  Rabi oscillations have been observed in many superconducting devices, and
represent prototypical logic operations for quantum bits (qubits) in a quantum
computer. We use a three-level multiphoton analysis to understand the behavior
of the superconducting phase qubit (current-biased Josephson junction) at high
microwave drive power. Analytical and numerical results for the ac Stark shift,
single-photon Rabi frequency, and two-photon Rabi frequency are compared to
measurements made on a dc SQUID phase qubit with Nb/AlOx/Nb tunnel junctions.
Good agreement is found between theory and experiment.
