Cooperative Decay of an Ensemble of Atoms in a One-Dimensional Chain with a Single Excitation

We present an analytic calculation of the cooperative decay of a one-dimensional chain of N two-level atoms in the single-excitation configuration. Whereas the subradiant decay is zero for infinite lattices, we prove that for finite lattice the subradiant decay rate decreases as 1/N. We compare the results obtained using the scalar and the vectorial model. The calculations provide simple analytic expressions for the decay rate of the excitation, for arbitrary lattice spacing.