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Hong–Ou–Mandel effecteffect

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Discovered in 1987 by Chung Ki Hong, Zhe-Yu Ou, and Leonard Mandel, this effect revealed strange quantum behavior: two identical photons meeting at a beam splitter always stick together. A beam splitter is like a half-silvered mirror, reflecting half the light and transmitting half. From a classical perspective, sometimes the photons would end up in different detectors, but in the quantum world, interference of probability amplitudes completely excludes that outcome. This is a vivid demonstration that photons are indistinguishable particles obeying Bose–Einstein statistics, which favors occupying the same state. The original experiment used parametric down-conversion to create photon pairs and revealed a sharp dip in coincidence counts.

How it works

The effect appears in experiments with single-photon sources. For example, if two photons from such sources are sent to a beam splitter (half-silvered mirror), the detectors at the outputs will never click simultaneously when the photons are perfectly identical. This is used to test the degree of indistinguishability of photons and in quantum communication for security.

💡 The 'Hong–Ou–Mandel dip' is so sensitive that it allows measuring delays of just a few femtoseconds (millionths of a billionth of a second), turning it into a tool for ultrafast synchronization.
|1,1\rangle \xrightarrow{BS} \frac{1}{\sqrt{2}}(|2,0\rangle - |0,2\rangle)
|1,1\rangle — initial state with one photon in each of the two inputs; BS — 50:50 beam splitter; |2,0\rangle and |0,2\rangle — states with two photons in the first or second output. This superposition means that the photons always end up together, but which output is random.
P_{coin}(\tau) = \frac{1}{2}\left[1 - e^{-\frac{(\Delta\omega \tau)^2}{2}}\right]
P_{coin} — probability of two detectors clicking simultaneously (coincidences); \tau — time delay between the arrival of photons at the beam splitter; \Delta\omega — frequency bandwidth of the photons (characterizes their spectral purity). For \tau=0 and perfect indistinguishability, P_{coin}=0.
Links in the knowledge graph 1
Discovered by
Jeff KimbleLeonard MandelRoy Glauber
Related concepts
quantum opticsphotoninterference
Related laws
superposition principleBorn rule

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