  In a recent work [T. C. H. Liew and V. Savona, Phys. Rev. Lett. {\bf104},
183601 (2010)] it was numerically shown that in a photonic 'molecule'
consisting of two coupled cavities, near-resonant coherent excitation could
give rise to strong photon antibunching with a surprisingly weak nonlinearity.
Here, we show that a subtle quantum interference effect is responsible for the
predicted efficient photon blockade effect. We analytically determine the
optimal on-site nonlinearity and frequency detuning between the pump field and
the cavity mode. We also highlight the limitations of the proposal and its
potential applications in demonstration of strongly correlated photonic systems
in arrays of weakly nonlinear cavities.
