Subradiant Emission from Regular Atomic Arrays: Universal Scaling of Decay Rates from the Generalized Bloch Theorem

The Hermitian part of the field-mediated dipole-dipole interaction in infinite periodic arrays of two-level atoms yields an energy band of the singly excited states. In this Letter, we show that a dispersion relation, ω_{k}-ω_{k_{ex}}∝(k-k_{ex})^{s}, near the band edge of the infinite system leads to the existence of subradiant states of finite one-dimensional arrays of N atoms with decay rates scaling as N^{-(s+1)}. This explains the recently discovered N^{-3} scaling and it leads to the prediction of power law scaling with higher power for special values of the lattice period. For the quantum optical implementation of the Su-Schrieffer-Heeger topological model in a dimerized emitter array, the band gap closing inherent to topological transitions changes the value of s in the dispersion relation and alters the decay rates of the subradiant states by many orders of magnitude.