Second Order Optical Process of A Randomly Modulated Multi-Level Atom

A stochastic model of a multi-level atom interacting with its environment randomly in its excited states is considered. Assuming a two state-jump model for the random intermediate-state interaction, analytical expressions of emission spectra of three- and four-level atoms in the second order optical process are obtained. In each case, the expression is shown to be separated into three types of terms. Two types of terms correspond to the pure Raman spectrum and the luminescence, respectively, while the other type of term bears a mixed character contributing to broadening of the Raman line when the random modulation is slow and merging into the luminescence when the modulation is fast. This characteristic behavior is discussed with the use of the analytical expressions.