Synthetic gauge fields for phonon transport in a nano-optomechanical system.

Gauge fields play important roles in condensed matter, explaining for example nonreciprocal and topological transport phenomena. Establishing gauge potentials for phonon transport in nanomechanical systems would bring quantum Hall physics to a new domain, which offers broad applications in sensing and signal processing, and is naturally associated with strong nonlinearities and thermodynamics. In this work, we demonstrate a magnetic gauge field for nanomechanical vibrations in a scalable, on-chip optomechanical system. We exploit multimode optomechanical interactions, which provide a useful resource for the necessary breaking of time-reversal symmetry. In a dynamically modulated nanophotonic system, we observe how radiation pressure forces mediate phonon transport between resonators of different frequencies, with a high rate and a characteristic nonreciprocal phase mimicking the Aharonov-Bohm effect. We show that the introduced scheme does not require high-quality cavities, such that it can be straightforwardly extended to explore topological acoustic phases in many-mode systems resilient to realistic disorder.