### 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 language | English (US) |
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Pages (from-to) | 3939-3948 |

Number of pages | 10 |

Journal | Physical Review A |

Volume | 43 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 1991 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Physical Review A*,

*43*(7), 3939-3948. https://doi.org/10.1103/PhysRevA.43.3939