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

TL;DR

This paper presents a theoretical framework and improved methodology for accurately estimating the photon number distribution and related characteristics of photon-pair sources, accounting for filtering, losses, and noise, with validation through simulations and experimental data.

Contribution

It introduces an analytic expression for the effective mode number and a new estimation method with enhanced accuracy for photon-pair source characterization.

Findings

The methodology improves estimation accuracy of photon number distribution.

Filtering and losses significantly affect photon-pair source metrics.

Validation shows reliable estimation from simulated and experimental data.

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. In this paper, we theoretically describe 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.