  In this paper, we begin with a model of a $\Lambda$-type atom whose both transitions are chirally coupled to a waveguide and then extend the model to its giant-atom version. We investigate the single-photon scatterings of the giant-atom model in both the Markovian and non-Markovian regimes. It is shown that the chiral atom-waveguide couplings enable nonreciprocal, reflectionless, and efficient frequency conversion, while the giant-atom structure introduces intriguing interference effects to the scattering behaviors, such as ultra-narrow scattering windows. The chiral giant-atom model exhibits quite different scattering spectra in the two regimes and, in particular, demonstrates non-Markovicity induced nonreciprocity under specific conditions. These phenomena can be understood from the effective detuning and decay rate of the giant-atom model. Our results have potential applications in integrated photonics and quantum network engineering. 
Nonreciprocal frequency conversion with chiral $\Lambda$-type atoms