Higher-Order Photon Statistics as a New Tool to Reveal Hidden Excited States in a Plasmonic Cavity

Among the best known quantities obtainable from photon correlation measurements are the g(m) correlation functions. Here, we introduce a new procedure to evaluate these correlation functions based on higher-order factorial cumulants CF,m that integrate over the time dependence of the correlation functions, that is, summarize the available information at different time spans. In a systematic manner, the information content of higher-order correlation functions as well as the distribution of photon waiting times is taken into account. Our procedure greatly enhances the sensitivity for probing correlations and, moreover, is robust against a limited counting efficiency and time resolution in experiment. It can be applied even in case g(m) is not accessible at short time spans. We use the new evaluation scheme to analyze the photon emission of a plasmonic cavity coupled to a single quantum dot. We derive criteria that must hold if the system can be described by a generic Jaynes–Cummings model. A violation of the criteria can be explained by the presence of an additional excited quantum dot state.