Fig. 1. (a) A ring resonator, composed by two types of single-mode waveguides A and B, undergoing the dynamic modulation. (b) A ring under the dynamic modulation supports a synthetic lattice along the frequency dimension. (c) The ring is coupled with the through-port and drop-port waveguides.

Fig. 2. Four-wave-mixing processes in a ring with a third-order nonlinear susceptibility including the hyper-parametric processes (SPM, XPM, and others) and the THG process.

Fig. 3. (a) A general four-wave-mixing process in a waveguide with the third-order susceptibility χ(3). (b) The plot of ΔI∝sinc2(ΔkL) showing the effect of the phase mismatching.

Fig. 4. Normalized distributions of the two-photon correlation probability Pm,n. (a)–(c) The input photon pair is |ϕ(−4,4)⟩ with g=0, g=2J, and g=10J, respectively. (d)–(f) The input photon pair is |ϕ(−15,−15)⟩ with g=0, g=2J, and g=10J, respectively. Positions inside two dashed lines correspond to Pm,m.