Many-Body, Non-Markovian, Collective Radiance in Waveguide QED

Multi-atom waveguide QED provides an ideal setting to explore emergent many-body behavior, including collective phenomena such as superradiance and subradiance. For atoms separated on macroscopic scales, photon propagation mediates retarded interactions due to finite traversal times. When propagation delays are short, it is common to adopt a Markovian treatment, effectively assuming inter-atomic feedback to be instantaneous. Here, we examine the validity of the Markov approximation as a function of atom number.

Using a delayed-feedback framework, we investigate the decay of single-excitation superradiant states in waveguide QED platforms. For small ensembles and short propagation delays, the resulting behavior is quantitatively well captured by the Markov approximation. Strikingly, this approximation breaks down for large atom numbers, even when the delay times remain small. We attribute this failure to competing timescales associated with individual-atom decay processes and collectively enhanced (superradiant) dynamics. Consequently, increasing the ensemble size drives a crossover from quasi-Markovian behavior to a regime in which decay is substantially shaped by time-delayed interactions, signaling an emergent non-Markovianity rooted in collective effects.