Tools of the Cold-Atom Trade: Magnetic Traps

We’re getting toward the end of the cold-atom technologies in my original list, but that doesn’t mean we’re scraping the bottom of the barrel. On the contrary, the remaining tools are among the most important for producing and studying truly ultra-cold atoms.

Wait, isn’t what we’ve been talking about cold enough? There is, as always, more art than science in the naming of categories of things. “Cold” and “ultra-cold” get thrown around a lot in this business, and the dividing line isn’t quite clear. Very roughly speaking, most people these days seem to use “cold” for the microkelving scale temperatures you can get with magneto-optical traps and optical molasses, but reserve “ultra-cold” for the sorts of temperatures you find in Bose-Einstein Condensates.

And those are lower than a millionth of a degree above absolute zero? Yeah. BEC itself, at least in dilute atomic vapor systems, gets into the regime where it doesn’t quite make sense to talk about temperature– you’re not going to get any closer to absolute zero than that, so what “temperature” you assign to it is just a matter of how patient you’re willing to be when expanding your trap to lower the energy of the lowest state. But the transition temperature where BEC occurs is well below a microkelvin– the exact number depends on the density of atoms in the trap, but it’s generally in the nanokelvin kind of range.

An you can do this all with lasers? Yes and no. You can make BEC by all-optical methods– collecting atoms in a MOT, cooling them with molasses, and loading them into a dipole trap for the final cooling. That can work very well, and is the fastest current path to BEC. But it wasn’t the first technique used– in fact, the first BEC experiments dispensed with lasers altogether for the final steps.

Why is that? I thought laser cooling was the key? Laser cooling is the key technology for enabling the production of BEC, but except in certain very unusual cases, laser cooling alone can’t get you to BEC. The problem is that laser cooling works by scattering photons, and transfers momentum to atoms in (very roughly speaking) multiples of the momentum of a single photon. This means it’s extremely difficult to get to temperatures lower than the “recoil temperature” corresponding to a sample where all the atoms have, on average, the momentum of a single photon of light at the cooling frequency. That can be very cold– hundreds of nanokelvin for rubidium– but it’s still too high to reach BEC at the densities you can get in a MOT. Those densities are also limited, because when you start to pack lots of atoms in a confined space, when one atom emits a photon, it can be re-absorbed by another atom in the sample before it leaves. That tends to screw up the cooling a tiny bit, and also creates a kind of outward force pushing the atoms apart, getting a lower density.

To reach BEC, you need a different means of cooling and trapping atoms, one that doesn’t involve the atms absorbing and emitting photons.

And going by the post title, I expect this will involve magnets in some way? Right. Historically, the first BEC’s were produced in magnetic traps, with no lasers at all. The essential physics here is something we’ve mentioned a few times already in this series, the Zeeman effect. When you apply a magnetic field to the atoms, it shifts the energy of the electrons in the atom around.

Now, in both of the previous mentions of this, we’ve talked about the Zeeman effect changing the frequency of light that atoms want to absorb. But if you’re not concerned about light, and have an atom with more than one sublevel in the ground state, you can use this to push atoms around with magnetic fields. The energies of those ground-state sublevels will shift as you apply a magnetic field.

So it’s like the light shift making a dipole trap? Similar. The light shift involves an oscillating field (it’s also sometimes called the “AC Stark effect,” because the shift of energy levels due to an electric field was discovered by Johannes Stark (who later became a creepy Nazi, but that’s a different subject)). The Zeeman shift involves constant magnetic fields, and only affects states with non-zero angular momentum. If you’ve got an atom with more than one sublevel in the ground state, though– and nearly all of the atoms people laser cool have this property– you’ll have some sublevels that shift up in energy as you increase the magnetic field, and others that shift down in energy.

So, like with the light shift, you just create a region of space with a big magnetic field in the center, and the atoms get trapped there? It would be nice if you could do that, but in fact, you can’t create a stable maximum of magnetic field in empty space. If you could, then you could create a region where the atoms whose energy decreases with magnetic field get stuck, and that would be nice. But that would violate a bunch of laws of physics.

Instead, you do the opposite– it is possible to create a local minimum in the field in empty space, as you do in making a MOT, where the field is zero in the center and increases as you go out. This turns out to be really easy, just requiring two coils with currents in opposite directions (the “anti-Helmholtz configuration” in AMO jargon). If you make the field really big, that lets you trap the atoms whose energy increases as the field goes up– their energy is lowest at the center of the trap, so they feel a force pushing them into that region.

And this lets you trap atoms without lasers, so you can use it to make BEC? Cool. Sadly, it’s not quite that simple. Because you still have those other states running around, the ones whose energy goes down as you go to higher fields. If the atoms move into those states, then they can lower their energy by moving out of the center, and you’re no longer trapping them.

So, how do you keep the atoms from flipping states? Well, for the most part, that happens automatically– the property that determines whether a given atom increases or decreases energy with magnetic field is the angular momentum, and angular momentum is conserved. The analogy most people use, because it lets us play with cool toys, is the Levitron levitating magnet. You can set up a field just like that in a magnetic trap that would hold a permanent magnet off the ground, provided the magnet is in a particular orientation– a ring of permanent magnets all with their north poles inward will do it. If you just put a magnet there and let it go, though, it will just flip over, at which point it’s attracted to the ring, and falls. If you put that magnet inside a spinning top, though, the angular momentum of the top prevents it from flipping over, and you can levitate the magnet in space. Which makes a great party trick or lecture demo.

Atoms in a magnetic trap are the same way. They can’t easily flip their states because of angular momentum conservation, so once you get them in the “low-field seeking” state that increases energy as the field goes up, they tend to stay there. Magnetic trapping works nicely, and was in fact demonsttrated in the 80’s.

So you brought up a problem that isn’t actually a problem? It’s not a problem, unless you’re trying to make BEC. See, the trapping state is defined by ts angular momentum, which is measured relative to some axis. That axis is defined by the magnetic field, so as long as there’s an applied field, the atoms are in a well-defined state, and can’t easily change it.

Right in the center of the trap, though, the field is zero. And when the field is zero, there’s nothing to define the angular momentum relative to, which means an atom in the zero-field region can flip from one state to another (this is called a “Majorana transition,” presumably relating to Italian physicist and international man of mystery Ettore Majorana). Which puts a big “leak” in the center of the trap. That’s not a big deal if you’re working with fairly hot atoms, which don’t spend much time in the center, but when you try to make BEC, you want to create high density by packing all the atoms into a really small region, which unfortunately sits right on top of the “leak.” At which point everything falls apart.

So you need some other clever trick to plug the “leak.” Exactly. The first experiment to make BEC in rubidium, by Eric Cornell and Carl Wieman in Colorado (shown in the “featured image” up top), used a “Time Orbiting Potential” or TOP trap, which fixed the problem by adding an extra field that changed in time. You can’t just add a constant field, because all that does is move the position of the zero around, but if you change the field quickly enough, the atoms can’t follow it, and what they see is a sort of average field. The TOP trap used an audio-frequency field– we used one for the squeezed state experiments I did at Yale, and the characteristic high-pitched whine of the TOP coils is one of my strongest memories of that lab– that pushed the zero point out of the center and spun it in a circle. The central region then looked like a rounded bowl sort of potential, with a non-zero field at the center.

Another approach, used by Wolfgang Ketterle’s group for the second BEC experiment, with sodium, is just to keep the atoms from being at the zero point by physically pushing them away. Ketterle used an “optical plug,” a laser focused down to the central point of the trap, with its frequency tuned to push atoms away from the light. That created a sort of donut-shaped trap, partly due to the Zeeman shift and partly due to the light shift, that plugged the leak in the center of the trap.

That sounds really tricky. It was fairly difficult, I think, and never really became all that popular, though some groups still use it.

Can’t you just make a different sort of trap that doesn’t involve a zero in the middle? You can. but it requires a more complicated system of coils. There are several different approaches to this that have been used over the years– a Ioffe-Pritchard trap, a “baseball” trap (because the coils to make it follow a pattern like the seams on a baseball), etc. All of them have the same general result, though: a magnetic field that is small but not zero in the center, and increases as you move out. There are pros and cons to all the methods, but they all work more or less the same way.

And all of these let you get to BEC? Yep.

How? The process is called “evaporative cooling,” and is really the simplest sort of cooling scheme you can imagine. It’s a little complicated to explain, though, and this is already almost 1900 words.

So, even though it wasn’t on your original list, you’re going to split it off into a new post. Yeah. Sorry about that.

2 thoughts on “Tools of the Cold-Atom Trade: Magnetic Traps

  1. I’m really enjoying this series, even though much more than I’d like is going over my head. I’m doing my best though – it’s my deficiency, not yours. I expect if I read them over a few times each, I’d get more of it.

    I did want to say, however, that I love the little bits of humorous phrasing that you occasionally drop in. Little titbits like “Italian physicist and international man of mystery Ettore Majorana” make me chuckle and offset my self-disgust at not picking up these ideas more quickly, despite your excellent and engaging explanations.

  2. Evaporative cooling? Ooh! Can I supply a “question” for your Q&A format?

    “Wait, that sounds a lot like Maxwell’s demon. Chad! In this lab we obey the laws of thermodynamics!”

    Use or not, as you wish (though please do address the thermodynamic issue).

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