How Do You Trap an Ion, Anyway?

One of the many physics stories I haven’t had time to blog about recently is the demonstration of relativistic time effects using atomic clocks. I did mention a DAMOP talk about the experiment, but the actual paper was published in Science (and is freely available from the NIST Time and Frequency Division (PDF file), because you can’t copyright work done at government labs) a month and a half ago, and generated a bit of buzz at the time.

Given the delay between publication of the article and me blogging about it, I feel obliged to provide a little more detail than you’ll get from the news stories. One of the main results depends on the details of the ion traps that form the basis of their ultra-precise optical clocks, so as a preliminary to talking about the actual paper, let me talk a bit about how ion traps work.

People are occasionally confused about what, exactly, an ion is, thinking it’s something more exotic than just an atom missing an electron or two, because otherwise why would it have a completely different name? Linguistic issues aside, though, an ion is nothing but an atom missing an electron (or occasionally one with an extra electron, though those tend not to last very long). It behaves exactly like an atom would, with a similar collection of internal states, plus a small electric charge. This electric charge is what makes them attractive (pardon the pun) for many experiments, as electromagnetic forces are very strong, making it relatively easy to push ions around: just bring an object with the appropriate charge close to the ion, and it will move. A neutral atom, on the other hand, which has no charge, will respond only weakly to nearby charges, making them much harder to manipulate.

Ion traps make use of these electrostatic forces to push the ions around, and confine them to a small region of space. It’s a little trickier to do than you might think, though– the simplest idea of how to make an ion trap, namely surrounding it with positive charges, turns out not to work.

You can see why from thinking about the picture at right, which represents a two-dimensional slice through an attempted ion trap, with four positively charged electrodes arranged in a square around the ion you want to trap. It’s true that if you set up this kind of arrangement, you’ll get a force pushing the ion away from each of the electrodes, so if it tries to move away from the center of the trap toward an electrode, it will be pushed back. However, if it tries to head out along a line between two of the electrodes, there’s nothing to stop it. In fact, once it gets started, the force will shoot it outward, in sort of the same way that squeezing down on a hard and slippery object will cause it to squirt out from between your fingers.

“That’s easy,” you say, “Just add some more electrodes to block the other paths out!” But it’s not that simple– any arrangement of electrodes short of a solid sphere will leave gaps that the ion can squirt out through. And what’s worse, as you make the coverage more complete, the force experienced by the ion gets smaller. When you enclose it completely within a spherical shell of charge, the force on it is zero everywhere inside the sphere. Which means it’s free to wander around through that whole volume, and not confined to a small region at the center, which is what we want.

OK, so positive charge is out. How about negative charge? That’s no good either, as you can see from the picture at right. While an ion on the outside would be drawn toward the negative charge, it will be pulled into the electrodes, not to the center of the trap. An ion at the precise center of the trap would feel zero force, it’s true (it would be pulled equally in all directions), but the slightest displacement from the center would see it pulled away from the center toward one of the electrodes, which is exactly what we don’t want.

This problem is an example of Gauss’s Law for vector electric fields. What we’re trying to do with an ion trap is to create a region of space in which a positive charge feels a force pushing it into the center. And the only way it’s physically possible to make such a pattern of force with static charges is by putting a negative charge at the center of that region. And if we knew how to stick a negative change in place at the cetner of our ion trap, we would already have the problem solved.

There’s a loophole in that statement, though: the word “static.” There’s no way to create a region of space where a positive charge always feels a force back to the center by using charges that are fixed in place. You can do it, though, if you use charges that change in time.

The scheme that nearly everybody uses to confine ions is called a “Paul trap” after Wolfgang Paul, who worked it out. The scheme works like this: you start with your four electrodes configured as shown at right, with two positive and two negative. This sets up a situation where the ion is pushed toward the center by two electrodes, and pulled out from the center by the other two. So, if it’s a tiny bit away from the center, it will start moving toward one of the negative electrodes.

Before it can go very far, though, you switch the polarity of the electrodes. The ones that were negative are now positive, so the ion is pushed away from them, back toward the center of the trap. At which point it will want to move toward one of the other two electrodes. Then you switch the electrodes back to the first configuration, and go back and forth between the two very rapidly.

By switching back and forth between these two configurations faster than the ion can move, you create a situation in which the average force it feels is back toward the center. At any instant, the force may be in a different direction, but over time, it feels pushed toward the middle of the trap, and will thus be confined there.

That’s a simple two-dimensional version of the full trap. The geometry used for most ion trap experiments is a little more complicated, and is shown in fake 3D below:

This kind of “linear Paul trap” holds ions along a line in the center using a set of four long electrodes around the outside (the four blue cylinders), with positive “end cap” electrodes (the short red cylinders at the end; the near end cap is left out of the picture so you can see how things fit together) to confine the ions in the third dimension (in and out of your computer screen). This creates an elongated region in which ions are confined along a line down the central axis of the trap.

The nice thing about this kind of trap geometry is that if you put several ions in, they will tend to arrange themselves in a line, one next to the other, spaced out due to their mutual repulsion. And the motion of one ion will affect the motion of its neighbors through the repulsive force between them, which lets you play all sorts of fun games using one ion to affect the other.

This kind of arrangement is at the heart of the clocks used for the relativity experiments, and also for all the quantum-logic experiments done by Dave Wineland’s group in Boulder. It’s key for the special relativity part of the recent experiments, but I have a meeting to run to, so that will wait for a later post.