Higher-order mean-field theory of chiral waveguide QED

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

Automated summary

Waveguide QED with cold atoms is a powerful tool for studying non-equilibrium, many-body, and open-system quantum dynamics. In recent experiments, even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions has led to strong correlations of transmitted photons. In this study, an improved mean-field theory based on higher-order cumulant expansions is applied to describe the theoretically elusive regime of weak coupling and strong driving of large ensembles, yielding insights into the role of many-body and long-range correlations.