Phase-modulated nonreciprocal photon blockade and transmission via optomechanically induced Kerr nonlinearity

We propose a scheme for implementing nonreciprocal transmission and a nonreciprocal photon blockade (PB) in a whispering-gallery-mode optomechanical resonator. By decoupling the mechanical degree of freedom under the Born-Oppenheimer approximation, the system is reduced to one incorporating Kerr-type nonlinearities induced by optomechanical coupling, including self-Kerr nonlinearities of the clockwise (CW) and counterclockwise (CCW) modes and cross-Kerr nonlinearity between these two modes, thereby strong nonreciprocal PB and transmission can be implemented. We demonstrate that the nonreciprocal PB and transmission are sensitive to the relative phase $\ensuremath{\theta}$ between CW and CCW modes, allowing for switching between reciprocity and nonreciprocity of PB and transmission through engineering the relative phase of external driving lasers. Numerical results obtained with experimental parameters validate the feasibility of achieving perfect nonreciprocal PB and transmission. Our paper presents a viable mechanism for the implementation of perfect nonreciprocal PB and transmission, along with a versatile approach of phase modulation, which holds great promise in serving as a chiral single-photon source in unidirectional quantum communications based on quantum nonreciprocal devices.