measured through spectroscopy,[@Xu05a] simultaneous state measurement,[@McDermott05a] and state tomography.[@Steffen06b]

In the phase qubit, higher excited states can impact the dynamics strongly, due to the nearly harmonic level structure within the potential well. The presence of these quantized energy levels has been clearly detected by monitoring the decay of a thermal population[@Silvestrini97a] and by microwave spectroscopy with single[@Martinis85a] and multiphoton[@Wallraff03a; @Strauch06a] transitions. Multilevel systems can, for example, be exploited for state initialization[@Valenzuela06a] and readout,[@Martinis02a] quantum logic gates[@Amin03a; @Strauch03a; @Wei08a] and algorithms,[@Ahn00a] and cryptography.[@Groblacher06a] However, when controlling the state of the phase qubit with a microwave current, off-resonant excitation of higher levels leads to leakage out of the desired qubit space and therefore a loss of quantum information.

Rabi oscillations serve as both a standard demonstration of quantum state manipulation and a diagnostic for decoherence and control fidelity. While these oscillations take on a simple form in a two-level system, several effects can occur in a multilevel system: the oscillations can distort, the higher states can become populated, and the basic resonance properties of the oscillations can undergo subtle shifts. Ultimately, to achieve fast and accurate control of the qubit state, all of these effects need to be carefully characterized. Progress in 