Dicke superradiance in atomic arrays: Part 1*

We investigate the physics of collective decay in ordered arrays. The decay of a fully inverted ensemble of atoms at a single point is well known: the emitted light initially grows in intensity and photons are emitted in a short burst, so-called Dicke superradiance. However, atoms separated by large distances act independently and their decay is exponential, monotonically decreasing in time. In the intermediate regime, where atoms have finite separation but still behave collectively, calculating the emission requires evolution in a Hilbert space that grows exponentially with atom number. However, the nature of the decay can be characterized from the statistics of the first two photons. This reduces the problem to a concise and exact inequality - which is applicable to arrays of any dimensionality and topology - that can be evaluated in linear time. This can be used to find the critical interatomic distance beyond which superradiance disappears.