Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment

Earlier this week, I talked about the technical requirements for taking a picture of an interference pattern from two independent lasers, and mentioned in passing that a 1967 experiment by Pfleegor and Mandel had already shown the interference effect. Their experiment was clever enough to deserve the ResearchBlogging Q&A treatment, though, so here we go:

OK, so why is this really old experiment worth talking about? What did they do? They demonstrated interference between two completely independent lasers, showing that when they overlapped the beams, the overlap region contained a pattern of bright and dark spots characteristic of interference.

How did they do that in 1967? What did they use, photographic plates? No, they used photomultiplier tubes, that produce an electrical pulse when a single photon falls on them.

But a PMT only detects photons in a single position. How did they make a picture out of that? They didn't, because they found a clever way to arrange it so they didn't need to. Here's a schematic of their apparatus:

All right, what are we looking at? In the upper left, you see a diagram showing the optical layout. They start with two independent lasers, and split off a small part of the light from each to go to a detector that monitors the frequency difference between the two lasers, and only turns on the detector system when the lasers are close enough in frequency to produce a good interference pattern.

Wait a minute. These are lasers, aren't they a single frequency? They are, but the frequency wanders around a little bit, just enough to change the interference pattern a little. As a precaution, they only look for the pattern at times when both lasers have wandered into the same basic range.

OK, so they've got two lasers. Then what? Then they take the two independent lasers and steer them together with mirrors, and overlap them with a small angle between the two. This should produce an interference pattern with a spacing between bright and dark fringes that depends on the angle between the beams. They put this pattern onto a specially made detector.

Yeah, that's the whole question. How does that work, when they just have PMT's as detectors? The detector they used (inspired by a Dr. Neil Isenor, who gets a footnote of thanks but not an author credit) is shown in the inset at the lower right. It's an array of small glass plates, cut like little prisms, with a thickness equal to roughly half of the spacing between one bright spot and the next in the expected interference pattern. The odd-numbered prisms-- first, third, fifth, etc.-- direct light falling on them to one PMT, while the even-numbered prisms-- second, fourth, sixth, etc.-- direct light hitting them to another PMT. When the light falls on the stack in just the right way, the bright spots in the pattern will fall on the odd-numbered prisms while the dark spots fall on the even-numbered prisms, so one detector will detect lots of photons, while the other sees almost nothing.

Yeah, but how do they get the pattern to line up? I mean, you said that the problem with this measurement is that the pattern changes position randomly all the time. That's the really clever part. They don't need to have a stable interference pattern, and they don't need to have the pattern line up precisely with one set of prisms. All they have to do is look at correlations between the detector signals.

You see, if the pattern falls with the bright spots on one set of prisms, one detector will get all the photons, while the other gets none. If you shift the pattern so the bright spots are on the other set, then the second detector gets all the light, and the first one gets none. Which shows that the signals from the two detectors should be anti-correlated-- when one gets a lot of light, the other gets very little.

But if you shift the pattern only halfway, then they each get half of the photons. True, but that's only true in a tiny range. Most of the time, one detector will get more photons than the other. That means that, statistically, you expect that any smallish sample of the count data will show a significant imbalance between the two. That's the thing they look for in the data.

And that worked? Yes. They have a table in the paper showing the counts on each detector for 25 different trials lasting 20 microseconds each. The average number of counts per detector over the whole sample was pretty close-- 5.08 for one and 4.40 for the other-- but the individual trials almost all show a significantly greater number on one detector than the other. The correlation coefficient between the two count rates is negative, as you would expect from an interference pattern falling on the detector.

I don't know, dude. It's not science without graphs. Isn't there a graph you could show? Ask, and ye shall receive:

This shows the correlation coefficient (plotted with negative numbers being up) as a function of the ratio of the thickness of the prisms L to the expected fringe spacing l. When the thickness is equal to the spacing, so that if one bright spot falls on an odd-numbered prism, the next bright spot will fall on the next odd-numbered prism, they see a maximum in the negative correlation, which drops off as the fringes get either closer together or farther apart. The lines in the graph are the predictions of a simple model of the expected statistics, for different values of the number of pairs of prisms illuminated. Their data agree very nicely with something between 2 and 3 pairs illuminated.

OK, so their detector shows an interference pattern between photons from two different lasers. How does that work, exactly? Do the two photons bounce off each other, or something? That's the other cool thing about this experiment. Before they sent the beams onto the detectors, they used big filters to knock the intensity way down. They used big enough filters that there was only one photon (on average) in the apparatus at any given time. They got around 10 photons per 20 microsecond data run, which gives an average spacing between photons of 2 microseconds, which corresponds to a spatial separation of about 2000 feet (the speed of light being very nearly one foot per nanosecond).

This large spacing means that this isn't an interference caused by two simultaneously arriving photons, but rather a single photon arriving and somehow knowing that it needs to form an interference pattern, even though it can only have come from one laser.

OK, that's just weird. How do you explain that? The key issue here is that you have no way of knowing for sure which laser the photon came from. That's what allows you to see interference. When they block one laser or the other, so that they know for sure which laser the photon came from, the interference goes away.

Yeah, but what's interfering? I mean, a photon can't really come from two places at once, can it? That's the tricky bit. They have a wonderfully deadpan way of putting this: "In terms of photons, the experiment raises one or two interesting questions of interpretation."

That's an understatement. Exactly.

There are two ways you can go with this. One is to view it as an interference created by the detection process. That's the language they use: "It seems better to associate the interference with the detection process itself, in the sense that the localization of a photon at the detector makes it intrinsically uncertain from which of the two sources it came." This is a little toward the Copenhagen side of things, interpretation-wise, though it could also be a little Bohmian. It says that the observed pattern is something to do with the detectors-- that configuring the detectors the way they did creates a situation in which the only possible outcome is an interference pattern.

Another way of putting it would be to use the language of field theory. That is, the photons we talk about as particles are really excitations of a mode of the electromagnetic field having a specific wavelength and direction. The interference pattern you see is an interference between two modes of the field, meaning that one photon coming in to the detector is necessarily an excitation of a field mode that contains the interference pattern within it.

In either case, the important thing here is that the photons are not strictly particles in the classical sense. There's something nonlocal about them, that allows an interference pattern to be produced even when you have only one photon, but aren't certain of its place of origin.

That's, um, really odd. Yes, yes it is. Which is why this experiment didn't go in the book-- it's a little too strange and requires a little too much hand-waving to explain. But it's a very cool experiment, and an impressive display of ingenuity.

Pfleegor, R., & Mandel, L. (1967). Interference of Independent Photon Beams Physical Review, 159 (5), 1084-1088 DOI: 10.1103/PhysRev.159.1084