Quantum theory of multiwave mixing. I. General formalism

Abstract

We present a theory that describes how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear two-level medium. The analysis is applicable to several popular problems with and without cavities. In particular, the theory treats laser and optical bistability instabilities, predicting when the instabilities grow from spontaneous emission. The theory is a multimode extension of Scully-Lamb theory that derives the equations that describe population pulsations, combination tones, mode locking, resonance fluorescence, Rayleigh scattering, and phase conjugation with quantum-mechanical fields. Hence the theory both presents new results on instabilities and phase conjugation, and also unifies the treatment of a variety of phenomena in the context of Lamb theory. The present paper (first of the series) presents the basic formalism, leaving most applications to subsequent papers in this series. The following paper presents equivalent derivations based on a purely operator formalism.