Continuous time crystal coupled to a mechanical mode as a cavity-optomechanics-like platform

Time crystals are an enigmatic phase of matter in which a quantum mechanical system displays repetitive, observable motion - they spontaneously break the time translation symmetry. On the other hand optomechanical systems, where mechanical and optical degrees of freedom are coupled, are well established and enable a range of applications and measurements with unparalleled precision. Here, we connect a time crystal formed of magnetic quasiparticles, magnons, to a mechanical resonator, a gravity wave mode on a nearby liquid surface, and show that their joint dynamics evolves as a cavity optomechanical system. Our results pave way for exploiting the spontaneous coherence of time crystals in an optomechanical setting and remove the experimental barrier between time crystals and other phases of condensed matter.