An asymmetric SQUID for measurement of ultra-small Josephson junctions

Ultra-small Josephson junctions offer a variety of potential applications, as well as an opportunity to probe the Josephson effect at the nanoscale. Such junctions, however, are susceptible to fluctuations in the phase difference, $\gamma _{1}$, across the junction, which leads to a suppression of the critical current I$_{01}$. The relevant energies which govern the physics of Josephson junctions are the charging energy E$_{C}$, the Josephson coupling energy E$_{J}$, and the thermal energy k$_{B}$T. Small junctions have E$_{C}$/E$_{J} \quad >>$ 1, while large junctions, with stable critical currents, have E$_{C}$/E$_{J} \quad <<$ 1. A potential method for stabilizing the phase across a small junction will be presented, which entails shunting it with an additional capacitance C$_{1 }$and incorporating it in a SQUID loop with another junction having a much larger critical current I$_{02}$. The SQUID loop inductance, L, couples $\gamma _{1}$ to the\textit{ stable} phase difference $\gamma _{2}$ of the large junction. Thus, by properly choosing L and C$_{1}$, the uncertainty in $\gamma _{1 }$should be reduced, allowing a precise measurement of I$_{01}$. In addition to the theoretical arguments behind this approach, experimental data incorporating these ideas will be presented. This work was supported by the National Science Foundation.