Analytic Few Photon Scattering in Waveguide QED

Abstract

We develop an approach to light-matter coupling in waveguide QED based upon scattering amplitudes evaluated via Dyson series. For optical states containing more than single photons, terms in this series become increasingly complex and we provide a diagrammatic recipe for their evaluation, which is capable of yielding analytic results. Our method fully specifies a combined emitter-optical state that permits investigation of light-matter entanglement generation protocols. We use our expressions to study two-photon scattering from a $\Lambda$-system and find that the pole structure of the transition amplitude is dramatically altered as the two ground states are tuned from degeneracy.

14 pages, 9 figures

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• Few-photon Fock-state wave packet interacting with a cavity-atom system in a waveguide: Exact quantum state dynamics
• Generating maximal entanglement between spectrally distinct solid-state emitters
• Few-photon Transport in Fano-resonance waveguide geometries
• Two emitters coupled to a bath with Kerr-like non-linearity: Exponential decay, fractional populations, and Rabi oscillations
• Correlated Dephasing Noise in Single-photon Scattering
• Single photons versus coherent state input in waveguide quantum electrodynamics: light scattering, Kerr and cross-Kerr effect
• Two-photon scattering in mixed cavity optomechanics
• Input-Output Hierarchical Equations Of Motion
• Two-Photon Scattering in USC regime
• Photon routing in disordered chiral waveguide QED ladders: Interplay between photonic localization and collective atomic effects