Observation of topological Floquet states interference

Periodic modulation of the Hamiltonian offers a powerful method to engineer Floquet band properties and create new gaps capable of hosting Floquet edge modes. However, there have been limited studies exploring the performance of Floquet edge modes in terms of dynamic control and interference properties. Here, we experimentally implement an array of staggered coupled plasmonic waveguides operating at microwave frequencies based on the Floquet Su-Schrieffer-Heeger model. Our observations reveal the coexistence of Floquet zero and $\ensuremath{\pi}$ modes within a specific periodic range of the quasienergy spectrum. Through near-field experiments, we observe a subharmonic response of the electric field propagation in the microwave, which is confirmed by the interference of eigenfields associated with the two topological end modes. Our work not only provides an approach for studying time-dependent Floquet Hamiltonians, but also opens the door to exploring period-doubling nonequilibrium topological phases.