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

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.

4 pages, 1 EPS figure

References in corpus (5)

• Linear stochastic wave-equations for continuously measured quantum systems
• Stochastic Schrodinger equations
• Low-lying bifurcations in cavity quantum electrodynamics
• Quantum projection filter for a highly nonlinear model in cavity QED
• Retroactive quantum jumps in a strongly-coupled atom-field system

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