Derivation of Maxwell-Bloch-type equations by projection of quantum models

TL;DR

This paper presents a straightforward algebraic method to derive Maxwell-Bloch-type equations from quantum models, incorporating corrections and stochastic effects, useful for simulating quantum optical systems.

Contribution

It introduces a simple projection technique to obtain Maxwell-Bloch equations from cavity QED models, including stochastic extensions with noise terms.

Findings

Derivation of Maxwell-Bloch equations from Jaynes-Cummings model.

Inclusion of state-dependent correction factors.

Development of stochastic models with multiplicative noise.

Abstract

A simple algebraic procedure is described for deriving Maxwell-Bloch-type equations from single-atom cavity quantum electrodynamics (cavity QED) master equations via orthogonal projection onto a manifold of semiclassical states. In particular the usual Maxwell-Bloch Equations are obtained--up to a state-dependent correction factor of order unity--straightforwardly from the unconditional Jaynes-Cummings master equation. The technique of projecting onto a semiclassical manifold can also be applied with conditional master equations (quantum filters), leading to stochastic simulation models that include multiplicative noise terms associated with fluctuations of the atomic dipole. The utility of such models is briefly explored in the context of single-atom absorptive bistability.