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

Abstract

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, ${\ensuremath{\omega}}_{k}\ensuremath{-}{\ensuremath{\omega}}_{{k}_{\mathrm{ex}}}\ensuremath{\propto}(k\ensuremath{-}{k}_{\mathrm{ex}}{)}^{s}$, 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 ${N}^{\ensuremath{-}(s+1)}$. This explains the recently discovered ${N}^{\ensuremath{-}3}$ 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.