for typical semiconductors in this wavelength range), from equation (\[shift\_kerr\]) we have an estimate for the single-photon nonlinearity on the order of $U_{\mathrm{nl}}\simeq 10^{-3}$ $\mu$eV. This is certainly a very small value, as compared to typical resonant nonlinearities induced by QD or QW transitions [@ciuti06prb]. However, we aim at exploiting the photon blockade mechanism in weakly nonlinear tunnel-coupled devices, as introduced in [@savona10prl]. To this end, we assume a very specific realization of such proposal involving coupled photonic crystal cavities and access waveguides integrated on the same photonic chip, as schematically represented in figure \[schema\]. In this case, typical tunnel coupled micro-cavities display modes with spectral splitting on the order of $\Delta E_{\pm}=2J\sim 1$ to few meV [@atlasov08oe; @caselli2012]. Finally, the quality factor of cavity modes in the near infrared is typically on the order of $Q\sim 10^4$ to $10^5$, and we can safely assume $Q\sim 30000$ as a realistic value, which gives a typical cavity mode linewidth $\hbar\gamma \simeq 0.025$ meV for a resonance around $\hbar\omega_1\simeq 0.8$ eV (the typical telecom wavelength $\lambda=1.55$ $\mu$m). Such realistic values for silicon or GaAs based photonic crystal chips at operational wavelengths in the most interesting telecom band allow to assume normalized parameters 