We report in figure \[fig:gamma\_star\] the calculated $g^{(2)}(0)$ as a function of $\gamma_{+}/\gamma$ for $\gamma_{-}/\gamma=0.2$ on increasing pure dephasing rate, $\gamma^{\ast}$. [ Suppression of antibunching occurs for values of loss rates on the order of $\hbar\gamma^{\ast}\sim U_{\mathrm{nl}}$. ]{} Interestingly, the SPS figure of merit tolerance is such that at $\hbar\gamma^{\ast}/U_{\mathrm{nl}}\simeq 10^{-2}$ and $\gamma_{+}/\gamma\simeq 1.2$, the system still displays an acceptable single-photon nonlinear behavior with $g^{(2)}(0) \simeq 0.1$, which confirms the robustness of such a scheme even with respect to loss channels that are difficult to control in an real experimental setting. [ On the other hand, we expect that pure dephasing effects are most probably going to play a marginal role in the present scheme, where small pump powers are required to efficiently operate the SPS.]{}

Conclusions {#sec:conclu}
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We have presented theoretical results supporting the proposal of a single-photon source built on an integrated photonic platform made of passive material components, where cavity-enhanced native nonlinearities are able to produce single-photon blockade. The building block is based on tunnel-coupled resonators, or photonic molecules, coherently driven by an external laser source. We have provided numerical evidence for the best combination of system parameters, such as cavity-laser detunings and modes losses, leading 