Gap Jumping

Tiny detectors on a person’s head have been used to sense tiny fluctuations in the brain’s magnetic field. These SQUIDS, short for superconducting quantum interference devices, are the most sensitive of any kind and rely on the Josephson Effect, in which the Cooper pairs of electrons in a superconductor can sometimes jump a physical spatial gap in the material to another part of the superconductor. Manufactured SQUIDS

have a thin film filling the gap. In fact, the direct current (DC) SQUID used in laboratories worldwide today for sensing small magnetic fields is a superconducting ring with two gaps! The best DC SQUIDS have an energy sensitivity capable of detecting a magnetic flux change corresponding to about 10^–34 joule in one second, about the mechanical energy required to raise an electron 10 centimeters in one second. Why do the paired electrons jump the gap?

Answer

This Josephson effect is really quantum mechanical tunneling across the physical gap because the wave function for the superconducting pair extends beyond the end of the material into the gap and to the other side. If the superconducting material is actually in the form of a ring, then matching of the wave function for the pair around the ring must be made, restricting their angular momentum quantization to multiples of h/2π.