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 $s_c<s\le 1$ 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.

Figure 1

The crossover coupling ${\alpha }_o(s,1)$ is plotted versus $s$.

Figure 2

Spectrum ${\chi }^{\prime \prime }\left(\omega \right)$ vs frequency at ${\omega }_c=10\Delta$ and $T=0$ for various couplings $\alpha$ and Ohmic fluctuations.

Figure 3

FWHM / ${\omega }_{\max }$ vs coupling strength $\alpha$.

Figure 4

Spectrum ${\chi }^{\prime \prime }\left(\omega \right)$ vs frequency at ${\omega }_c\to \infty$ and $T=0$ for various couplings $\alpha$ and sub-Ohmic fluctuations with $s=0.3$.