Collective photon emission from symmetric states created with Rydberg atoms on a ring lattice

We discuss the creation of non-classical light from collective atomic states that are prepared in a ring-shaped lattice. These states are realized by exploiting the strong interaction between atoms in high lying energy levels - so-called Rydberg states - and yield a resource for creating excitations of the electromagnetic field that carry few photons. We characterize the properties of these photonic states showing that they are determined by the interplay between the ring geometry, the structure of the atomic resource states and the collectivity in the photon emission which is controlled by the lattice spacing. The system permits the creation of single photons with well-defined orbital angular momentum and two-photon states that are entangled in orbital angular momentum.