We propose to achieve nonreciprocal quantum control of photons in a quadratic optomechanical (QOM) system based on directional nonlinear interactions. We show that by optically pumping the QOM system in one side, the effective QOM coupling can be enhanced significantly in that side, but not for the other side. This, contrary to the intuitive picture, allows the emergence of a nonreciprocal photon blockade in such optomechanical devices with weak single-photon QOM coupling. Our proposal opens up the prospect of exploring and utilizing quantum nonreciprocal optomechanics, with applications ranging from single-photon nonreciprocal devices to on-chip chiral quantum engineering.

We propose how to achieve quantum nonreciprocity via unconventional photon blockade (UPB) in a compound device consisting of an optical harmonic resonator and a spinning optomechanical resonator. We show that, even with very weak single-photon nonlinearity, nonreciprocal UPB can emerge in this system, i.e., strong photon antibunching can emerge only by driving the device from one side but not from the other side. This nonreciprocity results from the Fizeau drag, leading to different splitting of the resonance frequencies for the optical counter-circulating modes. Such quantum nonreciprocal devices can be particularly useful in achieving back-action-free quantum sensing or chiral photonic communications.

We study optomechanically induced transparency in a spinning microresonator. We find that in the presence of rotation-induced Sagnac frequency shift, both the transmission rate and the group delay of the signal are strongly affected, leading to a Fano-like spectrum of transparency. In particular, tuning the rotary speed leads to the emergence of nonreciprocal optical sidebands. This indicates a promising new way to control hybrid light–sound devices with spinning resonators.