For measurement, NbTi wires were attached to the Nb/Au pads using pressed indium. The samples were immersed in liquid He. Current was provided by a battery-powered low-noise current source, while the voltage was measured using a SQUID-based self-balancing potentiometer circuit with a voltage noise of a few pV/√Hz (31).

I-V characteristics are typical of overdamped Josephson junctions (32), but the I-V curves exhibit substantial rounding for currents less than the critical current, Ic, due to environmental and instrumental noise, as shown in Fig. 2B. Rounded I-V curves are well described by the Ivanchenko-Zil’berman (IZ) function (3335), while less-precise estimates of Ic can be obtained by fitting the data to the standard form for overdamped Josephson junctions: V = R × Real{(I2Ic2)½}. Because fitting I-V curves with the IZ function is computationally time-consuming, we carried out the initial data analysis shown in Fig. 2 using the simpler square-root fits and then used the IZ function to fit the data sets that will be subjected to further quantitative analysis, that is, the data shown in Fig. 3. When fitting single-junction or SQUID data with the IZ function, we have found that the effective noise temperature of our apparatus is typically about 40 K—considerably higher than the actual sample temperature [see Fig. 4 and Table 1 in (35)]. Nevertheless, the IZ function fits the data very well, and the IZ fits give consistent values of critical current, which vary systematically with applied flux, as shown in Fig. 3. When fitting data with the IZ function, we fit the positive and negative current sweep data simultaneously, with a common value for the normal-state resistance, R, but with separate values for the positive and negative critical currents, Ic+ and Ic−. That is required in principle because the values of Ic+ and Ic− are generally different for a SQUID unless the SQUID is completely symmetric, that is, the critical currents of the two junctions are identical and the inductances of the two arms are identical. In our SQUIDs, the inductances are identical to a very high degree, but the junction critical currents are not, especially when one of the junctions has switched into the antiparallel magnetic state while the other is still in the initial parallel magnetic state. Because our SQUIDs have low values of βL, however, we find in every case that Ic+ and Ic− are nearly equal, as shown in Fig. 3.

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