Higher-order mean-field theory of chiral waveguide QED

Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even weak coupling strong photon loss, collective enhancement light-atom interactions leads to correlations photons arising in transmission, as shown recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions describe experimentally relevant, but theoretically elusive, regime driving large ensembles. We determine transmitted power, squeezing spectra degree second-order coherence, systematically check convergence results by comparing that truncate cumulants few-particle at increasing order. This reveals important role many-body long-range between steady state. Our approach allows quantify trade-off anti-bunching output power previously inaccessible parameter regimes. Calculated show good agreement measured data, present here.