Quantum field theory of cooperative atom response: Low light intensity

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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, three, five, etc., ground-state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for a 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 noncooperative atoms by presenting a mathematical example in which this approach is exact.
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