Photons: Still Bosons

Last week, Dmitry Budker's group at Berkeley published a paper in Physical Review Letters (also free on the arxiv) with the somewhat drab title "Spectroscopic Test of Bose-Einsten Statistics for Photons." Honestly, I probably wouldn't've noticed it, even though this is the sort of precision AMO test of physics that I love, had it not been for the awesome press release Berkeley put together, and this image in particular (grabbed with its caption):

This is a nifty paper, and deserves a little explanation in Q&A format:

Is this another New Scientist style "Einstein was wrong" paper? No. If anything, it's an "Einstein was right" paper-- the experiment they describe shows that photons do, as expected, behave according to Bose-Einstein statistics.

OK. What does that mean, again? Physicists divide the world into two categories of fundamental particles: fermions, which obey Fermi-Dirac statistics, and bosons, which obey Bose-Einstein statistics. The most common application of this is the electrons in an atom: the consequence of Fermi-Dirac statistics as applied to the electrons in an atom is that no more than two electrons can occupy the same atomic energy level. This means that as you go to more complicated atoms with more electrons, later electrons go into higher energy states. This is what is responsible for all of chemistry, more or less.

Bosons, on the other hand, can happily occupy the same energy states as other bosons, which is what leads to phenomena like superconductivity and Bose-Einstein condensation. You can phrase the requirements of Bose-Einstein statistics in a negative manner, parallel to that used for electrons, though, which is that no two bosons will ever be found occupying an antisymmetric state. When applied to atomic barium, this negative statement of Bose-Einstein statistics says that a certain transition will never take place when the atoms are illuminated by laser light.

So, this is a paper where they measure nothing? Right. They measure nothing to extraordinary precision-- a few parts in a hundred billion.

So what sort of nothing did they measure? They looked for a two-photon transition between two particular states in atomic barium, which is forbidden when the two photons have the same frequency and opposite polarizations.

Wait, two photons? I thought photons were an all-or-nothing proposition? For two photons to be added together to make a transition from one atomic state to another requires the two photons to arrive at the atom at almost the same instant. This is incredibly unlikely in most normal situations, but if you have access to lasers at the right frequency, you can throw enough photons at an atom that it will happen occasionally. This generally requires a build-up cavity to get enough power to see it, which is what they do here.

OK, so they sent in lots of laser photons, and didn't see anything. How do they know they weren't just looking in the wrong place? That's where most of the work comes in. They had two dye lasers, charmingly dubbed "Scylla" and "Charybdis," that they used to make the photons, and they could arrange for the lasers to have either the same frequency, or slightly different frequencies (what matters for the two-photon transition is the sum of the two photons, so they can raise one a bit, and lower the other by a corresponding amount). They scanned the lasers over the range where they would expect to see the transition in both same-frequency and different-frequency configurations. When the frequencies were different, they saw the transitions as expected, and when they were the same, they saw no transition at all, as predicted by the theory.

Which is how they measured nothing to a few parts in a hundred billion? Exactly. They account for a bunch of other effects that might also come into play, and that's the limit they place on the nature of the photon: If photons have any non-bosonic character-- that is, any ability to exist in anti-symmetric states-- it's less than a few hundred-billionths of the bosonic part.

Is this a surprising result? No. Not at all. As far as we know, there's no reason to expect photons to deviate from Bose-Einstein statistics. This is just an exceptionally precise test of that expectation.

So why bother? There are certainly some physicists, mostly theorists, who think this sort of thing is a big waste of time. Then again, they tend to think that anything outside their particular area of theory is a big waste of time, so I don't take them too seriously.

The reason to do this is that we don't really know anything for sure until we measure it. It's exceedingly unlikely for photons to deviate from Bose-Einstein statistics, but it's (barely) conceivable that they might, and it's possible to test that, so it'd be crazy not to look. And if they did find some deviation, it would really stand a lot of physics on end, and that would certainly be worth seeing.

So it's a high-risk, high-payoff sort of thing. You probably wouldn't expend too much energy on this if it required a billion-dollar accelerator to do the test, but the nice thing about this experiment is that the whole thing fits in an ordinary laser lab. You need a couple of dye lasers, some vacuum hardware, and a lot of patience, but if you've got those things (as Dima Budker does), why not roll the dice?

But it's not really that high-risk, is it? What do you mean?

Well, their negative result, confirming conventional wisdom, landed in Physical Review Letters. That's a pretty good fallback option. Good point. It's in PRL mostly because the technical tricks used to make the measurement are pretty impressive in their own right, even if the end result was pretty obvious.

Of course, nice as PRL may be, if they'd gotten a positive result, they would've been looking at a paper in Nature and a probable trip to Stockholm, so it's not like they got the full payoff, either...

English, D., Yashchuk, V., & Budker, D. (2010). Spectroscopic Test of Bose-Einstein Statistics for Photons Physical Review Letters, 104 (25) DOI: 10.1103/PhysRevLett.104.253604