Resonant activation of a Brownian particle out of a potential well: Microwave-enhanced escape from the zero-voltage state of a Josephson junction.

Abstract

A current-biased Josephson tunnel junction in its zero-voltage state can be modeled as a Brownian particle in a potential well from which it can escape by thermal activation at a rate \ensuremath{\Gamma}(0). The enhancement \ensuremath{\gamma}=\ensuremath{\Gamma}(${I}_{m}$)/\ensuremath{\Gamma}(0) of the escape rate has been measured in the presence of a microwave current of amplitude ${I}_{m}$, which represents a weak, sinusoidal force driving the particle. When the microwave frequency is varied, ln\ensuremath{\gamma} peaks approximately at the natural frequency at which the particle oscillates at the bottom of the anharmonic potential well. At higher frequencies, ln\ensuremath{\gamma} exhibits a sharp roll-off that steepens as the quality factor Q of the junction is increased, while at lower frequencies ln\ensuremath{\gamma} has a long tail with a shape which is almost independent of Q. These features are qualitatively consistent with the theories of Ivlev and Mel'nikov and Larkin and Ovchinnikov, which we discuss. These theories however, are not able to predict analytically the behavior of ln\ensuremath{\gamma} near the peak. To overcome this difficulty a detailed series of computer simulations has been performed. These simulations, together with certain scaling properties of the theories, have been used to construct an empirical formula for ln\ensuremath{\gamma} that is in qualitative agreement with the experimentally determined frequency dependence of ln\ensuremath{\gamma}. The experimentally observed dependences of ln\ensuremath{\gamma} on temperature and microwave amplitude are in good quantitative agreement with predictions.