  In recent studies [Liew et al., Phys. Rev. Lett. 104, 183601 (2010); Bamba et
al., Phys. Rev. A 83, 021802(R) (2011)], due to destructive interference
between different paths for two-photon excitation, strong photon antibunching
can be obtained in a photonic molecule consisting of two coupled cavity modes
with weak Kerr nonlinearity when one of the cavity modes is driven resonantly.
Here, we study the photon statistics in a nonlinear photonic molecule with both
the two cavity modes being driven coherently. We show that the statistical
properties of the photons can be controlled by regulating the coupling constant
between the cavity modes, the strength ratio and the relative phase between the
driving fields. The photonic molecules with two driven modes can be used to
generate tunable single-photon sources or controlled photonic quantum gates
with weak Kerr nonlinearity.
