Illustrated Physics
physics, drawn
Concept

Bose einstein condensation — where it appears

The collection of a large share of a gas of identical bosons into its single lowest state below a critical temperature, with no attraction needed. It happens because the excited states can hold only so many particles at a given temperature, and the rest have nowhere else to go.

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

Two transitions, one shape and one not. The condensate fraction of an ideal Bose gas, 1 − (T/Tc)^3/2, drawn against the superfluid fraction of liquid helium-4, which goes as roughly 1 − (T/Tλ)^5.6. Both reach one at absolute zero and zero at their transition, and in between they disagree everywhere. The ideal calculation says why a transition has to exist; it does not describe the one that does, because its atoms do not interact and helium's do.

The liquid that will not slow down

Cool helium below 2.17 kelvin and it starts flowing through gaps no ordinary liquid could enter, climbs out of its own container, and circulates for as long as anyone has been willing to watch. The viscosity is not small. As far as any measurement can tell, it is zero.

quantum · Superfluidity The peak that rises out of a cloud. A slice through the shadow a released cloud of a million atoms casts after it has expanded, the measurement by which condensates are seen, at 1.1, 0.8 and 0.5 times the transition temperature: the thermal atoms, whose spread of speeds sets the cloud's width, give a broad rounded profile; the condensed atoms, all in one state with only the small spread of momenta their trap allowed, give a narrow peak at the centre, drawn here with the shape repulsion between the atoms gives it. Above Tc there is only the broad cloud. At 0.8 Tc a sharp peak stands up from its middle, holding 47 per cent of the atoms; at 0.5 Tc the peak holds 87 per cent and the thermal wings have shrunk. The two-component shape — a narrow peak on a broad base — was the signature that announced the first gaseous condensates in 1995.

The condensate a trap makes

A gas of atoms held in a magnetic trap and cooled to a few hundred billionths of a degree does something no gas in a box does at any temperature it can reach: a large share of its atoms falls into the trap's single lowest state, and a sharp peak rises out of the cloud. The reason is counting. The trap's excited states can hold only so many atoms at a given temperature, and the number grows as the cube of the temperature — so below one temperature the atoms run out of room, and every atom that does not fit has only one place to go.

quantum · Superfluidity

Named alongside it

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

Bose einstein statisticsChemical potentialDensity of statesEvaporative coolingHarmonic trapHeat capacityIndistinguishabilityLaser coolingOrder parameterPhase transitionQuantisationSuperfluidity

All concepts