Quantum Multiphoton Rabi Oscillations in Waveguide QED

The future of quantum information processing hinges on chip-scale nanophotonics, specifically cavity QED and waveguide QED. One of the foremost processes underpinning quantum photonic technologies is the phenomenon of Rabi oscillations, which manifests when a qubit is irradiated by an intense laser source. Departing from the conventional semiclassical framework, we expound on the more general, quantum-theoretic case where the optical excitation takes the form of a multiphoton Fock state, and the qubit couples to a continuum of radiation modes. By employing the real-space formalism, we analytically explore the scattering dynamics of the photonic Fock state as it interfaces with a two-level emitter. The resulting amplitude for atomic excitation features a linear superposition of various independent scattering events that are triggered by the potential of sequential photon absorptions and emissions. The lowest-order excitation event, initiated by the stochastic scattering of one of the several photons, aptly characterizes the dynamics in a weak-field environment. This is complemented by a multitude of higher-order scattering events ensuing from repeated atom-photon interactions. The temporal evolution of the qubit excitation in our configuration closely mirrors the semiclassical predictions, particularly in the strong-pumping limit where Rabi oscillations unfold. Notably, this compatibility with the semiclassical paradigm applies both to the weak-driving and large-detuning limits. Our analysis, therefore, extends the existing results on quantum Rabi oscillations pertinent to single-mode cavity QED, to the multimode, waveguide-QED configurations wherein flying photons are the information carriers. Finally, we explore the scattering dynamics of pulsed wave packets, highlighting the potential to substantially enhance excitation efficiency, even in scenarios involving just a few photons.