Tools of the Cold-Atom Trade: Magneto-Optical Traps

Today's dip into the cold-atom toolbox is to explain the real workhorse of cold-atom physics, the magneto-optical trap. This is the technology that really makes laser cooling useful, by letting you collect massive numbers of atoms at very low temperatures and moderate density.

Wait a minute, I thought we already had that, with optical molasses? Doesn't that make atoms really cold and stick them in space? Molasses does half the job, making the atoms really cold, but it doesn't actually confine them. The photon scattering that gives you the cooling force and Doppler cooling limit produces a "random walk" kind of motion on the part of the atoms. When the atoms absorb a photon, they tend to slow their motion in the direction the laser came from, but when they re-emit that photon in a random direction, they get a "kick" in the opposite direction from the departing photon. That means they bumble around constantly changing the direction of their motion, like a drunk frat boy wandering around a crowded party.

That's an analogy that goes over well in class, I'll bet. Most of the time when I talk about this stuff, it's to first-year physics majors, so there's less underage drinking than you might think.

Anyway, while the molasses force creates a region that's sort of "sticky," it doesn't actually prevent atoms from leaving. Any atom that makes it to the edge of the laser beams is free-- with no more light, there's no more force, and it just floats away. in whatever random direction it was headed when it hit the edge.

Now, the molasses beams can be pretty large, so you can get a decent number of atoms-- several million, say-- but that's not actually that many in the grand scheme of things. If you want to get really large numbers of atoms-- billions, say-- you need to do something to keep the atoms from wandering away. You need a force that depends on the position of the atoms, acting to push them back toward some central region.

And you do that with magnets? How the hell does that work? Well, as the name suggests, you do it not just with magnets, but with light, as well. It's a magneto-optical trap, and the optics are key.

The idea is basically a combination of an optical molasses with a weak magnetic field that varies in position. That lets you exploit the internal states of atoms, and the rules for interacting with polarized light that we talked about in the Sisyphus cooling post to create a new force that confines the atoms.

That sounds kind of complicated. Yes and no. It brings a bunch of stuff together, but the end result is a surprisingly simple and robust tool. The simplest version looks like this, schematically:

Schematic of a one-dimensional magneto-optical trap.

Oooh! Pretty colors! Yeah, well, they all mean something.

This is a cartoon representation of the energy states involved in making a MOT, at least in one dimension. You start with the simplest sort of multi-state atom, that has only one ground state level (the dark horizontal line at the bottom), but three excited-state sublevels (the red, green, and blue lines up top). In the absence of a magnetic field, these three levels have exactly the same energy, but if you apply a field, they shift around, one going up, one going down, and one staying put.

Which of the three goes up and which goes down, though, depends on the direction of the field. So, if you take a magnetic field that's zero at some point in space and increases linearly to either side, you get a picture like the cartoon above: on the left, the atom is in a magnetic field that shifts the red state down and the blue state up. In the center, the field is zero and there's no shift, so all the levels have the same energy. On the right, the atom is in a magnetic field that shifts the red state up and the blue state down.

Where does this shift come from? We've mentioned it before, when we talked about the slowing of beams-- it's the Zeeman Effect, pronounced "ZAY-mon," because he was Dutch.

Fun trivia: when I was an undergrad learning about this stuff, there were two names for this rattling around: a lot of people called it a "Magneto-Optical Trap" or "MOT," but some, principally the Wieman group at Colorado, called it a "Zeeman Optical Trap" or "ZOT." I liked the sound of that better, so my undergrad thesis uses "ZOT," but in grad school I joined a group that used "MOT" and got some gentle mockery about that. "MOT" eventually won out overall, another sad example of physicists choosing the more boring of two possible names.

You guys really need to hire some English majors to help with your branding. Whatever.

So, these energy levels, they go up and down, but how does that help? The key trick is, remember, the polarization of the lasers you send in determines which state you can go to. Now, in this system there's only one ground state so optical pumping isn't an issue, but if you shine in a laser of, let's say, left-hand circular polarization, that will excite the atoms only to the blue excited state, while right-hand circular polarization will excite only to the red excited state.

This gives you a way to add a spatial component to your optical forces. You detune your lasers to an frequency below the natural frequency that the atoms want to absorb, as if they were going to a lower energy state indicated by the dotted line. Most of the time, there's no state there so atoms won't absorb it, but on either side of the center, there's a point where the state that shifts down crosses that line. At that point, an atom that's standing still will happily absorb photons from a laser of the appropriate polarization.

So you choose the polarization of the lasers in the molasses to match the level that's shifting down? Exactly. The big red arrow represents a right-hand circular laser coming in from the left, which will get absorbed by even an atom at rest when it reaches the vertical red arrow. When it absorbs the light, it feels a force to the right, back toward the center of the trap.

On the other side of the trap, on the other hand, you have a big blue arrow representing a left-hand circular laser coming in from the right, which excites atoms to the blue state at the position of the vertical blue arrow. That also produces a force back toward the center. So, atoms on either side get pushed into the center of the trap, and kept there when they try to leave.

And do you still get the optical molasses effect? Absolutely. The Doppler shift of the atoms changes the position where they feel the MOT force slightly, but you still get a molasses-type force when atoms move in either direction, cooling them. In practice, the Sisyphus cooling isn't as effective inside the MOT-- the magnetic field changes things a bit, and the laser detuning for minimum temperature is different than the laser detuning for most effective MOT operation-- but you get a large number of very cold atoms that are stuck in a small region of space.

So this is why people were shining lasers with opposite polarizations on their atoms and accidentally doing Sisyphus cooling? Part of the reason, yes. It was a very happy accident, brought about by a clever trick for exploiting the magnetic sublevels to do trapping.

So the magnetic fields trap the atoms in a particular place? No, the magnetic fields are much too weak for that-- you can trap cold atoms with magnetic fields alone, but that requires larger fields than a MOT. The magnetic field of the MOT just serves to define a region of space where the trap will be located, while the actual confining force comes from the absorption of laser photons.

A fantastic demonstration of this is this famous photo:

Kris Helmerson of NIST looking into the vacuum chamber at a sodium MOT.

That's Kris Helmerson, one of the staff members in the laser cooling group at NIST when I was there (he's now a professor in Australia) looking into the vacuum system at a sodium MOT. The bright orange dot right in the center is a MOT containing several billion atoms, which are visible because they're constantly absorbing and re-emitting photons from the lasers that provide the confining force.

How big are these traps? In principle, there's no real limit, provided you can make a big enough magnetic field and large enough laser beams. In practice, the clouds of trapped atoms tend to be something on the short side of a millimeter across.

So, you've got a billion atoms in a cubic millimeter? Isn't that awfully dense? Hardly. The density of a pretty good MOT might be on the order of 10¹² atoms per cubic centimeter, which sounds like a lot, but is around a billion times less dense than air. It's a really diffuse vapor, which is why all these experiments have to be done in ultra-high vacuum chambers.

That is, however, an exceptionally pure sample of atoms-- you can pick the specific isotope of whatever element you want to trap-- at extremely low temperatures, so it's a fantastic resource for atomic physics. The MOT was invented in 1986-ish, but by the mid-1990's had become absolutely essential for atomic physics-- you can use it as a source of atoms for high-resolution laser spectroscopy, ultra-precise atomic clocks, and all sorts of cool quantum stuff that uses the slow velocity of the atoms to explore new regimes.

And once you've got all these atoms, you just fiddle with the lasers and magnets to make a Bose -Einstein Condenstate, right? For extremely difficult values of "fiddle," I suppose. It's actually much more complicated than that, though-- the density you need for BEC is much higher than you can get in a MOT, and the temperature much lower, by orders of magnitude. There was a lot of really clever additional work involved in getting to BEC. A MOT is just the starting point.

And I bet this additional work involved some new technology that you'll describe in a future post... I guess I am a little predictable with this...