  We study microwave-driven cooling in a superconducting flux qubit subjected
to environment noises. For the weak decoherence, our analytical results agree
well with the experimental observations near the degeneracy point and show that
the microwave amplitude for optimal cooling should depend linearly on the dc
flux detuning. With the decoherence increasing, more vibrational degrees of
freedom couple in, making the ordinary cooling method less effective or even
fail. We propose an improved cooling method, which can eliminate the
perturbation of additional vibrational degrees of freedom hence keep high
efficiency even under the strong decoherence. Furthermore, we point out that
the decoherence will modulate the frequency where microwave-driven Landau-Zener
transition reaches maximum in both methods, displaying the feature of
incoherent dynamics which is important for the optimal cooling of qubits and
other quantum systems.
