Antibunching correlations in a strongly coupled exciton - photonic crystal cavity system: Role of off-resonant coupling to multiple excitons

We employ a master equation approach to study the second-order quantum autocorrelation functions for up to two independent quantum dot excitons, coupled to an off-resonant cavity in a photonic crystal - single quantum dot system. For a single coupled off-resonant exciton, we observe novel oscillatory behaviour in the early-time dynamics of the cavity autocorrelation function, which leads to decreased antibunching relative to the exciton mode. With a second coupled exciton in the system, we find that the magnitude and the lifetime of these oscillations greatly increases, since the cavity is then able to exchange photons with multiple excitonic resonances. We unambiguously show that this spoils the antibunching characteristics of the cavity quasi-mode, while the autocorrelation of the first exciton is unaffected. We also examine the effects of detector time resolution and make a direct connection to a series of recent experiments.