Fig. 1: Resonance structure.

a Idealized intensity enhancement inside a single-ring resonator, showing the four-wave mixing processes that occur when two resonances P1 and P2 are pumped. b Idealized intensity enhancement of the two-ring photonic molecule, showing the splitting and detuning of the hybridized X1 and X2 resonances that arises from the strong linear coupling between the principal and auxiliary resonator. In both cases the desired process, dual-pump spontaneous four-wave mixing (DP-SFWM, shown in green), leads to squeezing of the S mode. The unwanted processes of single-pump spontaneous four-wave mixing (SP-SFWM, red) generate excess noise in the S mode, contaminating the output, while Bragg-scattering four-wave mixing (BS-FWM, orange) transfers photons away from the S mode as photons are exchanged between the two pumps. Both these unwanted processes are suppressed by the presence of the auxiliary resonator, without significantly affecting the desired squeezing process. The free spectral ranges of the auxiliary resonator is chosen to be one-third larger than that of the principal resonator, so that only every fourth mode of the principal resonator is hybridized.