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Reading on the Hong-Ou-Mandel (HOM) effect, I came to wonder how exactly we can be certain that interference that occurs in apparatuses such as a Michelson interferometer and Mach-Zehnder interferometer is truly an occurrence of single-photon interference rather than two-photon interference as seen in the HOM effect. So, my question is: how is it that we can be confident that the interference in such interferometers are truly single photon interactions or two photon interactions?

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    $\begingroup$ Isn't HOM explicitly about two photon interactions, i.e. when two photons, with similar waveforms, are incident on the beamsplitter? In this case all you need to do is detect two clicks and count them $\endgroup$
    – Cryo
    Commented Mar 4 at 7:57

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In all cases can you reduce the intensity to make it extremely unlikely that you have more than 2 photons in the HOM case, and more than one photon in the single-photon case. Moreover, in both cases the actual number of photons detected is the number expected in a run.

If you look at the data of the original HOM experiment, the count rate in 10mins is quite low (not even 1000 pairs). Indeed at the bottom of the dip the rate is 100ish coincidence events over 600 seconds, which is extremely low. A modern version have near 0 rates so you know you never detect two photons in different detectors.

Of course the theory could be wrong at every step, i.e. if could be that the modelling of the sources is wrong, the modelling of the detectors is wrong, and the modelling of the interferometer is wrong, but these are checked independently so the probability that something is misunderstood when the pieces are put together is minuscule: it is simpler to believe the current theoretical explanation than concoct some convoluted alternative.

The same holds for the single photon interference experiments.

Finally, these have been repeated multiple times: HOM is now used for benchmarking sources. You can be pretty sure that, if there was a bug or an inconsistency somewhere, it would be known by now. In other words, the weight of experimental evidence is now overwhelmingly in favour of the “traditional” explanations.

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So far I have seen no experimental explanation so I think this entry is also somewhat valuable.

Here are some excerpts from a presentation of the Max Planck Institute (MPI) about two photon interference:

https://www.mpq.mpg.de/5020845/0508b_two-photon_interference.pdf

A classical mach-zender interferometer would be similar to that of a quantum eraser:

Setup from Thorlabs https://www.thorlabs.com/NewGroupPage9_PF.cfm?ObjectGroup_ID=6957

You have a laser, a beam splitter that splits the beam power 50%/50%, a distance between the beams exactly the same on both arms (top and straight if you follow the beam path after the first beam splitter), then another beam splitter that is imaged onto a screen in the background. The quantum eraser is a different idea altogether so I will not go too deep into how it works, but here what is important is that when all the polarization filters are set to 0°, you can clearly see the classical interference of both arms in both screens.

HOM setup

Here you can see the setup originally suggested by HOM in their seminal paper, where essentially you need a "subpicosecond photon wave packet" for the experiment to work. This means that the laser is pulsed at a couple femtoseconds, in order to achieve the aforementioned photon packets. The interference then is related to the displacement of the beam splitter:

position of BS Vs coincidence

HOM do note that the apparent influence of the choice of position of the detectors and its relation to the counts as seen before:

"This conclusion is related to the fact that in quantum mechanics we cannot associate an objective physical reality with the two photons that is independent of the measurement we choose to make. The phenomenon involves the same violation of local realism that was recently tested in the experiments of Aspect and his collaborators, and was first discussed by Einstein, Podolsky, and Rosen"

In the framework that HOM establish the certainty is correlated to the choice of detectors and distance of the beam splitters, as they play a pivotal role in the measurements that you obtain.

There are more involved ways to obtain something close to "single photons", but you cannot directly (at least not in the sources where I looked it up) a single photon that interferes with another single photon. You can get a very close approximation and infere what happens with relation to the setup, but single photons are difficult to maneuver and a hot research topic.

You can see here such setup:

atom cavity system for single photon generation

The best way to consistenly know whether you have a photon or a wave is by having the 2 detectors (going back to my explanation of the MZI from Thorlabs, the screens are simply "visual" detectors):

https://www.qutools.com/files/quED/worksheets/qutools_HBT.pdf

Qutools gives a very succint image to explain the phenomenon:

From Qutools GmbH

Once light is indivisible in more fundamental units (or photons), the particles will travel through one path ONLY. You can tell if this occurs through the second order coherence function which is zero (the second order coherence function is smaller than the first order coherence function) for single photons. All other light sources have a value of exactly one (1) because there will always be an event where, for example, both detectors have a coincidence measurement (e.g. both detectors measure something, even random light from the room). At the point where there are no coincidences between detectors, a single photon has been detected.

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We can tune both arms of an MZ interferometer so that no photons go thru. So now we have 0 photon interference!

Photons will not travel the arms if the path length between mirrors is lambda x n + 0.5 lambda. ( n is an integer).

Per Dirac Feynman and many others each photon behaves on its own. It is the EM field that controls/guides the photons. The EM field sees all in the apparatus.

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In our current era of technology, this is pretty straightforward.

  1. Two Photon Interference: As you mention the HOM effect, I have the original 1987 paper they presented - still relevant today. Two photon interference requires indistinguishable photons, in this case produced from parametric down conversion (PDC). The key elements are that the range of the overlap of the photons is extremely small (femtosecond regime), and follows theory. The dip is clearly a result of destructive interference of the photon pair at the beam splitter. You know it is 2 photons because there are clicks at both detectors. To put it in perspective, the theoretical resolution of the overlap is on the order of 500-1000 nm or approx. 3 femtoseconds. Actual was not quite that. The photons were at a wavelength of about 752 nm.

Measurement of subpicosecond time intervals between two photons by interference

  1. On the other hand: single photon interference can be detected using PDC pairs as well. However, one is used as the the idler (A in the diagram) to herald the presence of the lone signal photon (D in the diagram) in the interferometer apparatus. So there cannot be 2 photon interference, as there is no point of overlap at all in the MZI (i.e. there is just one photon entering). The interference of the single photon between the 2 possible paths to D is constructive, while paths to the other output port cancel.

Using a Mach Zehnder Interferometer to observe Quantum Interference using a Single Photon Beam (a summary of Pearson & Jackson's paper "A hands-on introduction to single photons and quantum mechanics for undergraduates" which I could not locate other than as an abstract).

So in these cases, you know clearly whether you are observing single or double photon interference.

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