Geometric motion transfer between two indirectly coupled mechanical resonators

Phonon-mediated motion transfer plays an essential role in scalable phononic devices. We present geometric motion transfer between two mechanical resonators, which are indirectly coupled by parametrically coupling to the same intermediate mechanical mode. The phonon-mediated coupling is controlled so that the intermediate mode remains unoccupied after the system undergoes a cyclic evolution. Pure geometric motion transfer between the indirectly coupled mechanical resonators is achieved experimentally through a controlling motion evolution path in the Hilbert space. Because the geometric phase is robust against local fluctuation of the evolution path, our research provides a prospective scenario for noise-resilient phonon-based information processing.