Quantum and Nonlinear Effects in Light Transmitted through Planar Atomic Arrays. (arXiv:1907.07030v1 [quant-ph])

We identify significant quantum many-body effects, robust to position
fluctuations and strong dipole--dipole interactions, in the forward light
scattering from planar arrays and uniform-density disks of cold atoms, by
comparing stochastic electrodynamics simulations of a quantum master equation
and of a semiclassical model that neglects quantum fluctuations. Quantum
effects are pronounced at high atomic densities with the light close to
saturation intensity, and especially at subradiant resonances. We find an
enhanced semiclassical model with a single-atom quantum description provides
good qualitative, and frequently quantitative agreement with the full quantum
solution. We use the semiclassical simulations for large ensembles that would
otherwise be numerically inaccessible, and observe collective many-body
analogues of resonance power broadening and vacuum Rabi splitting, as well as
significant suppression in cooperative reflection from atom arrays.

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