The return of a hysteretic Josephson junction to the zerohyphen;voltage state:thinsp;thinsp;Ihyphen;Vcharacteristic and quantum retrapping

摘要

We study the behavior of a hysteretic currenthyphen;biased Josephson junction in the vicinity of its return to the zerohyphen;voltage states, with primary though not exclusive emphasis on the limit of weak damping (bgr;JLt;1), and under the assumption that the zerohyphen;point and thermal energies are both small compared toIcfgr;0so that fluctuation effects are important only very close to the return point. We consider in detail the resistively shunted junction (RSJ) and quasiparticlehyphen;tunneling models, and also make predictions for more general models. Denoting the value of imposed currentIat which return to the zerohyphen;voltage state would take place in the absence of fluctuations byIr, we study in particular (a) the dc currenthyphen;voltage characteristic in the running state forIminus;IrLt;Ir, and (b) the firsthyphen;passagehyphen;time statistics of the return to the zerohyphen;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 sgr; of the distribution of retrapping events as a function of imposed current; this prediction extends down to zero temperature and can be compared directly with the experimentally measured widths.Our two principal results are as follows: (a) In the running state, forILt;Ir, the currenthyphen;voltage characteristic should be given quite generally by the formula (Iminus;Ir)/Ir=lsqb;(AV0/V)+Brsqb;expminus;V0/V, whereAandBare constants specific to the model, andV0is a characteristic voltage which for the simplest models is given in the weakhyphen;damping limit byV0=ohgr;Jfgr;0+0(bgr;2J)thinsp;, with ohgr;Jthe junction plasma resonance frequency at zero current bias. (b) The square sgr;2of the width of the retrapping distribution plotted as a function ofI/Iris given to within logarithmic factors by sgr;2(T)=constthinsp;mgr;f(T), where mgr;equiv;planck;ohgr;J/Icfgr;0, the constant is of order 1, andf(T) is a function which tends to 1 asTrarr;0 and is proportional toTin the limit of highT; it is computed explicitly for the RSJ model. We also suggest an explanation (other than lead effects) of the lsquo;lsquo;forbidden voltage regionsrsquo;rsquo; which appear to be a characteristic of many highhyphen;quality junctions. We discuss the application of our results to the determination of the parameters of Josephson junctions necessary for the investigation of quantum effects on the macroscopic level.