Cooperative states and shift in resonant scattering of an atomic ensemble

TL;DR

This paper explores the spectral shift in collective forward scattering of cold atomic clouds, revealing two distinct types of shifts with different scaling laws and providing insights into the controversy over their origins.

Contribution

It introduces a Monte-Carlo simulation approach to distinguish two types of collective spectral shifts and clarifies their different scaling behaviors in dense atomic ensembles.

Findings

Two types of collective spectral shifts identified

One shift is density-insensitive, the other scales linearly with optical depth

Simulation clarifies the controversy over the scaling property

Abstract

Abstract We investigate the spectral shift in collective forward scattering for a cold dense atomic cloud. The shift, sometimes called collective Lamb shift, results from resonant dipole-dipole interaction mediated by real and virtual photon exchange, forming many-body states displaying various super- and subradiant spectral behavior. The scattering spectrum reflects the overall radiative behavior from these states. However, it also averages out the radiative details associated with a single collective state, causing ambiguity in explaining the origin of the spectral shift and raising controversy on its scaling property. We employ a Monte-Carlo simulation to study how the collective states are occupied and contribute to emission. We thus distinguish two kinds of collective shift that follow different scaling laws. One results from dominant occupation of the near-resonant collective states. This shift is usually small and insensitive to the density or the number of participating atoms. The other comes from large spatial correlation of dipoles, associated with the states of higher degree of emission. This corresponds to larger collective shift that is approximately linearly dependent on the optical depth. Our analysis provides not only a novel perspective for the spectral features in collective scattering, but also a possible resolution to the controversy on the scaling property that has been reported elsewhere because of different origins.