Subharmonic oscillations in the Floquet circuit with the frequency-synthesis dimension

The period-doubling oscillation emerges due to the coexistence of zero and π modes in Floquet topological insulators (FTIs). Here, leveraging the flexibility of the electric circuit, we construct a circuit with frequency-synthetic dimension to realize the FTIs of a periodically-driven model and demonstrate the topological edge states of zero and π modes. In contrast to the period-doubling oscillations observed in FTIs, the circuit exhibits deeply-subharmonic oscillations with periods extensively exceeding the doubling-driven period. Furthermore, we explore the band of the circuit with the equivalent-enhanced periodically-driven strength. Our method provides a flexible scheme to study Floquet topological phases, and open a new path for realizing the deeply subwavelength system.