  We investigate the scattering processes of two photons in a one-dimensional
waveguide coupled to two giant atoms. By adjusting the accumulated phase shifts
between the coupling points, we are able to effectively manipulate the
characteristics of these scattering photons. Utilizing the Lippmann-Schwinger
formalism, we derive analytical expressions for the wave functions describing
two-photon interaction in separate, braided, and nested configurations. Based
on these wave functions, we also obtain analytical expressions for the
incoherent power spectra and second-order correlation functions. In contrast to
small atoms, the incoherent spectrum, which is defined by the correlation of
the bound state, can exhibit more tunability due to the phase shifts.
Additionally, the second-order correlation functions in the transmission and
reflection fields could be tuned to exhibit either bunching or antibunching
upon resonant driving. These unique features offered by the giant atoms in
waveguide QED could benefit the generation of nonclassical itinerant photons in
quantum networks.
