Observation of Discrete Floquet Time Crystals in Periodically Driven Acoustic Bubbles

Abstract

We show experimentally and theoretically that the translation dynamics of acoustic bubbles in an acoustic standing wave field exhibit all the attributes of a discrete time crystal, the dynamics of which is described by Mathieu’s equation. Individual bubbles and synchronized bubbles in a self-organized chain undergo emergent slow persistent oscillations. The period of the emergent oscillations is longer than that of the driving acoustic wave by three orders of magnitude, therefore, breaking the discrete time translation symmetry of the driver.

Keywords

• acoustic bubbles
• time crystal
• Mathieu’s equation