  Non-reciprocal devices, such as circulators and isolators, are indispensable
components in classical and quantum information processing in an integrated
photonic circuit. Aside from those applications, the non-reciprocal phase shift
is of fundamental interest for exploring exotic topological photonics, such as
the realization of chiral edge states and topological protection. However,
incorporating low optical-loss magnetic materials into a photonic chip is
technically challenging. In this study, we experimentally demonstrate
non-magnetic non-reciprocity using optomechanical interactions in a
whispering-gallery microresonator, as proposed by Hafezi and Rabl.
Optomechanically induced non-reciprocal transparency and amplification are
observed, and a non-reciprocal phase shift of up to 40 degrees is demonstrated
in this study. The results of this study represent an important step towards
integrated all-optical controllable isolators and circulators, as well as
non-reciprocal phase shifters.
