Single photons versus coherent-state input in waveguide quantum electrodynamics: Light scattering, Kerr, and cross-Kerr effect

Abstract

While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock-state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock-state or coherent-state inputs. We particularly investigate light transport properties and the Kerr and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized description of the Kerr and cross-Kerr effect for different types of inputs is formulated using the first-order correlation function to compare the Kerr and cross-Kerr nonlinearity between two photons in these models.