Imposing chirality on a physical system engenders unconventional energy flow and responses, such as the Aharonov-Bohm effect1 and the topological quantum Hall phase for electrons in a symmetry-breaking magnetic field. Recently, great interest has arisen in combining that principle with broken Hermiticity to explore novel topological phases and applications2-16. Here we report phononic states with unique symmetries and dynamics that are formed when combining the controlled breaking of time-reversal symmetry with non-Hermitian dynamics. Both of these are induced through time-modulated radiation pressure forces in small nano-optomechanical networks. We observe chiral energy flow among mechanical resonators in a synthetic dimension and Aharonov-Bohm tuning of their eigenmodes. Introducing particle-non-conserving squeezing interactions, we observe a non-Hermitian Aharonov-Bohm effect in ring-shaped networks in which mechanical quasiparticles experience parametric gain. The resulting complex mode spectra indicate flux-tuning of squeezing, exceptional points, instabilities and unidirectional phononic amplification. This rich phenomenology points the way to exploring new non-Hermitian topological bosonic phases and applications in sensing and transport that exploit spatiotemporal symmetry breaking.
© 2022. The Author(s), under exclusive licence to Springer Nature Limited.