flux quantization
/ fluks kwon-tih-ZAY-shun /
Money comes in whole coins — you can have one cent or two, but never half a cent. Magnetic field through a superconducting ring obeys a strikingly similar rule. You cannot trap just any amount; the field can only come in whole, indivisible packets, as if nature only mints magnetism in a single fixed coin.
Flux quantization means the total magnetic flux threading a closed superconducting loop is always a whole-number multiple of one tiny fixed unit, called the flux quantum. The reason lies in the single shared quantum wave that all the Cooper pairs ride together: for that wave to join up smoothly around the ring without contradicting itself, the enclosed flux must take only these special values. The ring's own circulating supercurrent adjusts itself automatically to make the total come out to an exact whole number of quanta.
This matters because it is among the most direct proofs that superconductivity is a single quantum state spread over a whole object you can hold in your hand — quantum behaviour made macroscopic. Measuring the size of the flux quantum revealed something profound: it depends on twice the electron charge, hard experimental evidence that the current is carried by pairs. A common confusion is to expect the field everywhere to be quantized; only the total flux through the closed loop is.
In 1961 two teams measured the trapped flux in a tiny superconducting cylinder and found it came only in fixed steps — and the step size showed the charge involved was two electrons, not one, confirming Cooper pairing.
Trapped flux jumps in fixed steps whose size proves the supercurrent is carried by electron pairs.
The single flux quantum is fantastically small — roughly two-millionths of a billionth of a tesla times a square metre — which is why each vortex in a type-II superconductor carries exactly one, and why threading even a small ring takes a great many of them.