
The Purcell effect is the enhancement of spontaneous emission rate of an emitter due to its coupling to a resonant electromagnetic cavity.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.
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.
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.
This is the basis for bright single-photon sources for quantum cryptography and ultrafast LEDs in optical chips.
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.
| L_H | variable | Instantaneous non-thermal emission (luminosity) — luminosity watt |
| L_S | variable | Plasma heating rate (energy per time) — power watt |
| \frac{d}{dt} | operator | Computes the rate of change with respect to time — time derivative |





