Photon emission correlation spectroscopy as an analytical tool for quantum defects

Photon emission correlation spectroscopy is an indispensable tool for the study of atoms, molecules, and, more recently, solid-state quantum defects. In solid-state systems, its most common use is as an indicator of single-photon emission, a key property for quantum technology. Beyond an emitter's single-photon purity, however, photon correlation measurements can provide a wealth of information that can reveal details about its electronic structure and optical dynamics that are hidden by other spectroscopy techniques. This tutorial presents a standardized framework for using photon emission correlation spectroscopy to study quantum emitters, including discussion of theoretical background, considerations for data acquisition and statistical analysis, and interpretation. We highlight important nuances and best practices regarding the commonly-used $g^{(2)}(\tau=0)<0.5$ test for single-photon emission. Finally, we illustrate how this experimental technique can be paired with optical dynamics simulations to formulate an electronic model for unknown quantum emitters, enabling the design of quantum control protocols and assessment of their suitability for quantum information science applications.