Counting statistics of collective photon transmissions

We theoretically study cooperative effects in the steady-state transmission of photons through a medium of $N$ radiators. Using methods from quantum transport, we find a cross-over in scaling from $N$ to $N^2$ in the current and even higher powers of $N$ in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source.