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arXiv:2309.04217 · Optics Continuum

Estimation of photon number distribution and derivative characteristics of photon-pair sources

Sang Min Lee

Published Jul 4, 2024• 0 citations
arXivHTMLPDF

Abstract

The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the source. The photon number distribution, however, can be altered due to spectral or spatial filtering and optical losses, leading to changes in the above characteristics. This paper theoretically describes the effects of different filterings, losses, and noise counts on the photon number distribution and related characteristics. From the theoretical description, an analytic expression for the effective mode number of the joint spectral density is also derived. Compared with previous methods for estimating the photon number distribution and characteristics, an improved methodology is introduced along with a suitable metric of accuracy for estimating the photon number distribution, focusing on photon-pair sources. We discuss the accuracy of the calculated characteristics from the estimated (or reconstructed) photon number distribution through repeated simulations and bootstrapped experimental data.

DOI
10.1364/optcon.524729

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The evaluation of a photon-pair source employs characteristic metrics like the photon-pair generation rate, heralding efficiency, and second-order correlation function, all of which are determined by the photon number distribution of the source. The photon number distribution, however, can be altered due to spectral or spatial filtering and optical losses, leading to changes in the above characteristics. This paper theoretically describes the effects of different filterings, losses, and noise counts on the photon number distribution and related characteristics. From the theoretical description, an analytic expression for the effective mode number of the joint spectral density is also derived. Compared with previous methods for estimating the photon number distribution and characteristics, an improved methodology is introduced along with a suitable metric of accuracy for estimating the photon number distribution, focusing on photon-pair sources. We discuss the accuracy of the calculated characteristics from the estimated (or reconstructed) photon number distribution through repeated simulations and bootstrapped experimental data.
We analyse how imperfections in single-photon detectors impact the characterization of photon-pair sources. We perform exact calculations to reveal the effects of multi-pair emissions and of noisy, non-unit efficiency, nonphoton-number resolving detections on the Cauchy–Schwarz parameter, on the second-order auto-correlation and cross-correlation functions, and on the visibilities of both Hong–Ou–Mandel and Bell-like interferences. We consider sources producing either two-mode squeezed states or states with a Poissonian photon distribution. The proposed formulas are useful in practice to determine the impacts of multi-pair emissions and dark counts in standard tests used in quantum optics.
Photons in twin beams exhibit correlations in both photon number and spatial detection position. Here spatial correlations in detection positions are exploited to develop a method for reconstructing the joint photon-number distribution of a twin beam from the experimental photocount histograms. This considerably reduces experimental noise, making it superior to the usual methods. This practical reconstruction method for spatially resolved photon counting is suitable for any application that requires joint photon-number distributions of twin beams, in e.g.e.g.e.g. metrology, or future quantum communication protocols.
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source’s photon statistics and use it in the estimation of a quantum key distribution system’s key rate. This promises to be a useful tool for the certification of quantum-related technologies.
We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%. (C) 2013 Optical Society of America
We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%.
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.