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

Abstract

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 which integrate over the time dependence of the correlation functions, i.e., 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 quantum dot. We derive criteria which must hold if the system can be described by a generic Jaynes-Cummings model. A violation of the criteria is explained by the presence of an additional excited quantum dot state.

Nonequilibrium phase transition in a single-electron micromaser

“…As we will see in the following, the factorial moments and cumulants provide a convenient description of the single-electron micromaser. In particular, while ordinary cumulants are useful to describe continuous random variables, factorial cumulants are in some cases better suited to characterize discrete random variables, such as the number of counted electrons or photons [56][57][58][59][60][61][62][63][64][65][66][67].…”

“…Having characterized each of the two dynamical phases, we now go on to investigate the transition between them. To this end, we make use of Lee-Yang theory [29][30][31][32][33][34][35] by considering the zeros of the factorial moment generating function [56][57][58][59][60][61][62][63][64][65][66][67], which for our purposes plays the role of the partition function in equilibrium statistical mechanics [39][40][41][42][43][44][45][46][47]. However, in contrast to thermal phase transitions, we are not considering transitions between different equilibrium phases such as spin lattices with a vanishing or a finite average magnetization.…”

“…Here, by contrast, we show how the phase transitions can be directly observed from accurate measurements of the full counting statistics. In particular, we will see that factorial moments and factorial cumulants [56][57][58][59][60][61][62][63][64][65][66][67] are particularly useful to reveal the non-equilibrium phase transition, which may be observed in future experiments.…”

Nonequilibrium phase transition in a single-electron micromaser

“…As we will see in the following, the factorial moments and cumulants provide a convenient description of the single-electron micromaser. In particular, while ordinary cumulants are useful to describe continuous random variables, factorial cumulants are in some cases better suited to characterize discrete random variables, such as the number of counted electrons or photons [60][61][62][63][64][65][66][67][68][69][70][71].…”

“…Here, by contrast, we show how the phase transitions can be directly observed from accurate measurements of the full counting statistics. In particular, we will see that factorial moments and factorial cumulants [60][61][62][63][64][65][66][67][68][69][70][71] are particularly useful to reveal the nonequilibrium phase transition, which may be observed in future experiments.…”