QUANTUM-FIELD THEORY OF COOPERATIVE ATOM RESPONSE - LOW-LIGHT INTENSITY

We study the interactions of a possibly dense and/or quantum degenerat e gas with driving light. Both the atoms and the electromagnetic field s are represented by quantum fields throughout the analysis. We introd uce a field-theory version of Markov and Born approximations for the i nteractions of light with matter, and devise a procedure whereby certa in 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 fin d a hierarchy of equations of motion for correlation functions that co ntain 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 s ystem of electromagnetic fields and charged harmonic oscillators. We d iscuss the emergence of resonant dipole-dipole interactions and collec tive linewidths, and delineate the limits of validity of the column de nsity approach in terms of noncooperative atoms by presenting a mathem atical example in which this approach is exact.