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 C_F,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.