No oscillating subradiant correlations in a strongly driven quantum emitter array

Abstract

We theoretically study time-dependent correlations in a strongly driven array of $N$ two-level atoms, coupled to photons in a waveguide. We focus on the spectrum $\{\hat{I}»\}$ of the Liouvillian superoperator, which determines the correlation decay rates $-\Re \hat{I}»$ and the frequencies $\Im \hat{I}»$. Our main finding is the suppression of subradiant oscillating correlations between atomic states by a strong coherent drive of amplitude $\hat{I}\text{c◯}$: $|\Re \hat{I}»|\ge m{\hat{I}}^3/2$, where ${\hat{I}}^3$ is the single-atom spontaneous decay rate and $m=|\Im \hat{I}»/(2\hat{I}\text{c◯})|$ is a nonzero integer for correlations oscillating in time $\propto \exp (\pm 2im|\hat{I}\text{c◯}|t)$. This limit is independent of the number of atoms $N$; it holds both for small arrays and in the macroscopic limit. We demonstrate the suppression of subradiance numerically and provide a rigorous proof based on the analytical decomposition of the Liouvillian using spectral theory of simplicial complexes and posets.

6 pages, 3 figures + End Matter -- one missing word corrected in abstract in v2