Real Clock Tutorial: Atomic Clocks

In yesterday's post, I outlined the history of clocks starting from the essential feature of any clock, namely the "tick." I ended by saying that the best clock you can possibly make is one based off the basic laws of quantum physics, using the energy separation between two energy levels in an atom to determine a fixed frequency of light. In this case, the "tick" is the oscillation of the electromagnetic field-- whenever the electric field points "up," you count that as a "tick" of the clock. For light corresponding to the transition between the hyperfine ground states of cesium, those "ticks" come 9,192,631,770 times a second, which is kind of fast, but not too fast to be dealt with electronically.

But how do you actually make this work? That is, given a bunch of cesium atoms, and a microwave source, how do you go about making an atomic clock that's good to a part in 10¹⁵, or one second in twenty million years?

The simplest thing you might think of would be just to shine your microwaves at the atoms, and see if they absorb the light. That's actually not a terrible way to test things, as any given atom will only absorb an extremely narrow band of frequencies, but we don't usually work with single cesium atoms. And if you've got a whole bunch of atoms, what you end up getting is sort of the average of the frequencies of the individual atoms, which gives you kind of a broad range.

"Wait a minute," you say, "you just said that any individual atom absorbs only a narrow bandwidth. And all cesium atoms are identical, so why should averaging make any difference?"

The problem here is there are lots of effects that can change the frequency of light that an atom absorbs. Stray magnetic fields, stray electric fields, and collisions with other atoms all combine to cause slight shifts in the frequency for any given atom. And even if you get all those things under control-- shield out all the electric and magnetic fields, and keep the atomic density low enough that the collision rate is low-- you have to worry about the Doppler shift.

If you want to be able to get light in and out to interact with your atoms, you need to have them in a vapor, and atoms in a vapor are all moving in different directions. The moving atoms will see the frequency of the light Doppler shifted. Atoms moving toward the source will see the frequency shifted up, and absorb light at a frequency well below what a stationary atom would absorb. Atoms moving away see the frequency shifted down, and absorb a frequency that's too high for a stationary atom. If you take a whole bunch of atoms, moving in different directions with different speeds, you'll see absorption at a bunch of different frequencies.

That's not going to get you to a part in 10¹⁵. If you want to make a really good clock, you need to do something a lot more clever. The basic trick used these days is called the "method of separated oscillatory fields," or "Ramsey interferometry," after Norman Ramsey, who shared a Nobel Prize for developing it. (Actually, Ramsey's method is a refinement of an earlier technique developed by I. I. Rabi, but Ramsey's technique is what people use today.)

There are two ways to explain this: one is by analogy, the other requires some graphical techniques for visualizing the physics involved. I'll go with the analogy method here, and try the more complicated "Bloch sphere" business in a later post.

The analogy version (which I've lifted wholesale from Bill Phillips) is to consider the issue of finding the exact frequency of the microwaves as a matter of synchronizing two clocks. One "clock" is the microwave radiation, the other is the atoms themselves-- if you prepare a sample of atoms in exactly the right way, there's an internal oscillation of the atomic state that acts just like a little clock. These "ticking" atoms are perfect clocks, by definition, so the trick is to match the frequency of your microwave source to the frequency of the atoms.

You do this by essentially the same method as you would tune up a wristwatch. If you want to know whether your watch is keeping correct time, you compare it to a clock that you know is right-- the NIST web clock, for example.

You can do a crude synchronization by watching your watch tick at the same time as the clock on the screen, but it's really hard to see anything that way. You can do a better job by setting your watch to the correct time, going away for a while, and coming back. If you come back after a day or two, any small difference between the rate at which your watch ticks and the rate at which the NIST clock ticks has a chance to build up into an appreciable difference.

If you find that your watch is a little bit ahead, you adjust it to run slightly slower, then resynchronize it and check again in a couple of days. If you find that your watch is a little bit behind, you adjust it to run slight faster, then resynchronize it, and check again in a couple of days. If your watch has stopped, you throw it out and buy a new watch.

The Ramsey method for making an atomic clock works along the same basic lines. Sadly, my Google fu is too weak to find a good schematic of a traditional atomic clock, so you're stuck with my crude version:

Here's the idea: you start with a cesium atomic beam (basically a big can full of cesium with a hole poked in the side, so some of the vapor can escape, with a few extra gadgets to ensure they all start in the same state), and direct the beam through a microwave cavity connected to the source of microwaves you want to use as a clock. After the atoms leave the cavity, they pass through a region of empty space (ideally with no stray electric or magnetic fields), and then enter a second cavity connected to the same microwave source. After leaving the second cavity, they reach some sort of detector that measures the state of the atoms.

In this scheme, the two cavities play the role of your wristwatch comparisons. The first cavity prepares the atoms in a state where they act like little clocks, and synchronizes them with the microwave field (I'll try to explain this in a later post). The second cavity compares the microwaves to the atoms a second time, to see if they're still synchronized. If the frequency is exactly correct, all of the atoms will switch their states. If the frequency is a little bit off, there will still be some atoms in the original state, and you can correct your microwave frequency accordingly.

As with the wristwatch case, you can make a better frequency measurement by letting the atoms evolve for a longer time between the two cavities. This means either pushing the cavities farther apart, or making the beam of atoms move slower. Whichever method you choose, you're sort of limited in how much you can improve things, because the atoms start to fall under the influence of gravity, and miss the second cavity. Unless you do something really radical, like standing the whole thing on end...

But that's a topic for another post...