Single-photon scattering in giant-atom waveguide systems with chiral coupling

We study single-photon scattering spectra of a giant atom chirally coupled to a one-dimensional waveguide at multiple connection points, and examine chirality induced effects in the scattering spectra by engineering the chirality of the coupling strengths. We show that the transmission spectra typically possess an anti-Lorentzian lineshape with a nonzero minimum, but when the chirality satisfies some specific conditions independent of the number of coupling points, the transmission spectrum of an incident photon can undergo a transition from complete transmission to total reflection at multiple frequency ``windows'', the width of which can be flexibly tuned in situ by engineering the coupling strengths of a certain disordered coupling point. Moreover, we show that a perfect nonreciprocal photon scattering can be achieved due to the interplay between internal atomic spontaneous emission and the chirally external decay to the waveguide, in contrast to that induced by the non-Markovian retardation effect. We also consider the non-Markovian retardation effect on the scattering spectra, which allows for a photonic band gap even with only two chiral coupling points. The giant-atom-waveguide system with chiral coupling is a promising candidate for realizing single-photon routers with multiple channels.