the Hamiltonian ($\hbar=1$): $$\label{eq:HOmega}
\hat{H}=\frac{\Omega}{2}\left(\ket{g}\bra{e}+\ket{e}\bra{g}\right).$$ All decay channels are modeled following the scheme shown in Fig. \[fig:g2Model\]. The Lindblad operator is: $$\begin{aligned}
\label{eq:collaps}
\hat{\mathcal{L}}&=\sqrt{\Gamma_r}\ket{g}\bra{e}+\sqrt{\Gamma_A}\ket{p}\bra{e}+\sqrt{\Gamma_p}\ket{g}\bra{p}\\
&+\sqrt{\Gamma_{\text{out}}}\ket{b}\bra{p}+\sqrt{\Gamma_{\text{in}}}\ket{g}\bra{b}.\end{aligned}$$ We compute the steady-state density matrix, $\rho_s$, and obtain the auto- and cross-correlation by using the Quantum Toolbox in Python (QuTiP [@Johansson2013]). The operator for the resonant decay is $\hat{a}=\sqrt{\Gamma_r}\ket{g}\bra{e}$, and the operator for the radiative Auger decay is $\hat{a}_A=\sqrt{\Gamma_A}\ket{p}\bra{e}$. Auto- and cross-correlations are computed numerically by applying the quantum regression theorem. The auto-correlation of the resonance fluorescence is given by: $$\label{eq:autoCorr}
g^{(2)}(\tau)=\frac{\langle \hat{a}^{\dagger}(t)\hat{a}^{\dagger}(t+\tau)\hat{a}(t+\tau)\hat{a}(t)\rangle}{\langle \hat{a}^{\dagger}(t)\hat{a}(t)\rangle^2}.$$ The cross-correlation is given by: $$\label{eq:crossCorr}
g^{(2)}(\tau)=\frac{\langle \hat{a}_A^{\dagger}(t)\hat{a}^{\dagger}(t+\tau)\hat{a}(t+\tau)\hat{a}_A(t)\rangle}{\langle \hat{a}^{\dagger}(t)\hat{a}(t)\rangle\langle \hat{a}_A^{\dagger}(t)\hat{a}_A(t)\rangle}.$$ The auto-correlation of the radiative Auger emission is: $$\label{eq:autoCorrAuger}
g^{(2)}(\tau)=\frac{\langle \hat{a}_A^{\dagger}(t)\hat{a}_A^{\dagger}(t+\tau)\hat{a}_A(t+\tau)\hat{a}_A(t)\rangle}{\langle \hat{a}_A^{\dagger}(t)\hat{a}_A(t)\rangle^2}.$$ We multiply the result of this simulation by $1+c_1\cdot\exp\left(-\abs{\tau}/t_{bl}\right)$ to take into account a weak blinking on short time-scales [@Jahn2015], which might be caused by electron spin pumping enabled by a weak nuclear magnetic field [@Hansom2014]. Additionally, the model function is multiplied with a global prefactor $c_0$, which takes into account a weak blinking on a time-scale of $\sim0.1\ \text{ms}$, probably caused by charge noise. For the resonance fluorescence, a small fraction $c_l$ of reflected laser in the resonant emission is taken into account via $g^{(2)} \rightarrow g^{(2)}\cdot(1-c_l)+c_l$. 