Chiral and nonreciprocal transmission of single photons in coupled-resonator-waveguide systems

In this paper, we employ two two-level atoms and a $\mathrm{\ensuremath{\Lambda}}$-type atom to connect two one-dimensional semi-infinite coupled resonator waveguides, respectively. The first configuration is a chiral setup, where incident photons undergo an elastic scattering process. We investigate the influence on the single-photon transfer rate of spatial coupling points between the small or giant atom and the waveguides. Our numerical simulations demonstrate that additional coupling points in the giant atom system will modify the transmission rule observed in the small atom system due to their unique interference effects. The second configuration is a nonreciprocal setup, where the conduction direction depends entirely on the initial state of the $\mathrm{\ensuremath{\Lambda}}$-type atom. The incident photon undergoes an inelastic scattering process accompanied by frequency conversion.