  We consider the problem of a qubit driven by a harmonically oscillating
external field while it is coupled to a quantum two-level system. We perform a
systematic numerical analysis of the problem by varying the relevant
parameters. The numerical calculations agree with the predictions of a simple
intuitive picture, namely one that takes into consideration the four-level
energy spectrum, the simple principles of Rabi oscillations and the basic
effects of decoherence. Furthermore, they reveal a number of other interesting
phenomena. We provide explanations for the various features that we observe in
the numerical calculations and discuss how they can be used in experiment. In
particular, we suggest an experimental procedure to characterize an environment
of two-level systems.
