Correlation Localization in Waveguide QED with Delayed Interactions

We study the atom-atom correlation length in an atomic array coupled to a waveguide under the Bragg condition with delayed non-Markovian interactions caused by a finite photon propagation time. Starting from a single excited atom, the excitation partially spreads among all atoms, reaching a steady state. The remaining excitation localizes near the initially excited atom, and the atom-atom correlation length decreases as a power law with the interaction delay. This localization phenomenon reveals how the delay-induced non-Markovian behavior affects the correlation transport in waveguide QED systems.