The advent of high-$T_c$ superconductors gave great impetus to the development of thin-film superconducting quantum interference devices (SQUIDs) for operation at temperatures up to the boiling point of liquid nitrogen, 77 K. The spectral density of the white flux noise can be calculated analytically for rf SQUIDs and by computer simulation for dc SQUIDs; however, observed noise spectral densities are typically an order of magnitude higher. Low-frequency $1/f$ noise from thermally activated vortex motion is a much bigger issue in high-$T_c$ SQUIDs at 77 K than in low-$T_c$ SQUIDs because of the low flux-pinning energies in high-$T_c$ superconductors. The magnitude of the noise depends strongly on the quality of the thin films, and much effort has been expended to improve techniques for depositing ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ (YBCO) on lattice-matched single-crystal substrates. Substantial effort has also been invested in the development of new types of Josephson junctions, of which grain-boundary junctions are the most widely used in SQUIDs. Appropriate electronic read-out schemes largely eliminate $1/f$ noise from fluctuations in the junction critical current in both rf and dc SQUIDs. Typical levels of white flux noise are a few $\mu {\Phi }_0{\mathrm{Hz}}^{\mathrm{-}1/2}$ (${\Phi }_0$ is the flux quantum). Magnetometers—consisting of a superconducting flux transformer coupled to a SQUID—achieve a white magnetic-field noise as low as 10 fT ${\mathrm{Hz}}^{\mathrm{-}1/2}$, increasing to typically 30 fT ${\mathrm{Hz}}^{\mathrm{-}1/2}$ at 1 Hz. When these devices are operated in an unshielded environment, it is important to minimize the motion of trapped vortices and induced supercurrents, which can greatly increase the $1/f$ noise. The ambient noise is far greater than the intrinsic noise of the devices, but can be substantially reduced by various gradiometer configurations. There is now considerable effort to apply high-$T_c$ SQUIDs in magnetocardiology, nondestructive evaluation, microscopy, and geophysics.

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