passive interferometry [@kimble92pra] or active quantum feedback schemes [@smith02prl]. In this sense, we believe $g^{(2)}(0) \ll g^{(2)}(\tau)$ is a necessary condition to be optimized before realizing a SPS, but further analysis is needed to characterize its output, depending on the specific device implementation. Such analysis goes beyond the scope of the present work. ]{}

Effects of pure dephasing
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![Numerical solution for the zero-time-delay second-order correlation as a function of $\gamma_{+}/\gamma$, for different values of pure dephasing rate (assumed equivalent for both symmetric and antisymmetric modes). Parameters are as in figure \[fig:gamma\_pm\], with $\gamma_{-}/\gamma=0.2$.[]{data-label="fig:gamma_star"}](figure5.pdf){width="50.00000%"}

In photonic crystal molecules, the loss mechanism naturally leads to unbalanced quality factors for the symmetric and antisymmetric modes with respect to the quality factor of the isolated cavity that can be on the order of $Q_- / Q_+ = \gamma_+ / \gamma_-  \sim 1 \to 10$. Neglecting the counterintuitive effect of possible antisymmetric ground states [@caselli2012], the lower energy mode is usually the symmetric combination of the two isolated cavity states, which has a reduced quality factor as compared to the isolated cavity [@atlasov08oe]. Thus, we extract from the color plot in figure \[fig:gamma\_pm\] the curve corresponding to $\gamma_-= 0.2 \gamma$ (i.e. the quality factor 