  We propose a scheme to realize strong photon antibunching with lower photon
nonlinearity in a photonic molecule consisting of two photonic cavities, one of
which contains a quantum dot (QD). This strong photon antibunching is
attributed to destructive quantum interference effect which suppresses the
two-photon excitation of the cavity field. That g^2 (0)~10^(-4) can be achieved
with modest QD-cavity coupling strength g=1.1k and cavity tunneling strength
J=3k when the system is driven by single laser field. To further reduce the
requisite tunneling and make the system tunable, two laser fields are applied
to the system. The strong photon antibunching (g^2 (0)~10^(-3)) can be achieved
with a relatively large intracavity photon number by optimizing the phase
between two driving laser fields when J=0.9k. Moreover, the system shows a
strong robustness of maintaining strong photon antibunching within a large
parameter variation under the optimal phase condition. Our scheme provides a
flexible and efficient method for solid state quantum single photon sources.
