Quantum theory of propagation of nonclassical radiation in a near-resonant medium

Abstract

We develop the quantum theory of the propagation of nonclassical radiation in a nearly resonant medium. The medium is taken to have two levels, which are coupled by the radiation field. Heisenberg equations of motion are developed and compared with stochastic equations in a positive P representation. Initial conditions for absorbers and amplifiers are calculated, so that, for example, superfluorescence or self-induced transparency can be treated. The theoretical methods introduced here allow nonclassical statistics of the radiation field to be calculated such as photon antibunching or squeezing. Both radiative and collisional damping are included.