The return of a hysteretic Josephson junction to the zero‐voltage state: I‐V characteristic and quantum retrapping

We study the behavior of a hysteretic current‐biased Josephson junction in the vicinity of its return to the zero‐voltage states, with primary though not exclusive emphasis on the limit of weak damping (βJ≪1), and under the assumption that the zero‐point and thermal energies are both small compared to Icφ0 so that fluctuation effects are important only very close to the return point. We consider in detail the resistively shunted junction (RSJ) and quasiparticle‐tunneling models, and also make predictions for more general models. Denoting the value of imposed current I at which return to the zero‐voltage state would take place in the absence of fluctuations by Ir, we study in particular (a) the dc current‐voltage characteristic in the running state for I−Ir≪Ir, and (b) the first‐passage‐time statistics of the return to the zero‐voltage state induced by both classical and quantum fluctuations. With regard to (b), we express our results in the form of a prediction of the width σ of the distribution of retrap...