[Paper Review] The physics of Hanbury Brown--Twiss intensity interferometry: from stars to nuclear collisions

Gordon Baym|arXiv (Cornell University)|Apr 11, 1998

High-Energy Particle Collisions ResearchPhysics and Astronomy4 references147 citations

TL;DR

This paper provides a comprehensive theoretical overview of Hanbury Brown–Twiss (HBT) intensity interferometry, explaining its foundational principles in quantum mechanics and wave interference, and applying it to probe the space-time geometry of particle sources in high-energy nuclear collisions. It demonstrates that HBT correlations—measured via two-particle momentum correlation functions—yield information on source size, with key results showing a characteristic falloff at ~50 MeV/c in momentum space, corresponding to ~4 fm source radii, and identifies corrections from final-state Coulomb interactions and non-chaotic emission as critical factors in interpreting experimental data.

ABSTRACT

In the 1950's Hanbury Brown and Twiss showed that one could measure the angular sizes of astronomical radio sources and stars from correlations of signal intensities, rather than amplitudes, in independent detectors. Their subsequent correlation experiments demonstrating quantum bunching of photons in incoherent light beams were seminal in the development of quantum optics. Since that time the technique of "intensity interferometry" has become a valuable probe of high energy nuclear and particle collisions, providing information on the space-time geometry of the collision. The effect is one of the few measurements in elementary particle detection that depends on the wave mechanics of the produced particles. Here we discuss the basic physics of intensity interferometry, and its current applications in high energy nuclear physics, as well as recent applications in condensed matter and atomic physics.

Motivation & Objective

• To explain the fundamental physics of Hanbury Brown–Twiss intensity interferometry as a quantum mechanical probe of particle emission sources.
• To clarify how two-particle momentum correlation functions encode information about the space-time geometry of particle production in high-energy collisions.
• To address key uncertainties in HBT interpretation, such as final-state Coulomb interactions, non-chaotic emission, and coherence effects.
• To extend the applicability of HBT techniques beyond nuclear physics to atomic and condensed matter systems, including ultracold atoms and optical lattices.
• To provide a theoretical framework for interpreting experimental HBT data in terms of source size, emission duration, and particle identity.

Proposed method

• The paper uses a classical wave model to illustrate the basic HBT effect, showing intensity correlations between distant detectors due to incoherent wave sources.
• It derives the two-particle correlation function $ C(q) = \frac{\langle n_{\vec{p}_1} n_{\vec{p}_2} \rangle}{\langle n_{\vec{p}_1} \rangle \langle n_{\vec{p}_2} \rangle} $, where $ q $ is the momentum difference, and averages over center-of-mass momentum.
• Quantum mechanical treatment is applied to identical particles, showing that Bose-Einstein statistics lead to enhanced correlations at small $ q $, with a maximum of 2 for a fully chaotic source.
• The paper analyzes corrections due to final-state Coulomb interactions, deriving a shift in the extracted source radius by ~10% for $ Z_{\text{eff}} \sim 150 $, $ r_a \sim 7 $ fm, and $ p_a \sim 300 $ MeV/c.
• It examines the impact of non-chaotic emission and coherence lengths on the correlation function, showing suppression of the peak from 2 to ~1.5–1.6 in realistic nuclear collisions.
• Applications in atomic physics are discussed using time-resolved HBT measurements in laser-cooled 20Ne beams, where correlation times of ~0.5 μs indicate beam temperatures of ~100 μK.

Experimental results

Research questions

• RQ1 How does intensity interferometry using two-particle momentum correlations reveal the space-time extent of particle emission sources in high-energy collisions?
• RQ2 Why does the HBT correlation function peak at ~1.5–1.6 instead of 2 in nuclear collisions, despite the expectation for a chaotic source?
• RQ3 To what extent do final-state Coulomb interactions distort the extracted source size in HBT measurements?
• RQ4 How can HBT interferometry be used to probe the onset of Bose-Einstein condensation in ultracold atomic systems?
• RQ5 What are the implications of non-chaotic emission or finite coherence lengths for the interpretation of HBT correlation functions?

Key findings

• The HBT correlation function for pions in 200 GeV/A S+Pb collisions exhibits a momentum-space falloff at ~50 MeV/c, corresponding to a source size of ~4 fm.
• The correlation function for 450 GeV proton on Pb collisions is broader, indicating a smaller source size, consistent with shorter emission duration or smaller spatial extent.
• For 10.8 GeV/A Au+Au collisions, the HBT correlation function for $ \pi^+\pi^+ $, $ \pi^-\pi^- $, and $ K^+K^+ $ pairs shows a peak of ~1.5–1.6, indicating incomplete chaoticity or non-ideal emission.
• Final-state Coulomb interactions cause a ~10% shift in the extracted source radius, with opposite sign trends observed in E877 (positive) and NA44 (negative), highlighting the need for refined models.
• In ultracold 20Ne beams, HBT time correlations rise at separations < 0.5 μs, indicating a beam temperature of ~100 μK, consistent with thermal emission.
• HBT measurements in optical lattices using scattered light allow probing of atomic diffusion, with correlation functions reflecting dynamics in disordered systems.