The Rydberg blockade mechanism leads to an effective two-level physics when two photons are separated by less than the blockade radius resulting in a strong anti-correlation of two photons given by an avoided volume. For large separations the repulsive long-range interaction between the Rydberg atoms induces repulsive interactions between the photons leading to quasi-crystalline states of photons. Confining the system to one dimension the low-energy physics of the excitations can be described in terms of a Luttinger Liquid.

Using DMRG simulations the Luttinger K-parameter is calculated and conditions on the formation of long-range ordered states are derived. Implications of the formation of such hard-sphere photons for the recent experiment of Pritchard et al. [Phys. Rev. Lett. 105, 193603 (2010)] and the observation of long-range correlations in future experiments will be discussed.