Continuum-continuum population trapping

We consider the problem of coherent population trapping in a model quantum system consisting of two (and briefly three) coupled continua of energy levels. While an earlier study [Z. Deng and J. H. Eberly, Phys. Rev. A 34, 2492 (1986)] has demonstrated population trapping in a closely related system, it has done so only for the case of a broad featureless continuum. We will demonstrate, on the other hand, that the time evolution of the continuum is qualitatively very different when different types of continua are allowed, and that population trapping is not likely to occur except in the broad featureless continuum. We do show, however, that in some cases other counterintuitive results surface.