Theory of photon statistics in inverted waveguide-coupled atom arrays in the thermodynamic limit

Waveguide quantum electrodynamics (WQED) offers a powerful theoretical framework for controlling light–matter interactions and realizing collective phenomena such as super- and subradiance. In general waveguide settings, the quantum dynamics spans the full Hilbert space, rendering exact theoretical treatments exponentially difficult and currently out of reach, and only a few models admit exact analytical solutions. In this work, we treat the thermodynamic limit of the number of atoms, N → ∞, while the homogeneous atom–waveguide coupling β → 0, keeping the optical depth, 4Nβ, fixed. We derive exact analytical solutions for photon statistics in chiral and symmetric waveguide setups starting from full inversion. In this limit, a special time, ≈ 1.59 x the single-atom lifetime, separates super- and subradiant dynamics. Additionally, we show an exponentially enhanced superradiance as the optical depth is increased. We also show that the initial shot-to-shot fluctuations in the emitted photon number diminish in a chiral system and vanish in a symmetric system. Finally, the equal-time second-order correlation becomes trivial, showing that finite-size effects are essential to observe the emergence of second-order coherence. Our results illustrate finite- and infinite-body collective effects in symmetric and symmetry-lacking systems.