Relaxation and decoherence in a resonantly driven qubit

Relaxation and decoherence of a qubit coupled to the environment and driven by a resonant ac field are investigated by analytically solving the Bloch equation of the qubit. We found that the decoherence of a driven qubit can be decomposed into intrinsic and field-dependent decoherence. The intrinsic decoherence time equals the decoherence time of the qubit in a free decay while the field-dependent decoherence time is identical with the relaxation time of the qubit in driven oscillation. Analytical expressions of the relaxation and decoherence times are derived and applied to study a microwave-driven SQUID flux qubit. The results are in excellent agreement with those obtained from directly numerically solving the master equation. The relations between the relaxation and decoherence times of a qubit in free decay and driven oscillation can be used to extract the decoherence and thus dephasing times of the qubit by measuring its population evolution in free decay and resonantly driven oscillation.