  We study the photon statistics of symmetric and antisymmetric modes in a
photonic molecule consisting of two linearly coupled nonlinear cavity modes.
Our calculations show that strong photon antibunching of both symmetric and
antisymmetric modes can be obtained even when the nonlinearity in the photonic
molecule is weak. The strong antibunching effect results from the destructive
interference between different paths for two-photon excitation. Moreover, we
find that the optimal frequency detunings for strong photon antibunching in the
symmetric and antisymmetric modes are linearly dependent on the coupling
strength between the cavity modes in the photonic molecule. This implies that
the photonic molecules can be used to generate tunable single-photon sources by
tuning the values of the coupling strength between the cavity modes with weak
nonlinearity.
