Band structure and dynamics of single photons in atomic lattices
Phys. Rev. A 114, 033738 – Published 30 September, 2026
DOI: https://doi.org/10.1103/b5r3-k247
Abstract
We investigate single-photon band structure and dynamics of atomic lattices. The calculation of these quantities requires the accurate evaluation of slowly convergent lattice sums generated by long-range photon-mediated interactions. We develop a framework that treats infinite lattices directly without introducing an auxiliary short-distance cutoff, thereby connecting their collective spectra to real-space dynamics. In one and two dimensions, complex bands contain superradiant, subradiant, and dark modes, and radiative loss competes with excitation transport. In contrast, in three dimensions, the collective bands are real away from Bragg-resonant conditions, and coherent transport dominates radiative decay. These results reveal a qualitative change from radiative dynamics in lower-dimensional arrays to predominantly coherent propagation in three dimensions.
