= Solution
A <SQUID> converts <magnetic flux> into a periodic <interference> response of superconducting weak links. A <DC SQUID> has two <Josephson junctions> in a loop. For equal junction critical currents $I_0$ and negligible loop self-inductance, their <Gauge-invariant Josephson phases> differ by $2\pi\Phi/\Phi_0$, with $\Phi_0=h/(2e)$. Adding $I_0\sin\delta_1+I_0\sin\delta_2$ and maximizing over the common phase gives
$$
\boxed{I_c(\Phi)=2I_0\left|\cos\frac{\pi\Phi}{\Phi_0}\right|.}
$$
Thus the critical current repeats for every added flux quantum. A suitable current bias and dissipative junction dynamics convert the changing critical current into an observable voltage modulation. Junction asymmetry prevents exact zero minima, and appreciable self-inductance makes the flux include the circulating current's contribution; these require a modified response model. The <Jaklevic Josephson interference experiment> supplies an early experimental realization of the <interference> principle.
An <RF SQUID> instead uses one junction in a loop inductively coupled to a radio-frequency resonator. In either design, a pickup coil and flux transformer can couple a small external field into the sensor, and flux feedback can keep it near a sensitive operating point over a larger measurement range. Applications include weak-field magnetometry, measurements of magnetic susceptibility and persistent currents, geophysical surveys and precision low-current detection. Gradiometers suppress common external fields, while thermal, junction and environmental noise set practical sensitivity. The instrument measures a flux-dependent electrical response; sensitivity is not established solely by the small size of $\Phi_0$.
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