Externally Shunted Josephson Junctions: Generalized Weak Links

Abstract

Using externally shunted thin-film $\mathrm{S}\mathrm{n}\ensuremath{-}I\ensuremath{-}\mathrm{S}\mathrm{n}$ Josephson junctions, we have experimentally verified the Stewart-McCumber predictions for the current-voltage ($I\ensuremath{-}V$) characteristics of a generalized weak link treated as a lumped circuit consisting of an ideal Josephson junction with critical current ${i}_{c}$, conductance $G$, and capacitance $C$. In addition, we have shown experimentally and theoretically that the predictions for the amount of hysteresis in the $I\ensuremath{-}V$ characteristic as a function of the dimensionless circuit parameter ${\ensuremath{\beta}}_{C}=(\frac{2e}{\ensuremath{\hbar}}) ({i}_{c}\frac{C}{{G}^{2}})$ can be generalized to include shunt inductance $L$ by replacing the capacitance with an effective capacitance ${C}^{\ensuremath{'}}=C\ensuremath{-}{G}^{2}L$. An externally shunted Josephson junction acts as a generalized weak link in that it can reproduce the behavior of other types of weak links. In fact, if the temperature of a single shunted junction is varied between 1.12 and 3.7 K, or the applied magnetic field is varied between 0 and 1 Oe, ${\ensuremath{\beta}}_{C}$ can be varied over two orders of magnitude while the junction is in the cryostat. Since ${\ensuremath{\beta}}_{C}$ determines the qualitative nature of the $I\ensuremath{-}V$ characteristic, this variation of ${\ensuremath{\beta}}_{C}$ simulates widely different types of weak-link devices. Furthermore, the accessible range of ${\ensuremath{\beta}}_{C}$ for the single shunted junction can be changed while it is out of the cryostat by altering its external shunt conductance. Thus, externally shunted Josephson junctions are theoretically well-understood models of, and simulators for, the behavior of many weak-link junctions; they have the desirable property of adjustability both before and after cryostat installation. This versatility should find many significant applications.