Theory of cavity QED with 2D atomic arrays

TL;DR

This paper develops a quantum optical formalism for 2D atomic arrays in optical cavities, accounting for cooperative effects and demonstrating potential for enhanced optomechanical scaling, advancing many-body QED research.

Contribution

It introduces a cavity QED formalism that includes cooperative dipole-dipole interactions and applies it to non-saturated atom arrays, highlighting inhibited damping effects.

Findings

Scattering to non-cavity modes is largely suppressed by cooperative effects.

The formalism is independent of specific cavity structures.

Inhibited damping can improve optomechanical scaling in atom-array membranes.

Abstract

We develop a quantum optical formalism to treat a two-dimensional array of atoms placed in an optical cavity. Importantly, and in contrast to typical treatments, we account for cooperative dipole-dipole effects mediated by the interaction of the atoms with the outside, non-cavity-confined modes. Based on the observation that scattering to these modes is largely inhibited due to these cooperative effects, we construct a generic formalism, independent of the specific cavity structure, and apply it to an array of non-saturated atoms. By further considering the atomic motion, we show that the inhibited damping can lead to a favorable scaling of the optomechanical parameters of an atom-array membrane placed within a cavity. The developed formalism lays the basis for further investigation of many-body QED with atom arrays in transversely confined geometries.