---
title: "Glauber: coherence needs more than visible fringes"
description: "What can photon coincidences reveal that a spectrum or interference pattern cannot?"
canonical_url: "https://sandboxphysics.com/stories/probe-evidence/glauber-coherence-and-counting/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/probe-evidence/glauber-coherence-and-counting/"
last_modified: "2026-10-22"
---

[Controlled light and precision measurement](https://sandboxphysics.com/stories/probe-evidence/#light-tools)

Apparatus · Observation · Inference

# Glauber: coherence needs more than visible fringes

Sandbox Physics · 2026-10-22

What can photon coincidences reveal that a spectrum or interference pattern cannot?

1. Prepare a light field
2. Split or sample the field
3. Time-tag detection events
4. Estimate normalized correlations

These are detection events and statistical comparisons, not tracked trajectories of individual photons through an interference pattern.

## One successful interference test leaves questions open

Two sources can have similar spectra or first-order coherence yet different photon-counting statistics. Glauber’s 1963 paper introduced a hierarchy of field correlations suitable for discussing these distinctions. Its abstract explicitly notes that traditional optical coherence describes only the first order.

The 2005 recognition concerns a theoretical framework tied to observable detection statistics. It is not a claim that Glauber performed every photon-correlation experiment, nor that every narrow laser beam occupies an ideal coherent quantum state.

Sources: [2]

## A coincidence is conditioned on a delay

Split a stationary field and compare detection events in two channels at a specified delay. Normalize the joint rate by the product of single-channel rates. That comparison asks whether events arrive more or less often together than independent arrivals would predict.

For ideal single-mode counting, the zero-delay normalized correlation can be written using photon number. The subtraction of one counts distinct photon pairs in the same mode. The mean photon number must be nonzero; a vacuum record supplies no such normalized estimate.

$$
g^{(2)}(0)=\frac{\langle n(n-1)\rangle}{\langle n\rangle^2}
$$

Sources: [2]

## The ideal reference values need their assumptions

An ideal coherent state gives a value of one; a single thermal mode gives two; an ideal single-photon state gives zero. These are model limits. Combining many independent thermal modes reduces the bunching seen by a detector that does not resolve them.

Detector timing, dead time, background and afterpulsing also alter a measured histogram. A dip or peak should therefore be compared with the instrument response and acquisition window. The formula alone is not a certification procedure for a photon source.

Sources: [2]

## Coherence is not the same as monochromaticity

Glauber’s abstract states that coherent fields need not be monochromatic. A phase-related pulse contains a spectrum of frequencies. Conversely, spectral filtering can narrow a thermal source without turning its photon statistics into those of a coherent state.

This distinction connects the Michelson article’s visibility measurement with photon counting. First-order and higher-order experiments ask compatible but different questions about the same field.

Sources: [2] [1]

## Inspect the histogram before its fitted label

In the linked correlation Lab, compare the same counting duration across source models. Look for finite-count uncertainty and the effect of delay bins. Existing single-photon evidence articles then connect these statistics to particular historical source experiments; this article supplies the coherence framework.

Sources: [2]

## Explore the related models

Each link states what the existing model can explain and where the historical measurement goes further.

### [Compare delayed coincidences](https://sandboxphysics.com/labs/hbt-photon-correlation/)

Change source statistics and counting time.

Synthetic arrival records illustrate the ideal models; they are not Glauber’s experimental data or a source certificate.

## Sources and reading notes

The original author abstract was read. The single-mode number-state calculation is an explanatory ideal limit; publisher full text and a digitized historical histogram were not used.

1. [A. A. Michelson, Recent advances in spectroscopy (1907), length standards and visibility](https://www.nobelprize.org/uploads/2018/06/michelson-lecture.pdf)

   Length comparison and spectral visibility sections read in the Columbia-hosted lecture, especially pp.171–175; official PDF returned 403. [Read the hosted original](https://www.nevis.columbia.edu/~haas/documents/physics_nobel_lectures/physics01-21-1.pdf)

2. [R. J. Glauber, The Quantum Theory of Optical Coherence, Phys. Rev.130,2529 (1963)](https://journals.aps.org/pr/abstract/10.1103/PhysRev.130.2529)

   Author abstract read: the hierarchy of correlations, delayed coincidences and coherence without monochromaticity. Publisher full text not used.

[Probes, light and measurement: reading the evidence](https://sandboxphysics.com/stories/probe-evidence/) [The maser: selected molecules sustained a field](https://sandboxphysics.com/stories/probe-evidence/maser-inversion-and-feedback/) [Laser spectroscopy: a narrow feature inside a broad line](https://sandboxphysics.com/stories/probe-evidence/laser-spectroscopy-doppler-tests/) [Frequency combs: measuring where the ruler starts](https://sandboxphysics.com/stories/probe-evidence/frequency-comb-self-reference/) [Kao: guiding light was only half the problem](https://sandboxphysics.com/stories/probe-evidence/kao-loss-and-fibre-communication/) [CPA: amplify the energy while the pulse is long](https://sandboxphysics.com/stories/probe-evidence/cpa-stretch-amplify-compress/)