Single‐Excitation Scattering With Waveguide QED in A Cavity‐Trapping‐Two‐Atoms System

ABSTRACT

We propose a scheme for the single‐photon routing in a hybrid system composed of the cavity‐trapping‐two‐atoms system (CTAS) coupled to two one‐dimensional coupled‐resonator waveguides. By employing the discrete‐coordinate scattering method, exact analytical expressions for the single‐photon scattering amplitudes at the four ports are derived. The results demonstrate that the single‐photon routing characteristics depend not only on the coupling positions, coupling strengths, and local coupling phases between the CTAS and the waveguides, but also critically on the eigenstate structure of the CTAS. Further analysis reveals a clear correspondence between the single‐photon scattering spectrum and the eigenstates of the CTAS, which allows for the classification of the eigenstates involved in cross‐waveguide transport as bright and dark states. By tuning the local coupling phases, coherent enhancement of a specific bright state can be achieved, enabling deterministic single‐photon directional routing. Our work provides a theoretical reference for studies of single‐photon routing in cavity quantum electrodynamics and superconducting circuit platforms.