Spontaneous-emission feedback in a three-level quantum system: A case of conflict between semi-classical and quantum theories of radiation

Abstract

The behaviour of a three-level quantum system with a fundamental state and two closely grouped excited states is studied during its interaction with a strong monochromatic electromagnetic field. The EMF couples strongly and in a resonant manner the fundamental level (first level) with one excited level (second level) and couples weakly and in a nonresonant manner the fundamental level with the other excited one (third level). The semi-classical theory of radiation of Jaynes and Crisp and the quantum theory of radiation, in Lehmberg’s formalism, are successively used to calculate the density matrix of the system. It is found that, for given parameters characterizing the electromagnetic field and the first two levels, there are two particular values of the frequency gap between the excited levels for which the third level can be strongly populated. For the first value the two theories give consistent results and the third level is populated under both the effects of the external field and the field spontaneously emitted by the system (reactant or internal field). For the second value, only the semi-classical theory predicts a strong population for the third level and it is populated under the effect of the internal field alone. The values of the frequency gap are approximately predicted by using the concepts of « pseudolevels » in the semi-classical case and of « semi-dressed » system in the quantum case. The predictions are verified and improved by numerical calculations. It is proposed to use the discrepancy between the two theories in the second case to test experimentally the validities of the semiclassical and quantum theories of radiation.