Mode Conservation and Conversion in Polyatomic Phononic Crystals with Temporal Interfaces

A sudden change in material properties creates a temporal interface and forces a propagating wave to change its frequency while preserving its wave number. In contrast to monoatomic lattices with a single-frequency-wave-number pair, polyatomic lattices support multiple frequencies for each wave number. More importantly, polyatomic lattices can host nontrivial topological characteristics. To date, experimental observations are limited to topologically trivial monoatomic phononic systems. Here, we utilize analytical, numerical, and experimental methods to examine polyatomic phononic lattices subject to temporal interfaces. In particular, we realize phononic lattices demonstrating single-frequency shift (i.e., mode conservation) and multifrequency splitting (i.e., mode conversion) following a temporal interface. Accordingly, we generalize temporal analogs of Snell's law and Fresnel equations. Moreover, we utilize Bloch mode overlaps to obtain a phononic time lens and a classical analog of dynamic quantum phase transitions for phonons. Such overlap determines the probability of mode conversion or conservation after a temporal interface and, more importantly, can carry hidden topological characteristics. Our methodology paves the way for the use of temporal interfaces in probing phonon band topology and the realization of advanced acoustic devices.