# Cooperative light scattering from helical-phase-imprinted atomic rings. (arXiv:1801.00559v1 [quant-ph])

We theoretically investigate the light scattering of the super- and

subradiant states which can be prepared by the excitation of a single photon

which carries an orbital angular momentum (OAM).\ With this helical phase

imprinted on the stacked ring of atomic arrays, the subradiant modes show

directional side scattering in the far-field, allowing for light collimation

and quantum storage of light with OAM.\ For the excitations with linear

polarizations, we find a discrete $C_4$ rotational symmetry in scattering for

the number of atoms $N$ $=$ $4n $ with integers $n$, while for circular

polarizations with arbitrary $N$, the azimuthal and $C_N$ symmetries emerge for

the super- and subradiant modes respectively.\ When the radial and azimuthal

polarizations are considered, a mode shift can happen in the scattering

pattern.\ The forward scattering of the superradiant modes can be enhanced as

we stack up the rings along the excitation direction, and for the subradiant

modes, we find the narrowing effects on the scattering in the azimuthal and the

polar angles when more concentric rings are added in the radial direction.\ By

designing the atomic spatial distributions and excitation polarizations,

helical-phase-imprinted subradiant states can tailor and modify the radiation

properties, which is detectable in the directional super- and subradiant

emissions and is potentially useful in quantum information manipulations.