Tunable Photon-Photon Correlations in Waveguide QED Systems with Giant Atoms

We investigate the scattering processes of two photons in a one-dimensionalwaveguide coupled to two giant atoms. By adjusting the accumulated phase shiftsbetween the coupling points, we are able to effectively manipulate thecharacteristics of these scattering photons. Utilizing the Lippmann-Schwingerformalism, we derive analytical expressions for the wave functions describingtwo-photon interaction in separate, braided, and nested configurations. Basedon these wave functions, we also obtain analytical expressions for theincoherent power spectra and second-order correlation functions. In contrast tosmall atoms, the incoherent spectrum, which is defined by the correlation ofthe bound state, can exhibit more tunability due to the phase shifts.Additionally, the second-order correlation functions in the transmission andreflection fields could be tuned to exhibit either bunching or antibunchingupon resonant driving. These unique features offered by the giant atoms inwaveguide QED could benefit the generation of nonclassical itinerant photons inquantum networks.