Subradiant emission from regular atomic arrays: universal scaling of decay rates from the generalized Bloch theorem

TL;DR

This paper demonstrates that the decay rates of subradiant states in atomic arrays follow a universal power-law scaling determined by the dispersion relation near the band edge, with implications for quantum optical systems and topological transitions.

Contribution

It establishes a universal relation between dispersion relation exponents and subradiant decay scaling in atomic arrays, extending understanding of collective emission phenomena.

Findings

Decay rates scale as N^{-(s+1)} near the band edge.

The known N^{-3} scaling is explained by this universal relation.

Topological transitions can significantly alter decay rates by changing the dispersion exponent.

Abstract

The Hermitian part of the dipole-dipole interaction in infinite periodic arrays of two-level atoms yields an energy band of singly excited states. In this Letter, we show that a dispersion relation, $\omega_k-\omega_{k_\ex} \propto (k-k_{\ex})^s$, 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 (SSH) 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.