The dynamics of a superconducting Josephson qubit coupled to a bosonic bath has been studied by the quantum trajectory
method. The excitation of the qubit by Rabi pulses has been considered. Excited state dissipative dynamics
interrupted by quantum jumps has been simulated both for each single realization and for an average over the ensemble
of realizations. The transition to the averaged behavior, which is characterized by the intervals of longitudinal and
transverse relaxation, has been studied. The simulation results qualitatively agree with the recent single-shot measurements
of qubits.
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