Illustrated Physics
physics, drawn
Concept

Purcell effect — where it appears

The change in an emitter's spontaneous decay rate caused by placing it in a resonant cavity. The rate rises with the cavity's quality factor and falls with its volume, because those set how many modes per unit frequency the emitter can reach.

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

Two solutions, and nothing in the equations to choose between them. A spherical pulse leaving a point and a spherical pulse arriving at one, each drawn at three times 0.35, 0.6, 0.85 in units where the speed is one. Both are exact solutions of the same wave equation, which is checked here by differencing the drawn samples twice in space and twice in time and requiring the residual to vanish for each. The one on the left is what is always used; the one on the right is discarded, and the equations do not do the discarding. The incoming pulse grows as it converges for the same reason the outgoing one decays as it spreads — the same energy through a smaller sphere — and it is as consistent with conservation as its mirror image is.

The solution that is thrown away

Maxwell's equations admit a field that converges on a charge exactly as readily as one that leaves it, and nothing in them prefers either. Retardation is a boundary condition rather than a law. Which boundary condition is right has been argued about for a century, one of the answers makes the arrow of time a property of there being absorbers, and the laboratory version of the question — whether an atom emits at all — has a measured answer that depends on what is listening.

electromagnetism · Retardation A lifetime that oscillates with a distance. The rate at which an excited atom emits a photon, relative to its rate in empty space, against its distance from a perfect mirror in wavelengths, for its dipole pointing across the mirror and along it. On the mirror itself the rate doubles for the first and vanishes for the second. As the distance grows both swing about 1 with a period of half a wavelength and a shrinking size: at half a wavelength the along-mirror rate is 0.96, and at a wavelength 0.99. Nothing in the atom has changed; its excited electron and its transition are the same in every position. An emission rate is a property of an atom and of the room it is in.

The lifetime that depends on where the mirror is

A half-life is treated as the most private fact about an atom or a nucleus, and for a nucleus that is nearly true. An excited atom beside a mirror decays faster or slower depending on how many half-wavelengths away the mirror stands, and between two mirrors closer than half a wavelength it does not emit at all. The atom has not changed. A decay is a transition to a state with a photon in it, and the room decides whether that state exists.

quantum · Decay

Named alongside it

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

Spontaneous emissionAdvanced solutionArrow of timeBoundary conditionCausalityCavity qedDensity of statesDipole radiationImage dipoleInhibited emissionIrreversibilityLangmuir blodgett film

All concepts