Illustrated Physics
physics, drawn
Concept

Flux quantisation — where it appears

The restriction of the magnetic flux through a superconducting loop to whole multiples of h/2e. It follows from the wavefunction being single-valued round the loop, and the two in the denominator is the charge of a Cooper pair.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The size of the quantum says what is carrying the current. What the flux quantum would be for each candidate carrier charge, in units of 10⁻¹⁵ webers, against the measured value drawn as a line. A single electron would give 4.1357, a pair 2.0678, a triple 1.3786. The measurement is 2.0678, which picks the pair and excludes the others by a factor of two — not by a few per cent, so no question of experimental accuracy arises. The whole of the argument is that the condensate's wavefunction must come back to itself round the ring, which makes the enclosed flux a multiple of h over the carrier's charge; measuring the multiple therefore measures the charge, without any charge ever being measured. That is how the pairing was established in 1961, four years after it was proposed and by an experiment that looks nothing like a measurement of a charge.

The two in the flux quantum

A superconducting ring cannot hold whatever flux is applied to it. It holds a whole number of quanta and drives a current to make up the difference, and the size of that quantum is Planck's constant divided by twice the electron's charge. The factor of two was measured in 1961, four years after somebody predicted that the carriers are pairs — by an experiment in which no charge is measured at all.

electromagnetism · Superconductivity Outside the winding, where nothing is supposed to be. The mid-plane of a solenoid 20 radii long, wound at 8 turns per radius, with the field summed turn by turn rather than assumed. The upper curve is the axial field against distance from the axis: it holds up across the winding and collapses outside, reaching 0.47 per cent of its central value at 2 radii. The lower curve is the flux enclosed by a circle of that radius, which is what the vector potential integrates to. The two behave completely differently, and that difference is the whole subject: the field an electron outside can feel has effectively gone, and the flux it encircles has not. The enclosed flux does fall, by 3.29 per cent out to four radii, because the lines that leave the ends come back through the plane outside the coil — that return flux is the leak a real experiment has to defeat, and the reason the definitive versions used a closed toroidal magnet with no ends at all.

The phase a magnet leaves on a path it never touched

An electron beam split around a solenoid comes back with its fringes displaced, although neither path ever entered a magnetic field. What the electron responds to is the flux it went round, and the only local quantity that knows about that flux is the potential.

quantum · Matter waves

Named alongside it

The objects these essays reach for when they reach for this one.

CondensateCooper pairElectron chargeFlux quantumGauge invarianceInterferenceLittle parks effectLocalityMacroscopic quantum stateMagnetic fluxMatter wavePersistent current

All concepts