I found an interesting paper here a two level system is measured by a harmonic oscillator(the apparatus). the apparatus is coupled to its environment, a bath of oscillators. The article shows how the reduced matrix of S+ A decoheres (the off diagonal elements tend to zero). I am looking for a similar calculation with an environment reduced to a single oscillator. I think that we would find the off diagonal initial values after some time. So there would be a revival of coherence in a cyclic process. Have you a link?