Illustrated Physics
physics, drawn
Concept

Harmonic trap — where it appears

A confining potential that rises as the square of the distance from its centre, so that a trapped particle oscillates at one frequency whatever its energy. Magnetic and optical traps for cold atoms are harmonic near their centres, and their levels are evenly spaced by ħω.

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

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 The cloud that stops shrinking. The rms size of a cloud of 10⁵ ideal atoms in a harmonic trap, in units of the Fermi radius, against temperature in units of the Fermi temperature, for fermions, for bosons and for a classical gas. The classical cloud shrinks as the square root of half the temperature ratio, all the way to nothing. The bosons follow it down to their condensation temperature, 0.52 of the Fermi temperature, and then collapse into the trap's ground state, whose rms size is 0.054 Fermi radii. The fermions part from the classical line near the Fermi temperature and level off at one over the square root of eight, 0.354 of the Fermi radius: at a quarter of the Fermi temperature they are 1.17 times the classical size, and cooling further barely changes them. Mixed together in one trap, as lithium-7 and lithium-6 were in 2001, the two clouds start the same size and end 6.5 times apart in width for ideal atoms of these numbers — further still in volume. The fermions are held up by nothing but the rule that no two of them may share a state.

The cloud that stops shrinking

Two kinds of lithium atom, cooled together in one magnetic trap to a few hundred billionths of a degree, start as clouds of the same size and end very differently. The lithium-7 atoms, which are bosons, shrink with the temperature and then collapse into a condensate. The lithium-6 atoms, which are fermions, stop shrinking at about a quarter of their Fermi temperature and refuse to get any smaller, however much colder they become. Nothing pushes them apart but the rule that no two identical fermions may share a state. The photographs taken in 2001 were the first time Fermi pressure — the pressure that holds up white dwarfs — was seen as a picture.

quantum · Exclusion

Named alongside it

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

Bose einstein condensateBose einstein condensationBose einstein statisticsChemical potentialDegenerate fermi gasDensity of statesEvaporative coolingFermi energyFermi pressureFugacityHeat capacityLaser cooling

All concepts