  Relaxation and decoherence of a qubit coupled to environment and driven by a
resonant ac field are investigated by analytically solving Bloch equation of
the qubit. It is found that the decoherence of a driven qubit can be decomposed
into intrinsic and field-dependent ones. The intrinsic decoherence time equals
to the decoherence time of the qubit in 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 by 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.
