Twissa & Hanbra: Hanbury Brown–Twiss Effect
Optics, Waves & Sound arc, page 112 of 193. Back to The Pixelated Physics Universe
Who they are
Twissa and Hanbra stand back to back at their searchlight dishes under Sirius. Their photons like to bunch.
Twissa & Hanbra is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Correlating the intensity flickers at two separate detectors measures the coherence of light, and from it the angular size of a star. For thermal light the correlation at zero delay is 2 (bunching), for ideal laser light it is 1, and for single-photon sources it is below 1 (antibunching, a purely quantum effect). R. Hanbury Brown and R. Q. Twiss measured Sirius with two searchlight mirrors (Nature, 1956): angular diameter 0.0068″ ± 0.0005″.
$$ \begin{gathered} g^{(2)}(\tau) = \frac{\langle I(t)\,I(t+\tau)\rangle}{\langle I\rangle^{2}} \\ \text{thermal: } g^{(2)}(0) = 2, \quad \text{laser: } g^{(2)}(0) = 1, \quad \text{single photons: } g^{(2)}(0) < 1 \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $g^{(2)}(\tau)$ | normalised intensity correlation | 1 |
| $I$ | light intensity | W/m² |
| $t$ | time | s |
| $\tau$ | delay between the two detectors | s |
| $\langle\ \rangle$ | time average | 1 |
Honest caveat: The value 2 is the ideal for a single polarisation of thermal light; it is not what their 1956 electronics measured.
Sources
- Hanbury Brown & Twiss (1956) A Test of a New Type of Stellar Interferometer on Sirius, Nature 178, 1046
- Loudon (2000) The Quantum Theory of Light, 3rd ed., Oxford University Press, ch. 3 and 6
- Kimble, Dagenais & Mandel (1977) Photon Antibunching in Resonance Fluorescence, Phys. Rev. Lett. 39, 691
Crossovers
Twissa & Hanbra meets Radicane (Poisson Counting Statistics). Twissa and Hanbra find that thermal photons bunch. Radicane's √N rule holds only for independent Poisson arrivals; bunched light is noisier than Poisson, and that excess is what the HBT effect measures.
Twissa & Hanbra meets Specklorn (Laser Speckle). Specklorn's speckle is the intensity pattern of coherent light scattered off a rough surface, with contrast 1. Twissa and Hanbra measure the same statistics in time: chaotic light has g⁽²⁾(0) = 2.
Wear the lore
Concept keywords: Hanbury Brown–Twiss Effect, Twissa & Hanbra, Optics, Waves & Sound, physics lore, Pixelated Physics