Programmable nonlinear rotation of acoustically levitated chiral stars

Abstract

Acoustic levitation enables objects to be suspended and manipulated without physical contact, providing a versatile platform for studying the dynamics of freely suspended matter. Yet levitated objects, from droplets and thin films to particle assemblies, frequently rotate spontaneously, and this axial rotation often remains difficult to predict or control. There is no general understanding of how the shape of a levitated object determines whether it rotates, in which direction, or how its rotation changes with acoustic amplitude. Here, we establish how particle geometry and acoustic amplitude govern spontaneous rotation of acoustically levitated objects. We work with a family of shapes we call ``chiral stars'', within which we systematically vary handedness and number of arms. In a symmetric acoustic field, stars that preserve in-plane mirror symmetry do not rotate, while those that break it spontaneously rotate with a direction set by handedness. Beyond this symmetry requirement, we demonstrate that geometry, as encoded by the number of star arms, couples with acoustic amplitude to produce complex, nonlinear dynamics, including spontaneous reversal of rotation direction. To explain these behaviors, we develop a minimal torque model constrained by independent measurements of rotational drag, which captures the observed responses across all star geometries. We then demonstrate predictive power by designing a ``hybrid star'' with a prescribed amplitude-dependent response and reversal voltage. Our results not only establish how particle geometry and acoustic amplitude combine to govern rotation in acoustically levitated systems, but also reveal unanticipated higher-order couplings with the acoustic field. Beyond explaining spontaneous rotation, they open a route toward programmable rotational dynamics in acoustically levitated matter.