Maximization of the efficiency of the frequency conversion with a spin multiplet subjected to three frequency-correlated fields

Abstract

We investigate theoretically the coherent resonant enhancement of three-field mixing processes in a nonlinear medium characterized by a spin multiplet. The discussion is based on the analytical steady-state solutions of the density matrix equation. These solutions do not assume simplified approximations concerning the number of levels or the relative magnitudes of the Rabi frequencies and relaxation rates. Consequently, they contain interference effects among single- and multiplequantum absorption and emission processes, and parametric processes. This makes it possible to maximize the efficiency and the resonant enhancement of the frequency conversion in a nonlinear medium by manipulating the degree of coherent mixing. The highest efficiency and resonant enhancement of the frequency conversion could be obtained if the three fields are strong, their coherent mixing is negligible, and the differences of the corresponding Rabi frequencies are small. If these differences are large, the conversion efficiency is maximized if the coherent mixing is maximized too. For a spin multiplet, the resonant enhancements of three-field mixing processes have strong temperature dependences and exhibit maximum values at optimum temperatures that are relatively high. Although the discussion is applied to a spin multiplet, it can also be extended to the general case of multilevel atomic systems.