The detector reads an atom, not an absorbed photon
Guerlin and colleagues used successive off-resonant Rydberg atoms to interrogate a microwave field in 2007. The field changed the atomic phase; a Ramsey sequence converted that phase information into a binary atomic result. Several probes gradually distinguished possible photon numbers.
Begin with the actual record: an outcome, the selected analysis phase and its time. A displayed photon-number trace is an inference made from those entries. Colouring the most likely number cannot replace showing how an uncertain group of outcomes became that estimate.
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
Update the distribution, not just its favourite value
Let the lower-case ell denote the calibrated probability of the observed atomic result for a candidate photon number and chosen phase. For an interval in which number changes can be neglected, Bayes’ rule gives the update below. The denominator sums over all candidates and makes the probabilities add to one.
Keeping the whole distribution matters. Two nearly tied candidates and one overwhelmingly favoured candidate can have the same displayed best guess. They should trigger different confidence in a claimed jump, and they can respond differently to the next atomic result.
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
Imagine two possible photon numbers with equal prior probabilities. A particular result has probability four fifths for the first and one fifth for the second. After that result, their posterior probabilities become four fifths and one fifth. One clue favours an answer without proving it.
If a second probe has the same likelihoods and produces the same result, the first candidate has posterior probability sixteen seventeenths. If the second result instead has the complementary likelihoods, the two candidates return to equal weights. These arithmetic examples assume a fixed number and conditionally independent probes; neither sequence is historical data.
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
A phase clock has an ambiguity range
The experiment’s approximately one-eighth-turn phase shift per photon made the ideal response repeat after eight photons. Changing the analysis phase helped distinguish candidates within that range; it could not turn a periodic response into an unlimited absolute counter.
This is an inverse-problem lesson. Write down two candidates separated by one full response period and compare every possible outcome probability. If they agree, no quantity of otherwise identical probing distinguishes them. A prior restricting the occupied range is useful information, but it must remain visible in the inference contract.
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 has a named observable
Haroche’s account distinguishes retaining light from preserving all its quantum properties. In the ideal dispersive interaction, number is not changed by exchanging energy with each probe. Learning number nevertheless changes the conditional field state and can remove coherence between different number components.
A fair comparison therefore asks two questions separately: did the probe induce unwanted number transitions, and did the measurement reveal information? Cavity loss and thermal exchange add a third process. They can change the number during a long record, invalidating a fixed-number likelihood product unless the time evolution is included.
A sharp estimate needs checks outside the plot
For an audit, retain the atomic sequence and calibration, vary a deliberately broad prior, and check when the available record ceases to support a constant number. Show ambiguous intervals as distributions rather than drawing an uninterrupted certainty line through them.
The linked models explain Ramsey phase readout and decoherence separately. They do not replay the microwave experiment or certify its historical measurement fidelity. The lesson is how a physical probe and a calibrated likelihood support an estimate, with a clear boundary between data, conditional state and later visualization.