Wigner Crystallization of Single Photons in Cold Rydberg Ensembles. J. Otterbach, M. Moos, D. Muth and M. Fleischhauer in Phys. Rev. Lett. 111:113001 (2013).  What the paper says?

This paper interests us in connection to our perfect single-photon source and liquefaction of light, since it provides a mechanism to realize what we call photon liquids. This is particularly apparent from their Fig. 3:

where even the least correlated case (orange curve) displays oscillations as in our $N=3$ case. They also highlight the gap (where the correlation vanish over small distances). The large-$z$ behaviour given by Lieb-Liniger expression deserves further attention. Their numerical (Density matrix renormalization group) results are not exactly those of our analytical cascade mechanism, but is very close:

Otterbach is more correlated. While this is not in time, but properly in space, the transition could be made by a sudden switch-off the driving, to let free the "Wigner crustal and convert it into a stream of photons (our liquid light):

The "long-range" order is, however, limited to the extent of the medium, while our liquid light is of infinite extent (keep pumping).