Higher-order mean-field theory of chiral waveguide QED

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.

16+9 pages, 9+2 figures

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• Chiral Quantum Optics
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• Quantum Optics of Chiral Spin Networks
• Quantum marginal problem and representations of the symmetric group
• Collective shift in resonant light scattering by a one-dimensional atomic chain
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• Predicting correlations in superradiant emission from a cascaded quantum system
• Chiral SQUID-metamaterial waveguide for circuit-QED
• Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms
• Light scattering properties beyond weak-field excitation in atomic ensembles
• Emergence of second-order coherence in superfluorescence