Direct Observation of k-Gaps in Dynamically Modulated Phononic Time Crystal

Abstract: Floquet time crystals, characterized by momentum gaps (k-gaps), have sparked intense interest across various branches of physics due to their intriguing dynamics and promising applications. Despite growing theoretical efforts, the realization and observation of phononic time crystals, especially for airborne sound, remain significant experimental challenges. In this work, we demonstrate a phononic time crystal by integrating discrete resonant meta-atoms into a one-dimensional acoustic waveguide, effectively creating a homogeneous, time-varying metamaterial. By dynamically modulating the effective compressibility, we experimentally observe exponential acoustic wave amplification, offering clear evidence of k-gap formation. Furthermore, we showcase the versatility of our platform by inducing momentum band folding and double k-gap phenomena via quasi-periodic temporal modulation. This flexible and reconfigurable approach not only enables the design of tailor-made resonant responses but also opens new avenues for realizing higher-dimensional phononic time crystals and exploring nontrivial topological dynamics in time-modulated media.