Higher-order mean-field theory of chiral waveguide QED

TL;DR

This paper develops an advanced mean-field theory using higher-order cumulant expansions to accurately describe the complex quantum dynamics of large atomic ensembles in waveguide QED, especially under weak coupling and strong driving conditions.

Contribution

It introduces a systematic higher-order cumulant expansion approach to improve mean-field predictions for waveguide QED systems, capturing many-body correlations and long-range interactions.

Findings

Accurately predicts transmitted power and squeezing spectra.

Reveals the significance of many-body correlations in steady state.

Shows good agreement with experimental data.

Abstract

Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, 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 convergence 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.