Quantum theory of nondegenerate multiwave mixing. II. Adiabatic elimination via slowly varying amplitude approximation

Seng Tiong Ho*, Prem Kumar, Jeffrey H. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In this paper, we continue our development of the quantum theory of nondegenerate multiwave mixing in an atomic medium [Phys. Rev. A 37, 2017 (1988)]. In our development, the atomic variables are eliminated using a frequency-domain approach employing a slowly varying amplitude approximation that is more rigorous than the usual adiabatic approximation. We then specialize to the case of four-wave interaction with two strong pump beams and obtain noise correlations of the atomic polarization that are applicable to nondegenerate four-wave mixing. The noise correlations include the effect of atomic collisions that is crucial to the atomic-vapor experiments. After making the usual rotating-wave approximation, the atomic-polarization equations give us a set of temporal coupled-mode equations for the c-number variables corresponding to the annihilation operators. We then further specialize to the single-beam case in which all the relevant modes of interest are collinear and obtain a paired set of coupled-mode equations. In order to apply the theory to experiments employing traveling-wave interaction geometries, in the following paper of this series we will present a formalism to treat the spatial propagation of a quantum field.

Original languageEnglish (US)
Pages (from-to)3939-3948
Number of pages10
JournalPhysical Review A
Volume43
Issue number7
DOIs
StatePublished - Jan 1 1991

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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