Single-photon scattering by a giant molecule asymmetrically coupled to parallel waveguides

We investigate single-photon scattering in a waveguide-QED setup, where a giant molecule composed of two frequency-detuned giant atoms is coupled to two parallel waveguides via multiple connection points. The competition between coherent atom–atom coupling and the effective decay rates dictates the splitting of a single resonance into a doublet in the transmission (reflection) spectra. By tailoring the asymmetry of the decay rates and the atomic detuning, one can engineer photon-path interference to optimize the transfer between waveguides; under chiral coupling conditions, this interference can be further harnessed to realize fully deterministic routing. In the non-Markovian regime, retardation effects can reshape the spectra and actively drive transitions between the weak- and strong-coupling regimes, converting an unsplit Markovian resonance into a clearly separated doublet, or conversely merging a split doublet back into a single resonance. For sufficiently long time delays, it further generates multiple resonances and avoided crossings, enriching the spectral response. Our results demonstrate how atomic detuning, decay-rate asymmetry, and non-Markovian retardation cooperate to provide versatile, interference-based control over single-photon routing in multi-port quantum networks.