$\mu$eV, as explained above. The minimum value of $g^{(2)}(0)$ identifies the optimal operation detuning of the laser frequency from the bare resonators, which is $\Delta\omega_{1}=\Delta\omega_{2} \simeq 0.2$, for which $g^{(2)}(0)\simeq 0.42$.

![ Color scale plot of the numerical solution for the zero time-delay second-order correlation as a function of $\gamma_{+}/\gamma$ and $\gamma_{-}/\gamma$, with parameters (in units of $\hbar \gamma=25$ $\mu$eV): $\Delta\omega_{1}=\Delta\omega_{2}=0.2$; $F=15$; $U_{\mathrm{nl}}=4\times10^{-5}$, and $J=56$. []{data-label="fig:gamma_pm"}](figure4.pdf){width="50.00000%"}

While the previous parameter can be experimentally adjusted with a tunable laser as input source, there are characteristics that depend on the specific device implementation. In particular, coupled modes of photonic crystal molecules may display asymmetric losses according to the mode parity, i.e. $\gamma_{+}\neq \gamma_{-}$, as experimentally shown, e.g., in [@atlasov08oe]. This effect is not surprising, since unbalanced Q-factors of symmetric and antisymmetric modes can be traced back to the peculiar loss mechanism in such planar photonic crystal cavities, where perturbative coupling to radiative modes depends on the mode parity with respect to a defined symmetry plane of the system [@andreani06prb]. In figure \[fig:gamma\_pm\], we consider the case in which the two resonators possess the same basic characteristics, i.e. the same frequency detunings $\Delta\omega_{1}=\Delta\omega_{2}=0.2$, and the same dissipation rates for each isolated cavity mode, 