Crossover from coherent to incoherent quantum dynamics due to sub-Ohmic dephasing

We report exact results for the influence of purely sub-Ohmic dephasing on the dynamics of a quantum two-level system. From response functions, we determine a crossover coupling strength between oscillatory coherent and overdamped dynamics. Surprisingly, we find no overdamping even at arbitrary large dephasing for spectra with spectral exponent s < s(c). For s(c) < s <= 1 we observe a crossover to overdamped dynamics but a reemergence of oscillatory behavior at very large couplings. Thus experimentally tuning the character of fluctuations from relaxational to dephasing should allow us to suppress the dephasing character of sub-Ohmic and thus 1/f noise.