Treating Photons Like Atoms: “Bose-Einstein condensation of photons in an optical microcavity”

This paper made a big splash back in November, with lots of news stories talking about it; it even made the #6 spot on Physics World‘s list of breakthroughs of the year. I didn’t write it up then because I was hellishly busy, and couldn’t take time away from working on the book-in-progress to figure out exactly what they did and why it mattered. I’ve got a little space now between handing the manuscript in last week and starting to revise it (probably next week), so while it’s a bit late, here’s an attempt at an explanation of what all the excitement was about.

So, what’s this about, anyway? The authors created a Bose-Einstein condensate (BEC) out of a “gas” of photons inside a very small optical cavity filled with laser dye. They found that, when the number of photons inside the cavity got strong enough, they would “condense” into a single mode of the cavity with a narrow spread in frequency and a narrow spatial profile. They could get a substatial fraction of the photons inside the cavity to occupy that single mode, in much the same way that a BEC of atoms or molecules consists of a substantial fraction of the atoms in the sample occupying a single quantum state.

Wait, isn’t that just a laser? You might think that– it certainly has all the normal elements we associate with lasers: a cavity with photons inside, a narrow output beam, an organic dye (Rhodamine 6G), even a pump laser providing photons to the system. The difference between this system and a laser is very subtle, and making the distinction is complicated by the fact that people studying BEC will often refer to it as an “atom laser,” or use lasers as an example of a system in which large numbers of bosons occupy a single quantum state.

So, what is the difference between this system and a laser? The difference has to do with the way the photons behave. In a traditional laser, the photons are created in a single mode through a process of stimulated emission. Photons in the laser mode pass through the gain medium, and interact with atoms in an excited state, causing them to drop down to a lower-energy state by emitting a new photon with exactly the same energy as the first one. The number of photons in the mode is not conserved, but increases dramatically as energy is pumped into the system.

The key distinction between the recent experiment and a traditional laser seems to be that the number of photons in this system is constant. The BEC forms not because photons are created in that mode, but because photons that already exist in some other mode condense into the BEC mode.

OK, maybe we need to back up a little. What are these “modes” you’re talking about? Well, a “mode” is a particular combination of wavelength, frequency, and direction of motion. There are a discrete set of these states possible inside the laser cavity. The simplest sort of modes are “longitudinal” modes, because they go along the direction of the light’s propagation. If you think of the light like a wave, the amplitude of the wave needs to be zero at both ends of the cavity, whichis only possible if the wavelength of the light is just right– if an integer number of half-wavelengths can fit inside the cavity.

This kind of situation is known as a standing wave, and restricts the possible states of light inside the cavity. In this specific case, they construct their cavity so that there’s only a single longitudinal mode inside the cavity in the wavelength range where light interacts with the rhodamine dye.

When you add in the other dimensions, things get more complicated, because you can squeeze in some wavelengths that are slightly longer or slightly shorter by basically “tilting” the beam– rather than having an integer number of half-wavelengths going straight down the axis from the center of one mirror to the other, you have an integer number of them fitting along an angled line, say from the bottom of one mirror to the top of the other. These are more complicated to explain, but still constitute a discrete set of states, called “transverse modes.”

That’s all very nice, but we’re talking about photons as particles, not waves. Yes, but they’re quantum particles, which have wave-like characteristics. The detailed treatment is a little more complicated, but the end result is that the photons can only occupy modes with a combination of wavelength and direction that would work for a wave. So you can describe the same situation in terms of an amplitude of waves in a particular transverse mode, or a number of photons having the wavelength associated with that mode, and heading in the appropriate direction.

OK, so you’ve got photons bouncing around in a bunch of these modes. How do they all end up in one mode? They end up in one mode because of their interaction with the dye inside the cavity. As the photons travel through the cavity, they can be absorbed by dye molecules, and then re-emitted in a different direction, with a slightly different wavelength.

How does that help anything? Well, photons are bosons, which means that they “like” to be in the same state. So, when a dye molecule absorbs a photon, it’s more likely to emit it into another mode that already has photons in it. This is the same effect that allows the creation of a BEC with bosonic atoms– when two atoms in an ultra-cold gas collide with each other, they’re more likely to end up in states that are already occupied by other atoms. As you lower the temperature of the gas, the number of occupied states gets smaller and the quantum wavelength of the atoms gets longer, so the atoms become more “aware” of other populated states, leading to more scattering of atoms into those states. At some “critical temperature,” the atoms suddenly realize that there are lots of them, they’re all bosons, and they’d be happiest all occupying a single quantum state, which leads to the formation of the condensate.

So, how do you chill a gas of photons? Just lower the temperature of the dye? Well, you can’t do too much of that, because the dye is a liquid, and would freeze if you lower the temperature very much. What they do instead is to increase the number of photons in the cavity, which has essentially the same effect as increasing the wavelength of the atoms– the number of photons within one wavelength of one another goes up, and eventually all the photons become aware that there are lots of them, they’re all bosons, and they’d be happiest occupying a single mode.

They’ve got a really nice, dramatic picture of what happens in the paper:

On the left, you see camera images of the light coming out of the cavity. The top picture is just below the critical number of photons in the cavity, showing a broad and fairly uniform distribution of light, representing lots and lots of transverse modes. The bottom picture is just above the critical number, showing that most of the light is now concentrated in a very small, very bright point at the center, which is a single transverse mode. The top right graph shows profiles of the instensity distribution, and you can see that as you increase the photon number, moving from bottom to top in the graph, you go from a very smooth, broad distribution to something with a very sharp point, and there’s a fairly abrupt transition from smooth to pointy, between the second and third graphs up from the bottom.

That’s cool, and all, but I still don’t see how this is different from a laser. I mean, didn’t you say there was a pump laser driving the system? There is, but that’s not what’s causing this effect. The pump is just there to provide a few extra photons to replace the ones that leak out through the gap between the mirrors. In fact, they have a really nice demonstration of this, too, which uses a pump laser that is off-center from the mirrors:

This is a set of profiles of the output light, as they varied the wavelength. When they start with a long wavelength, too long to interact strongly with the dye, most of the output light is in the same spot as the pump laser (the small dashed line). As they move the laser wavelength down to a point where it interacts very strongly, you see the distribution shift over to the center of the mirrors, and eventually develop a point, indicating that it has formed a BEC.

So, while the pump does provide some additional photons, it’s not seeding a laser, which would happen at the same position as the pump. The photons injected by the laser bounce around inside the cavity, getting absorbed and re-emitted, and eventually condense into the BEC mode all on their own.

OK, I guess that’s convincing. So, what is this good for? Right now? Nothing. It’s just another really cool demonstration of the quantum nature of light. Some of the news stories make fanciful suggestions about concentrating diffuse light for more effective solar power generation, which sounds kind of implausible to me, but who knows.

It is, however, a new and clever means of manipulating the quantum state of light, and that’s always exciting. At least to a physicist.

Klaers, J., Schmitt, J., Vewinger, F., & Weitz, M. (2010). Bose-Einstein condensation of photons in an optical microcavity Nature, 468 (7323), 545-548 DOI: 10.1038/nature09567