N-atom optical Bloch equations: A microscopic theory of quantum optics.

Abstract

We present a microscopic optical-Bloch-equation model for N two-level atoms being driven by a monochromatic radiation field. The model is obtained from the equations of motion that result from the microscopic Hamiltonian by introducing at a certain stage an Ansatz that accounts for spontaneous emission and bath dephasing in a unitary manner. The equations of motion are a numerically tractable set of coupled c-number differential equations with a discrete, stochastic term deduced from the quantum-mechanical equations of motion. We apply these equations to various model problems and show that they correctly describe such varied optical phenomena as superradiance, photon echoes, and absorptive bistability. In particular, they yield an interesting microscopic picture of the dynamical phase transition that occurs in the latter example. We conclude that this unified approach has advantages that make it useful for studying a number of problems of current interest.