Photon-Photon Correlation Statistics In The Collective Emission From Ensembles Of Self-Assembled Quantum Dots

We present a theoretical analysis of the intensity correlation functions for the spontaneous emission from a planar ensemble of self-assembled quantum dots. Using the quantum jump approach, we numerically simulate the evolution of the system and construct photon-photon delay time statistics that approximates the second-order correlation functions of the field. The form of this correlation function in the case of collective emission from a highly homogeneous ensemble qualitatively differs from that characterizing an ensemble of independent emitters (inhomogeneous ensemble of uncoupled dots). The signatures of collective emission are observed also in the case of an inhomogeneous but sufficiently strongly coupled ensemble. Different forms of the correlation functions are observed in the intensity autocorrelations and in cross correlations between various spectral ranges, revealing the quantum state projection associated with the detection event and the subsequent interaction-induced redistribution of occupations. The predicted effect of collective dynamics on the correlation functions appears under various excitation conditions. Thus, we show that the second-order correlation function of the emitted field provides a sensitive test of cooperative effects.