  We present an analytical and comprehensive description of the quantum
dynamics of a microwave resonantly driven superconducting phase qubit coupled
to a microscopic two-level system (TLS), covering a wide range of the external
microwave field strength. Our model predicts several interesting phenomena in
such an ac driven four-level bipartite system including anomalous Rabi
oscillations, high-contrast beatings of Rabi oscillations, and extraordinary
two-photon transitions. Our experimental results in a coupled qubit-TLS system
agree quantitatively very well with the predictions of the theoretical model.
