Noise-induced dephasing of an ac-driven Josephson junction

We consider the phase-locked dynamics of a Josephson junction driven by finite-spectral-linewidth ac current. By means of a transformation, the effect of frequency fluctuations is reduced to an effective additive noise, the corresponding (large) dephasing time being determined, in the logarithmic approximation, by the Kramers expression for the lifetime. For sufficiently small values of the drive's amplitude, direct numerical simulations show agreement of the dependence of the dephasing activation energy on the ac drive's spectral linewidth and amplitude with analytical predictions. Solving the corresponding Fokker-Planck equation analytically, we find a universal dependence of the critical value of the effective phase-diffusion parameter on the drive's amplitude at the point of sharp transition from the phase-locked state to an unlocked one. However, for large values of the drive amplitude, saturation and subsequent decrease of the activation energy are revealed by simulations, which cannot be accounted for by the perturbative analysis. The same effect is found for a previously studied case of ac-driven Josephson junctions with intrinsic thermal noise. The predicted effects are relevant to applications to voltage standards, as they determine the stability of the Josephson phase-locked state.