  Recent experiments on Josephson junction qubits have suggested the existence
in the tunnel barrier of bistable two level fluctuators that are responsible
for decoherence and 1/f critical current noise. In this article we treat these
two-level systems as fictitious spins and investigate their influence quantum
mechanically with both analytical and numerical means. We find that the Rabi
oscillations of the qubit exhibit multiple stages of decay. New approaches are
established to characterize different decoherence times and to allow for easier
feature extraction from experimental data. The Rabi oscillation of a qubit
coupled to a spurious resonator is also studied, where we proposed an idea to
explain the serious deterioration of the Rabi osillation amplitude.
