Photonic molecules can be obtained by coupled resonant units, where light propagates in super-modes, analogous to molecular orbitals in atomic systems. They have been demonstrated to be versatile tools in a large number of applications, for instance: dispersion compensation, higher-order filters, gain induced spontaneous symmetry breaking and, most recently, as electronically programmable devices for light trapping and storage [1].

The possibility to shape and localize the electric field inside the different constituents of the molecule makes them attractive for cavity-enhanced nonlinear optics. We studied the coherent control of Four Wave Mixing in a molecule made by two indirectly coupled ring resonators on a Silicon nanophotonic chip. As shown in Fig. 1(a), we injected a Pump and a stimulating beam resonantly with ring 2, and we monitored the power of the generated Signal in the parameter space spanned by the inter-resonator phase and eigenfrequency detuning (φ, Δν). We indirectly observed collective excitations, analogous to sub-radiance and super-radiance of diatomic systems, with a respectively long (hundreds of ps) and short photon lifetime. Sub-irradiance is exploited to enhance the internal field, increasing the FWM signal by a factor of 5 compared to the maximum achievable from the single constituents of the molecule. Remarkably, from the detection of the top scattered light, we also observed molecular states characterized by perfect energy equipartition among the two rings. In these states, FWM is suppressed by the destructive interference of the Signal waves scattered from the two resonators in a common bus waveguide. We then compared the FWM conversion efficiency of the molecule to other geometries which make use of single rings. The comparison is shown in Fig. 1(b). The molecule, in the sub-irradiant state (φ ∼ 0.87π or φ ∼0.13π in Fig. 1(b)) shows a conversion efficiency which greatly exceeds the one of its internal constituents by approximately 12.5 dB, and overcomes also a critically coupled Add-Drop resonator (of same intrinsic quality factor) by 3.5 dB. The performance of the critically coupled All-Pass ring is, however, never exceeded. The photonic molecule, while being superior within the class of the considered four port devices, still remains a sub-optimal configuration if compared to the single bus one. This could be intuitively understood from the fact that our coupling scheme employs two decay channels into the external waveguides, while the single bus configuration only one. However, even if the photonic molecule is an intrinsically sub-optimal configuration for reaching record FWM efficiencies, its internal degrees of freedom allows a level of coherent control of the FWM signal which can not be reached by single bus resonators. As an example of application, fast phase shifters based on carrier-depletion could be used to switch between states where FWM is enhanced or suppressed, acting as a wavelength converter for high speed data communication.