Quantum theory of multiwave mixing

A theory describing how one or two strong classical waves and one or two weak quantum mechanical waves interact in a two-level medium is formulated and applied. The theory unifies many topics in quantum optics, such as resonance fluorescence, saturation spectroscopy, modulation spectroscopy, the build up of laser and optical bistability instabilities, and phase conjugation. The theory is based on a quantum population pulsation approach that resembles the semiclassical theories, but is substantially more detailed. Calculations are performed to include the effects of inhomogeneous broadening, spatial hole burning, and Gaussian transverse radiations. The resonance fluorescence spectrum in a high fitness optical cavity is analyzed in detail, demonstrating how stimulated emission and multiwave processes alter the spectrum from the usual three peaks. The effects of quantum noise during the propagation of weak signal and conjugate fields in phase conjugation and modulation spectroscopy are studied. Analysis demonstrates that quantum noise affects not only the intensities of the signal and conjugate, but also their relative phase, and in particular a quantum limit to the semiclassical theory of FM modulation spectroscopy. The corresponding theory for the two-photon, two-level medium is also derived. This yields the first calculation of the two-photon resonance fluorescence spectrum. Because of the greater number of possible interactions in the two-photon two-level model, the theoretical formalism is considerably more complex, and many effects arise that are absent in the one-photon problem.