Single-photon emission modeling with statistical estimators for the exponential distribution

TL;DR

This paper introduces a statistical framework and estimators for modeling single-photon emission processes, focusing on accurately estimating radiative decay times in quantum optics applications.

Contribution

It proposes and validates a set of statistical estimators for the exponential distribution tailored to single-photon emission data, including censored data scenarios.

Findings

Estimators accurately estimate decay times in experimental data.

Performance degrades gracefully with limited data.

Censored data handling improves estimator reliability.

Abstract

Single-photon sources are used in numerous quantum technologies, from sensing and imaging to communication, making the accurate modeling of their emissions essential. In this work, we propose a statistical framework for describing single-photon emission processes and implement estimators for the exponential distribution to quantify this phenomenon. Our approach provides a reliable method for estimating the radiative decay time, represented by the inverse rate parameter, which is crucial in quantum optics applications. We explore several statistical estimators, including maximum likelihood estimation, minimum-variance unbiased estimator, and best linear unbiased estimator. To validate our theoretical methods, we test the proposed estimators on experimental data, demonstrating their applicability in real-world settings. We also evaluate the performance of these estimators when dealing with censored data, a frequent limitation in photon emission experiments. The analysis allows us to track the performance of the proposed estimators as the amount of available data decreases, providing insights into their reliability for modeling single-photon emission events under limited resources.