In this paper, we study the statistical properties of light generated by two different types of quantum emitters embedded in an optical micro-cavity. These emitters are a single quantum dot (QD) and an artificial molecule (AM), which is made by two interacting QDs. The study of the statistical properties is done by means of the second-order correlation function, which can be calculated using the elements of the density matrix operator. Some non-Hamiltonian processes are considered such as incoherent pumping of photons, spontaneous emission, decay in leaky modes, phonon assistance to the main QD, and phonon assistance to the tunnelling mechanism. The effect of each one of those mechanisms in the emission properties of the system is analysed for a certain range of parameters. As a result, we observe that the tunnelling mechanism, as well as the phonon assistance mechanism to the main QD, are processes that can favour anti-bunching in the emitted photons. For the tunnelling phonon assistance, we find that these mechanisms attest against the non-classical character of the photons, changing its statistics by increasing the value of the second-order correlation function. However, the effect of the three mechanisms acting together on the system is a net diminish of the second-order correlation function, in comparison with the same system when all the mechanisms are turned off.
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