Topological degeneracy breaking in synthetic frequency lattice by Floquet engineering

Synthetic frequency dimensions provide important opportunities to investigate novel topological phenomena. Previously, many theoretical proposals have been studied and relevant experiments have been performed very recently. However, all these works consider models in the weak modulation regime, where static lattice models are constructed. Here we explore a Floquet Su-Schrieffer-Heeger (SSH) model with time-dependent hoppings in the frequency dimension by dynamically modulating ring resonators ultrastrongly, and find that the topological states, originally degenerate in conventional SSH lattices, are separated in eigenenergies. There exists a series of edge states from band folding at the 0 and p energy bandgaps, which exhibit complex multi-frequency oscillations due to the inclusion of counter-rotating terms with higher order oscillation frequencies. Such a system with stronger modulations can widen the bandgap and therefore it provides an effective way to localize pulses in synthetic frequency dimensions. Our work shows a photonic platform with the synthetic dimension in exploring exotic Floquet topological phenomena and shows potential applications in optical storage and communications.