Classic Edition: Not Just Air Conditioning the Laser Lab

I'm going to be away from the computer for the long weekend, but I don't want to have the site go completely dark, even over a weekend, so I'm going to schedule a few posts from the archives to show up while I'm away. Everyone else seems to be doing it (and pushing my posts off the front page, the bastards), so I might as well.

This goes back to the early days of the blog, back in July of 2002. If you're wondering what I need those diode lasers for, other than sharks with lasers on their heads, here's the beginning of an answer.

Last week, when talking about how to do a public lecture, I wrote that:

To get the basic message across, you really need to recall what it was about the field you're in or the problem you're working on that drew you in in the first place-- you just don't get to the Ph.D. level in a science without thinking, on some level, that the field you're in is just the absolute coolest endeavor ever conceived since our many-times-great-grandparents first rubbed two sticks together and set fire to the savannah.

For me, the thing that really drew me into atomic physics was the idea of laser cooling. It's a wonderful mix of simple and complex-- the basic idea behind it all is one of those forehead-slapping "Of course! Why didn't we think of that sooner?" sort of ideas (for a physicist, anyway), but when you sit down and go through it all in detail, it actually involves quite a bit of sophisticated atomic physics. To my mind, at least, it brings together all of the best things that physics has to offer: it's conceptually simple, but applying the concepts involves quite a bit of ingenuity; it makes manifest some of the weirdest behaviors in physics, but ends up having fairly concrete technological applications.

(It didn't hurt that one of the first times I heard about the field was as an undergrad physics major, when Claude Cohen-Tannoudji came to give a talk on campus. He's a wonderfully clear speaker, and does a marvellous job conveying the cool concepts without sacrificing theoretical rigor. His books tend to be exceedingly dry and formal, but he gives great talks...)

The essence of laser cooling is this: You take a sample of atoms, hit them with a laser, and the atoms get cold. "Laser Cooling" is not, as some people seem to think, about keeping your laser from overheating, but about using lasers to make things cold.

Right about there, I was hooked, just because it's such a wonderfully counter-intuitive idea. When you think about hitting something with a laser, you don't imagine that it'll get cold. You think of lasers cutting steel in industrial processes, or the Death Star blowing stuff up (real lasers don't merge like that, of course, but it sure does look cool...). So how do you use lasers to make things cold?

The first step in explaining this is to explain what, exactly, we mean by temperature-- before you can use lasers to make things cold, you need to know what it means to be cold. And the samples we deal with in laser cooling experiments are at least a million times less dense than air, so this isn't stuff you can just stick a thermometer into and read off a number. We need to look at what "temperature" means on a microscopic level.

Temperature is a measure of the average kinetic energy of a particle in the sample. A sample of gas is made up of millions of atoms zipping around with different velocities-- as a result, each of the atoms has some energy bound up in its motion. The average of this energy for all the atoms in the sample is what we call the temperature. In a "hot" sample, say a gas at room temperature, the atoms are moving at speeds comparable to the speed of sound. In a "cold" sample, they're moving much more slowly-- the molecules making up the liquid nitrogen I used for my demos on Saturday are moving at roughly half the speed of room-temperature nitrogen molecules. In a run-of-the-mill laser-cooled sample, the atoms are moving at something like 10 cm/s-- comparable to the speed of a running insect. Something that scuttles under the fridge when you turn on the light is moving about as fast as an atom in a laser-cooled sample.

So, the process of laser cooling involves using lasers to slow moving atoms down. That's a little more concrete, but not especially enlightening without two more key facts: First, that atoms have discrete energy states, and will only absorb or emit very specific colors of light; and second, that a beam of light can be thought of as made up of "photons," which behave like little particles.

The discrete nature of atomic states is the key to all of quantum mechanics. Indeed, it was the realization that atomic states have to be quantized that gives the theory its name. This is an idea that should be fairly familiar to anyone who's taken physics or chemistry in high school-- there are only certain very specific orbits which can be occupied by electrons in an atom, and each of those orbits has a very specific energy. Electrons can move between these states by absorbing energy from a beam of light, or by giving up some of their energy in the form of emitted light. The color of the light (or the frequency of the light wave) absorbed or emitted depends on the energy difference between states, so atoms will only absorb or emit light of very specific colors, determined by the limited number of transitions between allowed states. (There's a wonderfully cheesy applet demonstrating this at the Physics 2000 site.)

Physicists, fond as we are of abstracting away unimportant details ("Assume a spherical cow..."), prefer to talk about hypothetical atoms which only have two possible states, and thus only one transition between states. In reality, there are no two level atoms (and sodium is not one of them), and the multi-level nature of real atoms turns out to have significant consequences, but it's not a terrible approximation for a lot of systems, and it makes the explanation of basic laser cooling a lot simpler.

The light that's absorbed and emitted is also quantized, coming in discrete chunks called photons. Photons are generally described as "particles of light," and they carry the energy involved in the transition between states in the atom. As with everything else in the quantum world, they perversely insist on also having wave-like properties, so the energy carried by the photon is associated with a frequency, or the "color" of the light. If a photon of the appropriate energy comes along, it can be absorbed by the atom, which will use that energy to move to a higher ("excited") state. After some time in the higher energy state, the atom will spontaneously drop back down to the lower ("ground") state, emitting a photon with the same frequency as the one that was absorbed.

So far, so good (I hope...). The key to laser cooling is that, in addition to carrying energy, photons also carry momentum. In a very real sense, they behave like little particles-- when a photon strikes an atom and is absorbed, the momentum of the photon is transferred to the atom. A stationary atom hit by a photon will thus start moving, in the same way that a bullet fired into a block of wood will start the block moving.

The change in velocity isn't a big one-- a rubidium atom which absorbs a single photon changes its velocity by about half a cm/s, so it takes hundreds of thousands of photons to bring a room-temperature atom to a halt. But photons are cheap-- a fairly weak laser of the sort used as a pointer for a talk will deposit something like 10^15 photons on the screen in one second. That's a million billion photons per second, to wax Sagan-esque (well, OK, to really be Sagan-esque, I'd have to say "a miilllllion, biillllllion photons per second"). A hundred thousand photons is nothing.

So, light can be used to exert forces on objects. That's why it's so hard to get out of the house on a sunny Monday morning, right?-- you've got this constant hail of photons to fight your way through... OK, the force is actually pretty insignificant for a massive object, but for something sufficiently small, like a single atom, it can be substantial enough to make big changes in the motion.

(The other place this turns up is in the idea of a "light sail," common in science fiction. It's a different approach than laser cooling, but a similar idea-- rather than using smallish numbers of photons to produce big accelerations of small objects, you use astonishingly large numbers of photons to produce modest accelerations of big objects. If you could make a sufficiently large sail to catch the light of the Sun, you could actually generate a large enough force to move a space ship. You need a whole lot of photons, but again, photons are cheap, and for a big enough sail and a lightweight ship, you could theoretically move sizeable objects with the force of light...)

It's this light force that we use to cool atoms. Of course, they don't hand out Nobel Prizes for simple stuff, so there are a number of complications that have to be dealt with to get to cooling. Chief among them is the fact that the light force as described above is as likely to heat the sample as cool it-- you can use the light force to make fast atoms slow down, but you can also use it to make slow atoms speed up. To do cooling, you need to find a clever trick you can use to only exert forces that slow atoms down.

But this is running really long already, so that'll wait for another post...