The stationary SQUID

In the customary mode of operation of a SQUID, the electromagnetic field in the SQUID is an oscillatory function of time. In this situation, electromagnetic radiation is emitted, and couples to the sample. This is a back-action that can alter the state that we intend to measure. A circuit that could perform as a stationary SQUID consists of a loop of superconducting material that encloses the magnetic flux, connected to a superconducting and to a normal electrode. This circuit does not contain Josephson junctions, or any other miniature feature. We study the evolution of the order parameter and of the electrochemical potential in this circuit; they converge to a stationary regime and the voltage between the electrodes depends on the enclosed flux. We obtain expressions for the power dissipation and for the heat transported by the electric current; the validity of these expressions does not rely on a particular evolution model for the order parameter. We evaluate the influence of fluctuations. For a SQUID perimeter of the order of 1$\mu$m and temperature $0.9T_c$, we obtain a flux resolution of the order of $10^{-5}\Phi_0/$Hz$^{1/2}$; the resolution is expected to improve as the temperature is lowered.