MICROSCOPIC FOUNDATION OF THE PHENOMENOLOGICAL FEW-LEVEL APPROACH TO COHERENT SEMICONDUCTOR OPTICS

It is shown how a phenomenological few-level description of coherent s emiconductor optics is related to microscopic density-matrix theory. I t turns out that the few-level dynamics is not obtained by simply proj ecting the microscopic dynamics onto a suitable chosen set of energy e igenstates. Therefore, a new hierarchy of microscopic densities is int roduced with the property that their expansion in terms of energy eige nstates yields the level dynamics. The transformation rules between th e few-level variables and the traditional density matrices are establi shed. The problem of incorporating the coupling to continua into a few -level model is discussed. A refined few-level model approximating the influence of the continua by modified couplings between the levels is presented. The modified couplings turn out to be similar in structure to phenomenologically introduced refinements like local fields. The a nalysis makes clear that intuitively similar approximations have a dif ferent meaning when applied in the context of a few-level model or a t runcated microscopic hierarchy.