Quantum theory of multiwave mixing. V. Two-photon two-level model

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Abstract
We extend our theoretical formalism describing how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear medium to the ‘‘two-photon two-level’’ model. In this model, field transitions between two levels not connected by an electric dipole occur by means of a two-photon transition using off-resonant intermediate levels. This model has many similarities with, as well as significant differences from, the corresponding one-photon two-level model that has been treated in the previous papers in this series. The theory yields the first detailed calculation of the two-photon resonance fluorescence spectrum, as well as the complete set of four coefficients that describe the quantum theory of two-, three-, and four-wave mixing.