We propose how to realize nonreciprocity for a weak input optical field via nonlinearity and synthetic magnetism. We show that the photons transmitting from a linear cavity to a nonlinear cavity (i.e., an asymmetric nonlinear optical molecule) exhibit nonreciprocal photon blockade but no clear nonreciprocal transmission. Both nonreciprocal transmission and nonreciprocal photon blockade can be observed, when one or two auxiliary modes are coupled to the asymmetric nonlinear optical molecule to generate an artificial magnetic field. Similar method can be used to create and manipulate nonreciprocal transmission and nonreciprocal photon blockade for photons bi-directionally transport in a symmetric nonlinear optical molecule. Additionally, a photon circulator with nonreciprocal photon blockade is designed based on nonlinearity and synthetic magnetism. The combination of nonlinearity and synthetic magnetism provides us an effective way towards the realization of quantum nonreciprocal devices, e.g., nonreciprocal single-photon sources and single-photon diodes.
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