effect

Purcell effect

The Purcell effect is the enhancement of spontaneous emission rate of an emitter due to its coupling to a resonant electromagnetic cavity.
16 related articles · 1 formulas

Description

A nanosecond is an eternity for an excited atom. But in a microresonator, the same atom emits light in picoseconds. In 1946, Edward Mills Purcell noticed that a resonator changes the rate of spontaneous emission. The Purcell factor, the key formula, is proportional to the ratio of quality factor to volume: the tighter the cavity and the higher its quality, the stronger the effect. Just as a Stradivarius violin sounds different from a simple box, the microresonator tunes the voice of the atom.

History

The phenomenon was predicted by Edward Mills Purcell in 1946 in the context of nuclear magnetic resonance, when he considered the influence of a resonator on spin relaxation. In the 1980s, with the development of microstructures, the effect was observed in the optical range: in 1985, Gabriela Slater's group demonstrated suppression of spontaneous emission in a waveguide, and in 1987, Eli Yablonovitch introduced the concept of a photonic band gap. Today, it underpins cavity quantum electrodynamics.

How it works

It is used to create highly efficient single-photon sources (quantum dots in microresonators), superbright LEDs based on photonic crystals, and low-threshold lasers. Limits of applicability: the Purcell factor loses meaning in the strong coupling regime, where Rabi splitting occurs.

In practice

This is the basis for bright single-photon sources for quantum cryptography and ultrafast LEDs in optical chips.

Fun fact

Purcell came up with his formula during a coffee discussion with colleagues. A brief note in Physical Review gave birth to an entire field—cavity quantum electrodynamics.

Concept graph →

Formulas

$$L_H \propto \frac{dL_S}{dt}$$
Relates instantaneous non-thermal emission to plasma heating rate.
What is in the formula
L_HvariableInstantaneous non-thermal emission (luminosity) — luminosity watt
L_SvariablePlasma heating rate (energy per time) — power watt
\frac{d}{dt}operatorComputes the rate of change with respect to time — time derivative
l_h\propto\frac{dl_s}{dt} · 2606.25636

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