---
title: "Counting stored photons one atom at a time"
description: "How does a string of binary atomic outcomes become a photon-number estimate without absorbing the field?"
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---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Counting stored photons one atom at a time

Sandbox Physics · 2026-10-16

How does a string of binary atomic outcomes become a photon-number estimate without absorbing the field?

## The detector reads atoms and leaves the photons in place

In 2007 Guerlin and colleagues counted microwave photons while leaving the light stored in a cavity. Their probes were Rydberg atoms, whose outer electron is excited far from the atomic core. Each atom crossed the cavity with its transition tuned away from resonance, so the interaction shifted the atom’s phase without absorbing a photon.

Each atom acts like a small clock, prepared with two internal components whose relative timing, or phase, can change. The stored light shifts that timing by an amount that depends on photon number. A pair of Ramsey pulses compares the phase with a reference and converts it into one of two detectable atomic states. Each result is a partial clue; successive atoms gradually distinguish the possible numbers.

The detector recorded atomic outcomes, the chosen analysis phases and their times. From that sequence the researchers inferred how likely each photon number was. The resulting number trace was a measurement-based estimate, with uncertainty that could change after every atom.

Read the evidence: C. Guerlin et al. (2007), Progressive Field-State Collapse and Quantum Non-Demolition Photon Counting — author manuscript, arXiv:0707.3880; Nature 448, 889–893

## Try a two-candidate example

Suppose two photon numbers are equally likely at the start. A particular atomic result occurs with probability four fifths for the first candidate and one fifth for the second. Seeing that result changes their probabilities to four fifths and one fifth: the first candidate is now four times as likely.

If a second atom has the same likelihoods and gives the same result, the first candidate rises to sixteen seventeenths. If the second result instead has the likelihoods swapped, the two candidates are back to equal weight. This arithmetic assumes the photon number stays fixed and the atoms are independent for a given number; neither sequence comes from the experiment.

Read the evidence: C. Guerlin et al. (2007), Progressive Field-State Collapse and Quantum Non-Demolition Photon Counting — author manuscript, arXiv:0707.3880; Nature 448, 889–893

## Keep track of every possible number

The arithmetic is Bayes’ rule: multiply each candidate’s current probability by how likely it was to produce the new result, then rescale so the probabilities add to one. In the formula, P is the probability assigned to a photon number n after k detections; j is the next atomic outcome, phi is the chosen analysis phase, and ell is its calibrated probability for a candidate number. The denominator adds the weights over all candidate numbers r. This update assumes number changes can be neglected during the sequence.

Keeping the whole distribution matters. Two nearly tied candidates and one overwhelming favourite can show the same best guess, yet they justify different confidence in a claimed jump and can react differently to the next atomic result.

$$
P_{k+1}(n)=\frac{P_k(n)\,\ell(j_k\mid n,\varphi_k)}{\sum_r P_k(r)\,\ell(j_k\mid r,\varphi_k)}
$$

Read the evidence: C. Guerlin et al. (2007), Progressive Field-State Collapse and Quantum Non-Demolition Photon Counting — author manuscript, arXiv:0707.3880; Nature 448, 889–893

## The phase readout repeats after eight photons

Each photon shifted the atomic phase by about one eighth of a turn, so the ideal response repeated every eight photons. Changing the analysis phase helped tell candidates apart within that range, but it could not turn a periodic response into a counter with unlimited range.

Two photon numbers a full period apart give the same probabilities for every atomic result in this ideal response. Repeating those measurements therefore leaves the ambiguity in place. The experiment needs a stated range of candidate numbers; within it, changing the analysis phase makes successive atoms useful at separating the remaining possibilities.

Read the evidence: C. Guerlin et al. (2007), Progressive Field-State Collapse and Quantum Non-Demolition Photon Counting — author manuscript, arXiv:0707.3880; Nature 448, 889–893

## Non-demolition refers to one specific observable

Haroche’s account separates keeping the light from keeping all its quantum properties. In the ideal dispersive interaction, the probes exchange no energy with the field, so they do not change the photon number. Learning the number still changes the conditional field state and can remove coherence between different number components. This is a physical measurement backaction as well as an update of what can be inferred from the record.

Cavity loss and thermal exchange can change the number during a long record. A reconstruction must then include that time evolution as well as the probes. Keeping the atomic outcomes and calibration makes the reconstruction checkable: a broad initial distribution reveals how much the detections contribute, and ambiguous stretches remain visible as several competing candidates.

This made repeated observation possible. An estimate could settle near an integer and stay there through further probes, then change as the cavity lost energy. The same stored field could be followed across many measurements, one atomic result at a time.

Read the evidence: S. Haroche (2013), Nobel Lecture: Controlling Photons in a Box and Exploring the Quantum to Classical Boundary, Rev. Mod. Phys. 85, 1083–1102 — published version of the 2012 lecture

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Accumulate probe-atom outcomes and infer cavity photon number](https://sandboxphysics.com/labs/cavity-photon-qnd-feedback/)
- [See how a phase becomes a population readout](https://sandboxphysics.com/labs/ramsey-frequency/)
- [Distinguish information gain from coherence preservation](https://sandboxphysics.com/labs/decoherence-channels/)

## Sources and reading notes

The arXiv manuscript of Guerlin et al. (2007), especially the atom results, phase settings and number-dependent response, was consulted with Haroche’s published lecture. The two-candidate arithmetic is an invented example. The QND Lab generates synthetic atom outcomes for a declared finite-number model; it does not digitize the experimental sequence or certify its historical fidelity.

1. [C. Guerlin et al. (2007), Progressive Field-State Collapse and Quantum Non-Demolition Photon Counting — author manuscript, arXiv:0707.3880; Nature 448, 889–893](https://arxiv.org/pdf/0707.3880)
2. [S. Haroche (2013), Nobel Lecture: Controlling Photons in a Box and Exploring the Quantum to Classical Boundary, Rev. Mod. Phys. 85, 1083–1102 — published version of the 2012 lecture](https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.85.1083)

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