The experiment scanned a delay and counted pairs
Send one photon into each side of a balanced beam splitter. If the photons arrive in matching modes, they leave together through one output, and the two output detectors stop clicking in coincidence. Hong, Ou and Mandel used this effect in 1987: they made photon pairs by down-conversion and scanned the splitter’s position. The resulting dip resolved a relative time scale much shorter than the detectors could time directly.
The plotted coincidences have accidental coincidences subtracted. The electronics used a 7.5-nanosecond coincidence window, and a shifted window estimated the accidentals. The electronic window groups clicks into coincidences; the coherence time of about a hundred femtoseconds, inferred from the optical scan, describes the much shorter wave-packet scale revealed by interference.
Read the evidence: C. K. Hong, Z. Y. Ou and L. Mandel (1987), Measurement of Subpicosecond Time Intervals between Two Photons by Interference, PRL 59, 2044–2046 — scanned copy
Two alternatives cancel at full overlap
There are two ways for one photon to reach each output: both input photons can be transmitted, or both can be reflected. When the alternatives cannot be distinguished, quantum theory adds their amplitudes, the signed quantities whose squared sizes give probabilities. At full overlap the two amplitudes cancel. The photons remain in the outputs; they simply travel together.
The equation describes exactly one independent pure photon in each input, a lossless balanced splitter and ideal collection. Here tau is the scanned relative delay; f and g-tau describe the normalized wave packets, and the squared overlap between them measures how indistinguishable they are across all internal modes. Orthogonal polarizations or nonoverlapping arrival modes restore a coincidence probability of one half.
Read the evidence: C. K. Hong, Z. Y. Ou and L. Mandel (1987), Measurement of Subpicosecond Time Intervals between Two Photons by Interference, PRL 59, 2044–2046 — scanned copyA. M. Brańczyk (2017), Hong–Ou–Mandel Interference — author notes, arXiv:1711.00080
A mixed input gives a shallower dip
Identical spectra are not enough to justify the pure-product formula. In our own mixed-state example with two orthogonal modes, each photon is in either mode with equal probability. Half the pairs then match and half do not, so the average coincidence probability at zero delay is one quarter.
Even with otherwise perfect optics, the dip goes only halfway down from the distinguishable level. If the photons’ spectra are correlated, the calculation needs their joint state. The historical down-conversion calculation and our pure-packet example therefore answer related questions under different assumptions about the input.
Take an invented lossless splitter that reflects 0.60 of the intensity and transmits 0.40. Perfectly matched photons then give a coincidence probability of 0.04, and distinguishable photons give 0.52. The visibility is about 0.923. Here the nonzero minimum comes entirely from the imbalance.
The matched result comes from adding the signed amplitudes for double reflection and double transmission, then squaring. Adding their probabilities instead gives the distinguishable level. This gives an independent check on the dip: reaching zero requires both a balanced splitter and matched photons.
Read the evidence: A. M. Brańczyk (2017), Hong–Ou–Mandel Interference — author notes, arXiv:1711.00080C. K. Hong, Z. Y. Ou and L. Mandel (1987), Measurement of Subpicosecond Time Intervals between Two Photons by Interference, PRL 59, 2044–2046 — scanned copy
Say how the curve was normalized
In another invented example, a bin far from zero delay holds 110 events and the dip bin holds 20, each with a separately estimated constant background of ten. The raw visibility is about 0.818; after subtracting background it is 0.90. Both numbers are legitimate, but a report must say which one it gives.
Report the exposure time, source drift, how the accidental window was scaled and how uncertainties were propagated along with the curve. A displacement must also be converted to delay through the actual path geometry. Moving a reflector can change a round-trip path by twice the displacement, so relabeling a distance axis as a delay axis can misstate the width.
Read the evidence: C. K. Hong, Z. Y. Ou and L. Mandel (1987), Measurement of Subpicosecond Time Intervals between Two Photons by Interference, PRL 59, 2044–2046 — scanned copy
The dip tests one component, not the whole protocol
Good two-photon interference helps a Bell-state analyzer work as intended. On its own, it does not certify polarization entanglement, close the detection loophole or make a complete quantum communication channel. Those tasks need more settings and a full account of resources.
This interference supplies an important ingredient for joint photon measurements. In swapping and dense coding, the analyzer combines alternatives at a beam splitter before a detector pattern is interpreted as a particular joint result. The coincidence dip tests how well that ingredient works.
Read the evidence: A. M. Brańczyk (2017), Hong–Ou–Mandel Interference — author notes, arXiv:1711.00080J.-W. Pan, D. Bouwmeester, H. Weinfurter and A. Zeilinger (1998), Experimental Entanglement Swapping, PRL 80, 3891–3894