energy levels much smaller than the cavity mode linewidth. Though very small, this anharmonic shift is enough to introduce a phase shift between different excitation pathways to the two-photon state, which for well chosen values of the system parameters suppresses its occupation as a result of destructive interference, leading to antibunching of the output light. We notice that an analogous mechanism had already been characterized in the simplest CQED system – a two-level atom coupled to a single mode resonator – in a seminal work by H. Carmichael [@carmichael85]. For a given value of the anharmonic shift, this scheme is able to relax by more than three orders of magnitude the cavity loss rate over conventional photon blockade devices, making the mechanism perfectly viable, for example, with commonly achievable defect cavities in photonic crystal structures. For such structures, we further show that the photon antibunching is robust to typically expected rates of pure dephasing. A generalization of this scheme to multi-cavity arrays might give rise to interesting perspectives for the generation of continuous variable entangled states on chip [@liew2012]. [ In the present work we concentrate our analysis on the optimization of $g^{(2)}(0)$ as a figure of merit for SPS, 