(Solved): C. Josephson Junctions and the SQUID Students will become familiar with the operational principle o ...

C. Josephson Junctions and the SQUID Students will become familiar with the operational principle of the Josephson junction, and how that relates to the superconducting order parameter, as well as look at their application in SQUIDs (superconducting quantum interference devices). It is expected that students can answer the following questions - How is the current through a Josepshon junction related to the phase of the superconducting order parameter? [See the First Josephson Equation]. - How does the phase of each superconductor, ${?}_1,{?}_2$ (comprising a single Josephson junction) depend on an applied voltage, $V$ ? Similarly how does the phase difference $?={?}_2?{?}_1$ depend on $V$ ? [See the Second Josephson Equation]. - Based on the Second Josephson Equation, two cases need to be understood - (i) $V=0$ and (ii) $V=$ constant $?=0$ - for each case, what is the corresponding current? - The current through a (symmetric) SQUID is given by $I=I_0\sin \left(\frac{{?}_n+{?}_0}{2}\right)\cos \left(2??/{?}_0+2n?\right)$, with ${?}_a$ is the phase difference across one of the Josephson junctions, and ${?}_b$ is the phase difference across the other. Questions: (a) Why can a SQUID detect magnetic fields? (b) What determines the sensitivity in detecting magnetic fields/flux?