Photon antibunching in strongly coupled exciton-semiconductor cavity systems: Role of off-resonant coupling to multiple excitons

We present a master equation approach to study the second-order quantum autocorrelation functions for up to two quantum-dot excitons, coupled to an off-resonant cavity in a semiconductor-single quantum-dot cavity system. For a single coupled off-resonant exciton, we observe unusual oscillatory behavior 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. These results demonstrate that for incoherent pumping, the ubiquitous two-level atom model completely breaks down and that multiple excitonic resonances act in concert to spoil the antibunching characteristics of the cavity quasimode. We connect these findings to a series of recent surprising experimental results for single quantum dot-semiconductor cavity systems, including photonic crystal systems and micropillar cavities.