  We study the coherent single-photon scattering in a one-dimensional waveguide
coupled to a giant artificial molecule consisting of two coupled giant atoms.
Since each giant atom couples to the waveguide via two coupling points, the
couplings of the molecule with the waveguide have three different coupling
configurations: the separated-, braided-, and nested-coupling cases. We obtain
the exact expressions of the single-photon transmission and reflection
amplitudes with the real-space approach. It is found that the behavior of the
scattering spectra depends on the phase shift between two neighboring coupling
points, the coupling configuration, and the coupling between the two giant
atoms. Concretely, we study the photon scattering in both the Markovian and
non-Markovian regimes, in which the photon propagating time between two
neighboring coupling points is neglected and considered, respectively. Under
the Markovian limit, the asymmetric Fano line shapes in different coupling
configurations of the giant-molecule waveguide-QED system can be obtained by
choosing proper phase shift, and the transmission window can be adjusted by the
coupling strength between the two giant atoms in these three coupling
configurations. In particular, multiple reflection peaks and dips in these
configurations are revived in the non-Markovian regime. This paper will pave
the way for the study of controllable single-photon devices based on the
giant-molecule waveguide-QED systems.
