlations in a (temporal) multimode mesoscopic ($\ensuremath{\sim}{10}^{3}$ detected photons) twin beam produced by picosecond-pulsed spontaneous nondegenerate parametric down-conversion. We have separately detected the signal and idler distributions of photons collected in twin coherence areas and found that the variance of the photon-count difference goes below the shot-noise limit by 3.25dB3.25\phantom{\rule{0.3em}{0ex}}\mathrm{dB}3.25dB. The number of temporal modes contained in the twin beam, as well as the size of the twin coherence areas, depends on the pump intensity. Our scheme is based on spontaneous down-conversion and thus does not suffer from limitations due to the finite gain of the parametric process. Twin beams are also used to demonstrate the conditional preparation of a nonclassical (sub-Poissonian) state.