Breaking the Exponential: Decoherence‐Driven Power‐Law Spontaneous Emission in Waveguide Quantum Electrodynamics

We investigate the spontaneous emission of a two‐level system coupled to a photonic waveguide, showing that dynamical dephasing in the photon modes profoundly alters the decay law. In the absence of dephasing, the emitter displays conventional exponential decay followed by a long‐time power‐law tail – observable only at extremely low survival probabilities. Strikingly, when dephasing is introduced, a robust power‐law decay emerges already at short times, driven by photon diffusion in the dynamically disordered environment rather than spectral edge effects. These results reveal a novel, decoherence‐induced mechanism for non‐exponential spontaneous emission in waveguide QED platforms.