Quantum field theory of cooperative atom response: Low light intensity

TL;DR

This paper develops a quantum field theoretical framework to analyze the response of dense or quantum degenerate atomic gases to low-intensity light, revealing collective effects and the limits of traditional approaches.

Contribution

It introduces a field theory approach with a hierarchy of equations for atom-light correlations, enabling analysis of cooperative phenomena at low light intensities.

Findings

Derivation of a hierarchy of equations for atom-light correlation functions.

Identification of conditions for the emergence of collective dipole-dipole interactions.

Demonstration of the limits of the column density approach for non-cooperative atoms.

Abstract

We study the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field theory version of Markov and Born approximations for the interactions of light with matter, and devise a procedure whereby certain types of products of atom and light fields may be put to a desired, essentially normal, order. In the limit of low light intensity we find a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact.