Collective dipole-dipole interactions in an atomic array

The coherent photon scattering of atoms in an atomic array is studied. It is found that due to cooperative photon exchanges, the excitation probability of an atom in an array parallel to the direction of laser propagation ((k) over cap) will either grow or decay along (k) over cap, depending on the detuning of the laser. The symmetry of the system for atomic separations of a = j lambda/2 causes the excitation distribution and scattered radiation to abruptly become symmetric about the center of the array, where j is an integer and lambda is the transition wavelength. For atomic separations of a = lambda/2, a collection of nonradiating states (Gamma similar to 0) disrupts the described trend. In order to interpret this surprising result, a band-structure calculation in the N -> 8 limit is conducted, where the decay rates and the collective Lamb shifts of the eigenmodes versus quasimomentum are obtained. This calculation shows that the collective exchange of photons in an array strongly affects its scattered radiation, allowing one to easily manipulate the collective Lamb shift and directly excite either superradiant or subradiant eigenmodes by correctly choosing the angle of the driving laser.