Photon induced atom recoil in collectively interacting planar arrays

We study the recoil of atoms due to the emission or absorption of photons in atomic arrays with sub-wavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low intensity limit. Shining uniform light on the array gives rise to interesting patterns of excitation and recoil in the array. These arise due to the interference of different eigenmodes of excitation. We study the recoil effects of these eigenmodes and the directional properties of the recoil. The recoil experienced by the array was found to be proportional to the lifetime of the excitation eigenmode, i.e., a subradiant collective decay experiences a substantially larger recoil than from independent atom decay. Pronounced recoil effects can also be seen in highly subradiant cavities made of two curved atomic arrays. We further describe a method to calculate the rate of recoil energy deposited in a steady state situation with a constant incident laser.