ObjectiveIn quantum optics, (nature) atoms are orders of magnitude smaller than the wavelength of the light they interact with, which justifies the dipole approximation by allowing them to be viewed as point-like emitters. However, recent experiments extending the small (nature) atom platform to artificial 'giant' atomic systems built from superconducting circuits, represent a breakdown of the dipole approximation and have attracted significant attention. The waveguide quantum electrodynamics systems with giant atoms have emerged as a new promising platform for engineering transport of photons and single-photon routing. The system enables strong tunable atom-waveguide coupling and manifests multiple-point self-interference in the photon scattering spectra. Recently, a setup with chiral interfaces between giant atoms and waveguides is no longer challenging based on technological progress, in particular, the chiral coupling can also allow decoherence-free states, nonreciprocal photon transport, and tunable Markovianity. Few studies have also considered the unequal local phases at different coupling points for photon routing. Nevertheless, here we study the single-photon scattering problem by considering chiral local coupling phases.MethodWe consider the system Hamiltonian in real-space and linear dispersion relation. We solve the Schrödinger equation within the single-photon manifold by considering the δ-function potential effect of the atom at the coupling point, where an appropriate ansatz is used for the probability amplitudes of the system's state, and the transmission and reflection coefficients are found with the direction-dependent propagating phases. The effects induced by chiral phases in the scattering spectra are studied by engineering the local coupling phases and coupling strengths.Results and DiscussionsWe show that the transmission spectrum of an incident photon can transition from complete transmission to total reflection when the chiral phases satisfy specific conditions, regardless of the number of coupling points. In particular, the Lamb shifts vanishes at resonance, allowing for in situ control of the photon transport by varying the propagating phases. Moreover, when the internal atomic spontaneous emission is introduced, we show that perfect nonreciprocal photon scattering can be achieved by engineering the chiral local phases, in contrast to the non-Markovian retardation effect.ConclusionWe have studied the effect of chiral local coupling phases on single-photon scattering. By engineering the chiral phases, it is not only possible to flexibly control the single-photon scattering properties, but also to achieve perfect nonreciprocal photon scattering. The findings of this study indicate that the giant-atom-waveguide system with chiral local coupling phases is a promising candidate for realizing single-photon routers and has potential applications in quantum network engineering and quantum information processing.