Macroscopic Approach to Quantum Optics

Abstract

This paper investigates how an approach alternative to the canonical quantization schemes may be used to describe Quantum Optics phenomena. By utilizing the approach pioneered by Keldysh, we derive equations for the time dependent correlation functions of the quantized optical fields. These contain the coupling to matter in linear and nonlinar response functions which replace the material parameters of phenomenological macroscopic theories. We present these results as alternatives to existing theoretical methods in Quantum Optics. The paper presents the general formulation of the theory, derives the equations in some specific cases relating to non-linear optics, and solves some illustrative special cases. We regain known results but also some additional terms deriving from the quantum fluctuations of the material media.