Correlation Signatures For Coherent Three-photon Scattering in Waveguide QED

We study the correlation signatures of a coherent three-photon scattering process by computationally investigating scattering photon wavefunctions, correlation functions, and nonlinear conditional phases. It is shown that both the three-photon bound states and the hybrid states, which consist of two-photon bound states and one unbound photon, contribute to all the correlation signatures. All computational correlation signatures are in good agreement with a recent experiment, wherein a weak coherent photonic state propagates through a quantum nonlinear Rydberg medium [Liang et al., Science359, 783 (2018)SCIEAS0036-807510.1126/science.aao7293].