of the antisymmetric mode is larger than the one of the isolated cavity). The curve is plotted in figure \[fig:gamma\_star\] (curve corresponding to $\gamma^{\ast}=0$), showing a close-to-ideal anti-bunching of $g^{(2)}(0) \simeq 7\times 10^{-5}$ for $\gamma_+ \simeq 1.2 \gamma$, remarkably not far from the realistic ratio $\gamma_+ / \gamma_- \simeq 3$ reported in literature [@atlasov08oe] for coupled photonic crystal cavities.

A possible source of unwanted loss channels that could potentially spoil the effects of photon blockade induced by tunnel-coupling is pure dephasing. In a semiconductor cavity, dephasing can be due to thermal fluctuations or other nonlinear mechanisms enhanced by the same electromagnetic field confinement, giving rise to index fluctuations within the cavity region and hence a pure dephasing rate. Even if such effect is usually neglected, and it is difficult to attribute a pure dephasing rate that is generally valid for any type of mechanism and material, it is of utmost importance to estimate such detrimental effects on the SPS figure of merit for the purposes of the present work. As discussed in section \[sec:model\], the effects of pure dephasing can be simply modeled by solving the master equation after adding the Liouvillian term of the form represented in equation (\[eq:deph12\]). 