Dicke superradiance in ordered lattices: role of geometry and dimensionality.

We investigate the role of dimensionality and geometry on the collective decay of large atomic arrays. A fully inverted ensemble of atoms at a single point is well known emits a short burst of light that initially grows in intensity and photons are emitted in a burst, so-called Dicke superradiance. For mesoscopic systems, the nature of the decay can be characterized from the statistics of the first two photons, which we evaluate in linear time. For 1D arrays, Dicke superradiance occurs due to suppression of decay channels, is bounded, and cannot occur for any atom number above a particular distance. In 2D and 3D, it occurs due to constructive interference. In 2D, the maximum interatomic distance for it scales sub-logarithmically with atom number, and as a power law for 3D. In contrast to Dicke's original work, we show that superradiance survives in arrays where the smallest interparticle distance is larger than a wavelength.