# Classic Edition: Clever Tricks and Cooling

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. This is the second part of the explanation started in the previous post.

So, at the end of yesterday's post, I had talked about how to use light to exert forces on atoms, and change their velocity. This is the basic tool used to do laser cooling, but it doesn't get you all the way there.

The problem is that, in the simple approximation we've been using thus far, the scattering force is as likely to cause an atom to speed up as to slow down. If you know what direction an atom is moving, you can aim the laser in the opposite direction, and use the force to slow them down (this is often compared to hitting a rolling bowling ball with a steady stream of ping-pong balls-- any one ping-pong ball doesn't make much of a difference, but enough of them striking the bowling ball in succession will bring it to a stop). You can even use this method to slow down a beam of atoms, but eventually they'll stop, turn around, and accelerate back the other way. And, anyway, we'd like to cool a gas of atoms, where the velocities are randomly directed.

To do real cooling with lasers, you need some sort of clever trick to arrange for the atoms to only absorb photons when absorbing photons will make them slow down. That is, they should only absorb when they're headed toward the laser. The quirk of physics which makes this possible is the Doppler Effect.

The Doppler effect is one of the great "you know this, but don't even realize it" effects in physics. It says that the frequency of waves emitted from a moving source will be shifted, depending on the direction of motion. It's most commonly encountered with sound (Doppler demonstrated his effect by putting a brass band on a moving train, and having them play a constant note as the train went down the track)-- sounds emitted from an object moving toward have a higher pitch (higher frequency) than the same sounds emitted from a stationary source, and sounds emitted from an object moving away from you have a lower pitch (lower frequency). This accounts for the way that a police or fire engine siren seems to change pitch when it passes you, and for the characteristic two-tone engine noise of NASCAR telecasts (rendered imperfectly in text as a sort of "EEEEEEEEEEEooowwwwwwwww" thing) and little kids pretending their bikes are cars, and for the way an aggrieved younger sibling's cry of "MMMMOOOOooooommm!!!!" changes pitch as he runs off to tattle. Well, OK, maybe not the last one-- the shift also depends on the magnitude of the velocity, and few small children move fast enough to produce significant Doppler shifts.

The Doppler effect affects light waves as well (as noted previously, like all quantum objects, light insists on being both a particle and a wave, at the same time). Doppler shifts of light emitted by distant galaxies are the primary evidence of the expansion of the Universe, and even smaller Doppler shifts of the light emitted by single stars are used to detect the presence of extrasolar planets.

The Doppler shifts seen by moving atoms (the effect is the same if the source is stationary and the receiver is moving) are a tiny fraction of the frequency of light waves, but atoms are incredibly sensitive frequency detectors. Atoms will absorb and emit only very specific frequencies of light, and a tiny change in the frequency of the light is enough to prevent absorption. Or allow it.

The trick to laser cooling is to set your laser to a frequency slightly below the frequency required to make a transition between two states in the atom (this is referred to as "red detuning" since the frequency is tuned to something other than the atomic transition frequency, and since red light has the lowest frequency in the visible spectrum). In that case, an atom at rest will see light that's not the correct frequency to be absorbed, and ignore it. No photons will be absorbed, so the atom will feel no force. An atom moving away from the laser (in the same direction as the beam) will see the light shifted even further down in frequency, and again, will do nothing.

An atom moving toward the laser, though, will see the light shifted up in frequency, and will absorb photons. When it absorbs photons, it feels a force in the direction of the laser, a force which acts to slow it down. Using a red-detuned laser, then, we can generate exactly the force we want to do cooling-- atoms which move toward the laser will be slowed down, while atoms moving away from the laser or standing still won't be affected at all.

If you take a single red-detuned laser, and direct it opposite a beam of atoms, you can slow and stop the beam, without having to worry about turning the atoms around and accelerating them in the other direction. With two beams of light aimed in opposite directions, you can cool atoms in one dimension-- an atom moving to the right will see the left-bound laser shifted up in frequency, absorb photons, and feel a force slowing it down, while an atom moving to the left will absorb from the right-bound laser, and slow down. Three such pairs of beams will get you cooling in three dimensions. Atoms in such a laser field are in the same predicament as a person trapped in a vat of sticky fluid-- no matter what direction they try to move, they feel a force opposing their motion. In honor of this sort of viscous behavior, this arrangement of lasers acquired the name "optical molasses" (one of my predecessors on my undergrad thesis project lobbied hard for changing the name to "optical treacle," but to no avail. He was a weird dude...).

(There are still some technical details and additional complications before you can use this to do real cooling of real atoms-- the biggest issue being that as the atoms slow down, the Doppler shift changes, and they stop absorbing photons. To slow or stop a beam of room-temperature atoms, you need to do something to compensate for the changing Doppler shift, either by changing the frequency of the laser ("chirping" the laser), or by changing the frequency the atoms want to absorb by applying magnetic fields to the atoms ("Zeeman slowing," after the Zeeman effect, which causes a shift of the energy levels for an atom in a magnetic field. Zeeman slowing is the idea that got Bill Phillips his share of the Nobel Prize for laser cooling.). Happily, the atomic transitions aren't infinitesimally narrow (a consequence of the uncertainty principle), rather there's some range of frequencies over which the atoms will absorb light, which means that you don't have to perfectly match the Doppler shift to get cooling. Once you've slowed a beam of atoms down from room temperature velocities, this allows you to cool atoms with a small range of velocities in optical molasses using a single laser frequency.)

Doppler cooling and optical molasses are the basis for all the success laser cooling has enjoyed. Further refinements of the basic scheme allow you to trap atoms (that is, confine them to a small region of space-- optical molasses is "sticky," but atoms can still wander out of the molasses region) as well as cool them to temperatures well below the limits suggested by the simple theory (For those keeping score at home, trapping was Steve Chu's contribution, while Claude Cohen-Tannoudji explained and improved the sub-Doppler cooling mechanisms. A fairly readable summary of the field's history (it really only dates from 1975) is provided by the Nobel Foundation. I won't go into any detail about that stuff right now...).

The laser cooling mechanism is strongly dependent on the specific properties of the atoms you're trying to cool-- you need a different laser frequency for each type of atom you want to cool, and only certain kinds of atoms turn out to have properties suitable for laser cooling. We're nowhere close to being able to laser cool beer. To date, something under twenty different atomic species (of a hundred-odd known elements) have been laser cooled (a partial list: lithium, sodium, potassium, rubidium, cesium, francium, calcium, strontium, helium, neon, argon, krypton, xenon. A few other species have been laser cooled as ions, not neutral atoms, and I'm sure I'm forgetting some others).

Still, to say that laser cooling has revolutionized atomic physics would probably be an understatement. Whole classes of experiments have been opened up that were previously thought to be impossible (we ran across a paper from the early 80's once that proposed an experiment, but then pooh-poohed it as wildly unrealistic. We found the paper because we had done the experiment described, and were looking for something to help explain the results...): ultra-cold collisions, ultra-precise spectroscopy, ultra-cold plasmas, atom interferometry, quantum state engineering, Bose-Einstein Condensation, and more. There are also numerous technological applications-- already, the world's best sensors of acceleration, rotation, and gravity gradients are based on laser-cooled atoms, not to mention the very best atomic clocks in the world (at NIST in Boulder and LPTF in Paris). In the future, laser cooling techniques could potentially have a huge impact on everything from atom lithography to nanotechnology, to nuclear physics, to quantum computing.

And all of that comes from the appealingly simple and wonderfully counter-intuitive idea that you can shine a laser on something, and make it cold. Even now, more than ten years after I first heard the idea, I still think that's just the coolest thing ever. Bringing this full circle to the beginning of yesterday's post, that's what got me into grad school, and got me to where I am today. I'm not sure whether that's an inspirational tale, or a cautionary one, but there you go.

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