Quantum nonlinear response of few photon Fock-state pulses to a chiral-emitter waveguide-QED system

The study of waveguide-QED systems, where a continuum of quantum field modes is coupled to qubits or two-level systems, has improved our ability to manipulate quantum light-matter interactions on chip. In the typical theoretical approaches to waveguide QED, there are a few necessary approximations, e.g., considering the system in the weak excitation regime, or treating the waveguide as a bath. However, these inherent approximations can break down with short pulse excitation. Here, we investigate the few-photon quantum nonlinear response of chiral qubits, when excited with one and two-photon Fock states. Our theory uses a numerically exact approach, based on Matrix Product States, avoiding the limitations of the usual waveguide-QED approximations. Using a chiral-emitter waveguide system, we show explicitly the breakdown of the weak excitation approximation, and study the single and two-photon nonlinear responses. We demonstrate the impact on the qubit population, and discuss how the phase change can be examined from the photon quantum correlation functions, seeing a radical departure from scattering theory solutions.