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Photon counting registers discrete detector events and their times. A beam splitter sends the selected light to two photodetectors; a coincidence circuit or time-recording system compares the outputs. With a vacuum input at the unused optical port, splitter fractions $R,T$ and independent quantum efficiencies ${\eta }_1,{\eta }_2$, a selected input photon reaches the two recorded channels with probabilities $p_1=R{\eta }_1$ and $p_2=T{\eta }_2$. Conditional on input occupation $N$, each pair of distinct photons contributes $p_1{p}_2$ to the cross-channel pair moment. ThereforeTheir normalized ratio recovers $g^{(2)}(0)$. This assumes number-resolving counts, or sufficiently dilute gates for threshold detectors to approximate them. One photon cannot create both channel counts in this ideal model.

Quantum optics studies light using quantum states of the electromagnetic field and their interaction with matter. Photon statistics asks how detections fluctuate; the quantum theory of optical coherence relates those detections to field correlations. A coherent state, thermal light, and a Fock state can have the same mean photon number yet different pair counts. This distinction makes photon counting useful for testing sources intended to emit one photon at a time.

In 1977, H. Jeff Kimble, Mario Dagenais, and Leonard Mandel excited a dilute sodium atomic beam with a resonant dye laser. Apertures restricted the observed atoms; a microscope objective collected fluorescence perpendicular to both beams. A beam splitter sent the collected light to two photomultipliers. Shaped pulses drove the start and stop inputs of a time-to-digital converter; its delay histogram rose away from zero delay, indicating photon antibunching. Turning the atomic beam off measured scattered-laser backgrounds. More than one contributing atom and scattered light limited the comparison with an ideal isolated two-level system; the paper explicitly treated corrections.^[ref]

A simple reason for suppressed immediate re-emission is visible in an ideal two-level system. After spontaneous emission, the atom is in $|g⟩$. Its emission operator ${\sigma }_{-}=|g⟩⟨e|$ obeys ${\sigma }_{-}^2=0$, so two instantaneous emissions are impossible. Excitation must rebuild the excited-state population before another emission. This argument explains the zero-delay idealization; the actual photon counting record additionally depends on collection, background, timing, and the number of contributing atoms.