Diagrammatic approach for analytical non-Markovian time evolution: Fermi's two-atom problem and causality in waveguide quantum electrodynamics

Abstract

Non-Markovian time evolution of quantum systems is a challenging problem, often mitigated by employing numerical methods or making simplifying assumptions. In this work, we address this problem in waveguide quantum electrodynamics (QED) by developing a diagrammatic approach, which performs fully analytical non-Markovian time evolution of single-photon states. By revisiting Fermi's two-atom problem, we tackle the impeding question of whether the rotating-wave approximation violates causality in single-photon waveguide QED. Afterward, we introduce and prove the no upper half-plane poles (no-UHP) theorem, which connects the poles of scattering parameters to the causality principle. Finally, we visualize the time-delayed coherent quantum feedback mediated by the field and discuss the Markovian limit for microscopically separated qubits where short-distance causality violations occur and the emergence of collective decay rates in this limit. Our diagrammatic approach is a method to perform exact and analytical non-Markovian time evolution of multiemitter systems in waveguide QED.