A photon announces when to look for its partner

A first click opens a short gate

A dim light beam leaves a detector silent most of the time. Silence alone tells little about how many photons arrive when it does click. In 1986 Grangier, Roger and Aspect used atoms that emitted two photons in succession. The first photon’s detection announced when to look for the second. A beam splitter then offered that second photon two output paths, each ending at a detector.

The announcement opened a short counting interval, called a gate. An ideal single photon gives one output click at most. The experimenters therefore asked how often both output detectors clicked in the same gate, compared with how often either detector clicked on its own.

The measurement needs four counts from the same run: the gates opened, the clicks in each output and the joint clicks within a gate. A small joint count means little on its own if almost no light reaches either detector. The single-detector counts and the gate count set the scale it is compared with.

Read the evidence: P. Grangier, G. Roger and A. Aspect (1986), Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter, EPL 1, 173–179 — institutional copy

What a classical wave would give

In the expression, N-gate counts the opened intervals, N-A and N-B count clicks at each output, and N-AB counts intervals with both clicks. A semiclassical comparison treats light as a fluctuating wave and detections as random clicks. In its weak-response limit, each output’s click probability is proportional to the same nonnegative light intensity integrated over the gate. Efficiencies stay fixed, and the detections are independent once that intensity is specified.

Fluctuating intensity can increase joint clicks, but its variance cannot be negative. That gives the normalized parameter alpha a lower bound of one in this classical model. Ideal single-photon input instead gives zero joint clicks.

This sets a lower bound of one on the normalized anticorrelation parameter. An ideal single photon gives no joint detections at all. For this comparison, numerator and denominator must use the same gate definition and the same treatment of background, saturation and electronic cross-talk.

\begin{gathered}\alpha=\frac{N_{\mathrm{gate}}N_{AB}}{N_A N_B}\geq 1\\\text{(classical, linear response)}\end{gathered}

Read the evidence: P. Grangier, G. Roger and A. Aspect (1986), Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter, EPL 1, 173–179 — institutional copy Institut d’Optique, Lab work in photonics, Single-Photon Interferences: Grangier–Roger–Aspect, pp. 71–95

A worked example with a small count table

Take an invented run with ten thousand gates, one thousand clicks in output A, eight hundred in output B and eight joint clicks. The normalized parameter is one tenth. Sorted into events, that is eight joint events, 992 A-only events, 792 B-only events and 8,208 empty gates.

Listing events this way stops joint clicks from being counted again as extra trials. It also makes the analysis repeatable, since changing the coincidence window changes which clicks count as one event. The example is only arithmetic and claims no significance; a real confidence interval must account for the joint count and the shared denominators.

Read the evidence: P. Grangier, G. Roger and A. Aspect (1986), Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter, EPL 1, 173–179 — institutional copy

Loss and background do different things

In the linear-response approximation, independent losses in each output cancel from this ratio. Low efficiency can still leave most gates empty. Even a joint probability of exactly zero cannot tell a photon in every heralded trial from an ideal mixture of many empty trials and trials with at most one photon.

Dark counts, unrelated emission and multiple cascades can add coincidences. Detector dead time or shared electronics can also suppress joint clicks artificially. To judge a source, measure how often a herald is followed by a photon and check the background as well as the anticorrelation, keeping raw and corrected counts clearly labeled.

Take our own Poisson example, with a mean of one tenth of a photon per chosen pulse. About nine and a half percent of pulses contain any light, and about 4.9 percent of those nonempty pulses still hold two or more photons. Dimming mostly adds empty pulses; it does not guarantee exactly one photon when something does arrive.

In the ideal model, attenuation keeps the statistics Poissonian. A herald helps because it changes which trials are tested, but its conditional counts must be measured too. Calling both sources simply faint would hide the very difference the triggered experiment was designed to test.

Interference asks another question

The same source was also sent through an interferometer. Fringes test how alternatives combine with their phases; anticorrelation at the outputs tests joint detection statistics. An attenuated classical field can show excellent fringes, so visibility alone cannot replace the triggered counting test.

Together, the two measurements asked how a source behaves in two arrangements. A beam splitter revealed the conditional joint-count statistics; an interferometer revealed how the alternative paths combined. Characterizing the source first makes the later interference experiment easier to interpret.