  We consider an ensemble of quantum systems whose average evolution is
described by a density matrix, solution of a Lindblad-Kossakowski differential
equation. We focus on the special case where the decoherence is only due to a
highly unstable excited state and where the spontaneously emitted photons are
measured by a photo-detector. We propose a systematic method to eliminate the
fast and asymptotically stable dynamics associated to the excited state in
order to obtain another differential equation for the slow part. We show that
this slow differential equation is still of Lindblad-Kossakowski type, that the
decoherence terms and the measured output depend explicitly on the amplitudes
of quasi-resonant applied field, i.e., the control. Beside a rigorous proof of
the slow/fast (adiabatic) reduction based on singular perturbation theory, we
also provide a physical interpretation of the result in the context of
coherence population trapping via dark states and decoherence-free subspaces.
Numerical simulations illustrate the accuracy of the proposed approximation for
a 5-level systems.
