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International Conference on Transparent Optical Networks

Impact of FWM process on the statistics of a co-propagating quantum signal in a WDM lightwave system

Álvaro J. Almeida, Nuno A. Silva, Paulo Sérgio de Brito André, Armando N. Pinto

Published Jul 1, 2012• 0 citations
Publisher

Abstract

We present an experimental characterization of the evolution of the photon statistics of a quantum signal, in a wavelength-division multiplexing (WDM) environment. We use an on/off avalanche photodetector operating in the Geiger mode to measure the photon counts, and the maximum-likelihood estimation (MLE) method and the expectation-maximization (EM) algorithm to reconstruct the photon statistics. We found that the statistics of the quantum signal changes from Poissonian to thermal when it contains only a few photons per pulse. When the quantum signal carries a higher number of photons per pulse, it is verified that its statistics remains Poissonian.

DOI
10.1109/icton.2012.6253799

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We present an experimental characterization of the evolution of the photon statistics of a quantum signal, in a wavelength-division multiplexing (WDM) environment. We use an on/off avalanche photodetector operating in the Geiger mode to measure the photon counts, and the maximum-likelihood estimation (MLE) method and the expectation-maximization (EM) algorithm to reconstruct the photon statistics. We found that the statistics of the quantum signal changes from Poissonian to thermal when it contains only a few photons per pulse. When the quantum signal carries a higher number of photons per pulse, it is verified that its statistics remains Poissonian.
We discuss the statistics of Poissonian and thermal sources, and verify that as an approximation to a single-photon source, both Poissonian and thermal sources can be used, when the average number of photons per pulse is of the order of 0.1. An experimental characterization of the photon statistics of a single-photon source obtained from the four-wave mixing (FWM) process in optical fibers is presented. We employ an on/off avalanche photodetector operating in the Geiger mode, and use the maximum-likelihood estimation (MLE) method and the expectation-maximization (EM) algorithm to reconstruct the data. We find that the statistics of the source goes from thermal, at a low signal power regime, to Poissonian, in a high signal power regime.
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.
Many quantum communication systems operate based on weak light pulses which by design are assumed to operate in isolation from regular data traffic. With the widespread availability and commercialization of these systems comes a need for seamless integration already at the physical layer. In particular for optical fiber links where wavelength division multiplexing (WDM) is the dominant data transmission technique this results in the propagation of very weak quantum signals against a strong data signal background. With this work, we present a novel theoretical approach that studies the evolution of co-propagating quantum and classical signals that are launched using WDM. The important factors that contribute to crosstalk, such as the launch power of the classical signal and the separation between the two signals in terms of wavelength, are comprehensively analyzed. Interestingly, calculations show that only the first two nearest channels from the classical channel experience noticeable crosstalk whereas other distant channels have negligible crosstalk effect. This reflects the WDM technique is in principle robust in the integration of weak quantum links into classical data traffic.
The photon statistics of a strongly attenuated continuous-wave laser (1550 nm), characterized by an Avalanche Photodiode operating in Geiger mode, was reconstructed with the aid of an iterative Maximum Likelihood Estimation model and without photon counting. Statistical analysis of the reconstructed distribution was performed to determine the algorithm convergence criteria. Parameters such as reconstruction error, Fischer Dispersion Index, chi-square, and p-value were evaluated. The photon number distribution for attenuated coherent sources was successfully reconstructed according to the defined convergence criteria.
We report on the theoretical statistical characterization of a single-photon source based on the stimulated four-wave mixing process inside an optical fiber. We quantify the photon statistics by means of the expectation number of photons generated on the signal and idler waves, 〈Ňs〉 and 〈Ňi〉 respectively, and Mandel's Qsand Qiparameters. The obtained solutions take into account the spontaneous and stimulated Raman contributions for the generation of the idler wave. Results show that the idler wave generated inside the fiber follows a super-Poissonian statistics. Findings also show that the signal wave change their own statistics from a Poissonian to a super-Poissonian, due to the interaction with the pump field and the optical fiber.