Nonreciprocal Wave-Mediated Interactions Power a Classical Time Crystal.

An acoustic standing wave acts as a lattice of evenly spaced potential energy wells for subwavelength-scale objects. Trapped particles interact with each other by exchanging waves that they scatter from the standing wave. Unless the particles have identical scattering properties, their wave-mediated interactions are nonreciprocal. Pairs of particles can use this nonreciprocity to harvest energy from the wave to sustain steady-state oscillations despite viscous drag and the absence of periodic driving. We show, in theory and experiment, that a minimal system composed of two acoustically levitated particles can access four distinct dynamical states, two of which are emergently active steady states. Under some circumstances, these emergently active steady states break spatiotemporal symmetry and therefore constitute a classical time crystal.