Purcella

Purcella, a fae of light, holds a glowing atom between two mirrors that change how fast it can shine.

The Physics

An excited atom's spontaneous emission rate is not fixed: it depends on the electromagnetic modes around it. Put the atom in a small, high-quality resonant cavity tuned to its transition and it can emit much faster than in free space. E. M. Purcell pointed this out for nuclear magnetic moments at radio frequencies in a short abstract (“Spontaneous Emission Probabilities at Radio Frequencies”, Phys. Rev. 69, 681, 1946). The enhancement is the Purcell factor.

F = 3Q(λ/n)³ / (4π²V)

• F: Purcell factor, emission rate in the cavity over the free-space rate
• Q: quality factor of the cavity
• λ: free-space wavelength of the transition (m)
• n: refractive index of the cavity medium
• V: mode volume of the cavity (m³)

A high Q and a tiny mode volume mean a big enhancement. The effect is used in single-photon sources, small lasers and quantum-dot devices.

Honest caveat: This is the maximum, for an emitter exactly on resonance, at the field maximum and aligned with the field. Off resonance or detuned, the cavity can suppress emission instead.

On the sticker

Purcella holds a glowing atom between two round glass mirrors with light running between them. Printed text: PURCELLA with the line F = 3Q(λ/n)³/(4π²V). Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.