Origin of strong photon antibunching in weakly nonlinear photonic molecules

In a recent work [Liew and Savona, Phys. Rev. Lett. 104, 183601 (2010)] it was numerically shown that a resonantly driven photonic "molecule" consisting of two coupled cavities can exhibit strong photon antibunching with a surprisingly weak Kerr nonlinearity. Here, we analytically identify the subtle quantum interference effect that is responsible for the predicted efficient photon blockade effect. We then extend the theory to the experimentally relevant Jaynes-Cummings system consisting of a single quantum emitter in a coupled-cavity structure and predict the strong antibunching even for single-atom cooperativity on the order of or smaller than unity. The potential of this quantum interference effect in the realization of strongly correlated photonic systems with only weak material nonlinearities is assessed by comparing on-site and inter-site correlations in a ring of three coupled photonic molecules.