Measuring higher-order photon correlations of faint quantum light: a short review

TL;DR

This review discusses methods for measuring higher-order photon correlations in faint quantum light, highlighting their importance for state classification, characterization, and non-classicality detection, with emphasis on experimental feasibility.

Contribution

It provides a comprehensive overview of techniques for measuring normalized higher-order photon moments in free-traveling light, emphasizing their robustness and applications.

Findings

Normalized higher-order moments are often loss-independent.

Various measurement methods include photon-number-resolving detection, coincidence counting, and homodyne detection.

These moments are useful for quantum state classification and non-classicality criteria.

Abstract

Normalized correlation functions provide expedient means for determining the photon-number properties of light. These higher-order moments, also called the normalized factorial moments of photon number, can be utilized both in the fast state classification and in-depth state characterization. Further, non-classicality criteria have been derived based on their properties. Luckily, the measurement of the normalized higher-order moments is often loss-independent making their observation with lossy optical setups and imperfect detectors experimentally appealing. The normalized higher-order moments can for example be extracted from the photon-number distribution measured with a true photon-number-resolving detector or accessed directly via manifold coincidence counting in the spirit of the Hanbury Brown and Twiss experiment. Alternatively, they can be inferred via homodyne detection. Here, we provide an overview of different kind of state classification and characterization tasks that take use of normalized higher-order moments and consider different aspects in measuring them with free-traveling light.