Crossover of phase qubit dynamics in the presence of a negative-result weak measurement

The coherent dynamics of a superconducting phase qubit is considered in the presence of both unitary evolution due to microwave driving and continuous nonunitary collapse due to a negative-result measurement. In the case of relatively weak driving, the qubit dynamics is dominated by the nonunitary evolution, and the qubit state tends to an asymptotically stable point on the Bloch sphere. This dynamics can be clearly distinguished from conventional decoherence by tracking the state purity and the measurement invariant. When the microwave driving strength exceeds a certain critical value, the dynamics changes to nondecaying oscillations: any initial state returns exactly to itself periodically in spite of the nonunitary dynamics. The predictions can be verified using a modification of a recent experiment.