HOW SCIENCE WORKS · OPTICS
Find your route through the Hanbury Brown–Twiss effect
The Hanbury Brown–Twiss effect measures correlations between intensity fluctuations rather than the phase of an electric field. By comparing when two detectors click, scientists can reveal thermal photon bunching, distinguish light statistics and infer the angular size of a distant source.
Chapters 1–3.2. Work through the model
Chapters 4–5.3. Evaluate the evidence
Chapters 6–8.
Open the chapter index · Jump to limits · Explore Optics · How Science Works master guide
A mechanism-focused enrichment guide for curious students, parents and teachers. Worked numbers are explicitly hypothetical; research links identify supporting scientific studies. This is not an examination-syllabus claim or a laboratory operating procedure.
Chapter index
Mechanism · Chapters 1–3
Model · Chapters 4–5
Evidence and limits · Chapters 6–8
A beam is divided between two detectors. Instead of averaging each detector separately, the experiment records how often their signals rise together as a function of time delay or detector separation.
The quantity of interest is second-order coherence: whether pairs of detections occur more often, less often or exactly as often as independent events would predict.
Chaotic or thermal light contains fluctuating modes whose amplitudes sometimes reinforce. For ideal single-mode thermal light, the zero-delay correlation g(2)(0) reaches 2.
A coherent laser field is approximately Poissonian with g(2)(0) near 1. An ideal single-photon source can show antibunching with g(2)(0) below 1.
For an extended star, light arriving at separated telescopes loses mutual coherence as the baseline grows. The decline of intensity correlation is related to the Fourier transform of the source’s brightness distribution.
This allowed stellar diameters to be inferred without maintaining optical phase stability between telescopes. Electronic correlation can tolerate path disturbances that would destroy ordinary amplitude interferometry.
Suppose independent detector rates predict 1,000 accidental coincidences in a chosen set of time bins, but 1,200 are measured near zero delay after background correction.
The illustrative normalised value is g(2)(0) = 1,200/1,000 = 1.20, indicating bunching. Detector dead time, timing resolution and multiple modes can reduce the ideal thermal value.
| Light field | Ideal g²(0) | Interpretation |
|---|---|---|
| Single-mode thermal | 2 | Bunched arrivals |
| Coherent laser | 1 | Poisson-like arrivals |
| Single-photon source | Below 1 | Antibunching |
| Many unresolved thermal modes | Between 1 and 2 | Bunching diluted by mode averaging |
Thermal bunching can be described using classical random fields and intensity fluctuations. Antibunching cannot be reproduced by a classical field with a positive probability distribution and is a quantum signature.
The HBT apparatus is therefore not tied to only one interpretation. Its correlation function becomes a common language for classical coherence and quantum photon statistics.
Experiments measure dark counts, afterpulsing, detector dead time, electronic cross-talk and background light. They shift timing windows to estimate accidental coincidences.
A correlation peak is persuasive when its width and dependence on filtering, baseline or source state match the predicted coherence time and geometry.
A 2007 Physical Review Letters experiment used a modified Hanbury Brown–Twiss interferometer to measure second-order coherence and photon antibunching in continuous-variable optical states.
Related methods now measure photons, atoms, electrons and phonons. The shared idea is to learn about a source from pair correlations that ordinary intensity averages erase.
Finite detector resolution averages over rapid fluctuations, while many spatial or spectral modes dilute bunching. Loss alone often reduces count rate without changing an ideal normalised g², but background can push it toward 1.
The effect shows that timing relationships are evidence. Two sources with the same mean brightness can have very different second-order statistics and therefore very different physical states.