Tunable photon statistics in weakly nonlinear photonic molecules

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.