We propose to construct a nonreciprocal single-photon frequency converter via multiple semi-infinite coupled-resonator waveguides (CRWs). We first demonstrate that the frequency of a single photon can be converted nonreciprocally through two CRWs, which are coupled indirectly by optomechanical interactions with two nondegenerate mechanical modes. Based on this nonreciprocity, two different single-photon circulators are proposed in the
T-shaped waveguides consisting of three semi-infinite CRWs, which are coupled pairwise by optomechanical interactions. One circulator is proposed by using two nondegenerate mechanical modes and the other one is proposed by using three nondegenerate mechanical modes. Nonreciprocal single-photon frequency conversion is induced by breaking the time-reversal symmetry, and the optimal conditions for nonreciprocal frequency conversion are obtained. These proposals can be used to realize nonreciprocal frequency conversion of single photons in any two distinctive waveguides with different frequencies and they can allow for dynamic control of the direction of frequency conversion by tuning the phases of external driving lasers, which may have versatile applications in hybrid quantum networks.
Quantum frequency up-conversion is a cutting-edge technique that leverages the interaction between photons and quantum systems to shift the frequency of single photons from a lower frequency to a higher frequency. If a photon before up-conversion was part of an entangled pair, it becomes crucial to comprehend the time-frequency entanglement after up-conversion. In this study, we present a theoretical analysis of the transformation of the time-dependent second-order quantum correlations in photon pairs and find the preservation of such correlations under fairly general conditions. Furthermore, we analyze Hong-Ou-Mandel interference between the signal and frequency-converted idler photons to gain insight into the indistinguishability of the two photons. The visibility of two-photon interference is sensitive to the magnitude of frequency conversion and improves as the frequency separation between two photons decreases.