Hong-Ou-Mandel effect

In plain terms

A beam splitter is a half-silvered mirror, so light that hits it is either transmitted straight through or reflected, and for a single photon, a single particle of light, the choice is random with equal odds. Now send two photons at the splitter from opposite sides so they arrive at the same instant, with a detector waiting at each exit. Simple counting suggests that half the time the photons should leave through different exits, with one detector clicking on each side, an event called a coincidence.

The experiment says never. If the photons are truly identical, the two histories that lead to a coincidence, both transmitted and both reflected, cancel each other. In quantum mechanics each possible history carries a number called an amplitude, and when different histories end in the same outcome their amplitudes are added before the probability is worked out, so for the coincidence outcome the two amplitudes are equal and opposite and their sum is zero. Both photons always leave through the same exit, and coincidence counts drop to nothing.

The signature is the Hong-Ou-Mandel dip. Scan the time offset between the photons' arrivals and watch the coincidences vanish as the two become simultaneous. The depth of the dip measures how identical the photons are, and its width measures their coherence time, the stretch of time over which each photon's wave keeps step with itself. What began as a demonstration is now a workshop tool, the standard ruler for indistinguishability in photonics.

In CSD

The Hong-Ou-Mandel effect is one of the programme's empirical twins, the flagship experiments CSD's machine-checked corpus reproduces as pass-or-fail tests, and it was chosen because it probes a different organ from the Bell family of experiments. There's no separation here and no question of locality at all, only two alternatives cancelling. The question it puts to any account of quantum mechanics is pure, as it asks what, in your description of the world, is the difference between both photons transmitted and both reflected, such that the two can annihilate.

For a theory with an underlying substrate the question has bite, because naively the two configurations differ only by a relabelling that nothing could observe. Reproducing the dip is therefore a real constraint on how CSD's regions and volumes handle the exchange of identical particles, which is exactly why the case is carried.

Mathematically

For two indistinguishable bosons at the input ports of a balanced beam splitter, the both-transmitted and both-reflected amplitudes cancel, so the output is a superposition of both-photons-left and both-photons-right and the coincidence rate is zero.

Partial distinguishability revives coincidences in proportion, which makes the visibility of the dip a quantitative measure of photon identity.

The name

Chung Ki Hong and Zheyu (Jeff) Ou were graduate students of Leonard Mandel at the University of Rochester when the three demonstrated the effect in 1987, in a paper whose stated headline was metrological, measuring sub-picosecond time intervals by counting coincidences, decades before femtosecond lasers made such numbers routine.

Mandel (1927-2001), born in Berlin and brought to Britain as a refugee in 1938, took his degrees at Birkbeck College London and moved to Rochester in 1964, where he effectively founded experimental quantum optics, and half the field's senior figures passed through his group. Ou went on to a professorship at IUPUI in Indianapolis.

Related entries

• Mach-Zehnder interferometerSplit a single particle down two paths and recombine them, and where it lands depends on both paths, including the one you can prove it never took.
• Elitzur-Vaidman bomb testerYou can certify that a bomb is live without a single photon touching it, so the absence of an interaction becomes the measurement.
• Bell state is not a joinThe arena CSD assigns to two systems together is strictly larger than the two arenas simply paired, and the Bell state is a point of the excess, so entanglement is located exactly.
• Typicality volumeAlmost every way the experiment could have started gives the quantum statistics, and that isn't an assumption about probability, as it's a measured volume.
• Ramsey interferometryTwo brief nudges separated by a long stretch of doing nothing measure a frequency more sharply than any amount of continuous pushing, and every atomic clock runs on this trick.