Temporal super-cell engineering and acoustic amplification in dispersive phononic time crystals

Floquet time crystals, characterized by momentum band gaps (k-gaps), offer powerful mechanisms for exotic wave control. However, selectively harnessing the Floquet band structure and opening multiple k-gaps remains a significant challenge in experiment. In this work, we construct a phononic time crystal by integrating discrete resonant meta-atoms into a one-dimensional acoustic waveguide, effectively creating a time-varying metamaterial. Through dynamic compressibility modulation, we observe amplified transmission and strong emission enhancement for a compact Floquet slab at the k-gap-associated frequency. Based on this versatile platform, we further extend the Floquet band physics by introducing a temporal-supercell concept that creates multiple k-gaps via momentum band folding. By suitably designing the compressibility in each phase of the supercell, we experimentally observe two clear amplified transmission frequency ranges around half and quarter of the original modulation frequency, for a corresponding compact Floquet slab with a band-folding-induced k-gap. This reconfigurable platform enables tailored parametric processes and unlocks pathways to higher-dimensional time crystals and topological temporal phenomena.