$\gamma$. We then study the behavior of the SPS in terms of the symmetric and antisymmetric modes losses. Numerical solutions are reported for the zero-time-delay second-order correlation as a function of $\gamma_{+}/\gamma$ and of $\gamma_{-}/\gamma$. Quite remarkably, the figure of merit is optimal for unbalanced losses, i.e. $\gamma_{+} \neq \gamma_{-}$. In fact, breaking the symmetry of the system and for appropriate resonators parameters the photonic molecule in exam represents an almost ideal source of single-photon Fock states (down to $g^{(2)}(0) < 10^{-4}$). Incidentally, this is exactly the situation that is most naturally realized in a photonic crystal molecule [@atlasov08oe], although not generally valid for any type of tunnel-coupled photonic resonators (such as, e.g., coupled microdisks or micropillars).

[ The numerical results reported in figure \[fig:gamma\_pm\] can be understood by employing a perturbative analytical treatment [@ferretti2010; @bamba]. The pump laser frequency in the present scheme is strongly off-resonance with respect to the two eigenfrequencies of the system, corresponding to the $\hat{a}_{+}$ and $\hat{a}_{-}$ modes, respectively. Hence, even under the conditions $F/ (\hbar\gamma) \gg 1$, a low occupancy of the two modes is expected and the Hilbert space can be truncated to the two-photon occupancy in the basis of Fock states $\{ 