Collective decay in inverted three-dimensional and two-dimensional atomic arrays

Since the first studies of super radiance by Dicke in the 1950s, collective effects have caught the interest of the physics community. Although in this first study all particles were assumed to be in the same position, super and sub radiance persist even for extended samples larger than a resonant wavelength. We hereby study the collective decay of inverted three- and two-dimensional arrays with sub wavelength spacing using the Keldysh contour formalism and show that the time evolution of the system presents a super radiant outburst and a subradiant regime for small enough spacings. These systems can be currently realized experimentally.