  Recent experimental evidences point to two-level defects, located in the
oxides and on the interfaces of the Josephson junctions, as the major
constituents of decoherence in superconducting qubits. How these defects affect
the qubit evolution with the presence of external driving is less well
understood since the semiclassical qubit-field coupling renders the
Jaynes-Cummings model for qubit-defect coupling undiagonalizable. We analyze
the decoherence dynamics in the continuous coherent state space induced by the
driving and solve the master equation with an extra decay-cladded driving term
as a Fokker-Planck equation. The solution as a distribution in the quadrature
plane is Gaussian with a moving mean and expanding variance. Its steady-state
reveals as a super-Poissonian over displaced Fock states, which reduces to a
Gibbs state of effective temperature decided by the defect at zero driving
limit. The mean follows one out of four distinct dynamic phases during its
convergence to a limit cycle determined by the competing driving strength and
defect decays. The rate of convergence differs according to the initial state,
illustrated by a Poincare map.
