Controllable nonreciprocal single-photon frequency conversion in a T-shape giant-atom waveguide-QED system

-type atom coupled to a T-shaped waveguide. By controlling local coupling phases to engineer quantum interference, perfect directional frequency conversion is achieved without an engineered chiral waveguide structure. The multi-path interference of the giant atom, combined with local phase tuning, enables flexible control over photon transmission direction and frequency, supporting multiple directional conversion channels. In the Markovian limit, the cavity-mediated structure realizes two fully efficient directional channels, while under non-Markovian conditions, retardation effects open several distinct frequency conversion windows. This phase-controlled, multi-frequency directional architecture provides a versatile platform for frequency-multiplexed quantum routing and networking.