Point Sources and Towers: "Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry"

A little over a year ago, I visited Mark Kasevich's labs at Stanford, and wrote up a paper proposing to use a 10-m atom interferometer to test general relativity. Now, that sounds crazy, but I saw the actual tower when I visited, so it wasn't complete nonsense. And this week, they have a new paper with experimental results, that's free to read via this Physics Focus article. Which might seem to make me blogging it redundant, but I think it's cool enough that I can't resist.

OK, dude, "Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry" is not the sexiest title in the world. What's so cool about this? Well, it's an atom interferometer inside a ten-meter vacuum tower. Just the scale of the thing is pretty amazing.

More than that, though, they use this to explore some clever new wrinkles in the interferometer business. That's the "point source atom interferometry" art of the title-- they have a new trick that makes this sensitive to a wider range of effects than you might otherwise expect.

Which would be the "multiaxis intertial sensing" part of the title? Exactly. You're getting the hang of this.

The hang, maybe. The idea, not so much. What's point source atom interferometry? The idea is that because their interferometer is so big, and atoms take such a long time to pass through it, the velocity spread in their initial sample means that (loosely speaking) they're actually doing a bunch of different experiments in parallel.

How do you figure? Well, it depends on the details of the interferometry process, so let's review that, first. The basic sequence looks like this:

Cartoon of the atom interferometry sequence.

That's really complicated, dude. We're going to walk through it. It'll be fine. The key here is to remember that this is a series of images showing a single vertical path. Each slide of the figure is an image of their tower.

You start with a ball of atoms at the bottom of the tower, moving up, and hit them with a pair of lasers that make a "π/2-pulse," which means it moves an atom halfway from one internal state to another. This creates a superposition, with the atoms half in the original state (the green ball in the second slice), and half in the second state plus a bit of extra momentum from absorbing and emitting two photons (the purple ball in the second slice).

So, half of the atoms are moving faster than the other half? Close. Each atom is half in the original state at the original speed, and half in the second state, moving a bit faster. That's crucial for making this an interferometer.

As the atoms move up, these pieces separate. They also slow down due to the influence of gravity, and at the very peak of their flight (third slice of the figure), they send in a second set of two lasers to do a "π-pulse," that flips the state completely, so the colors of the two balls reverse. This also transfers momentum, giving the lower ball a bit of an upward kick, so on the way down, the two come back together.

And when they're at the bottom, they overlap with each other, and you get interference? Close-- because the pieces are in different internal states, they don't quite interfere the way you'd like. It takes one more set of pulses, a second π/2-pulse, to recombine the states. Then you get some fraction of the atoms in the original state, and some fraction in the second internal state, with the exact ratio of the two depending on what went on during the flight through the interferometer.

So, what do they measure, again? The signal is the fraction of the atoms that are in each of the two states. They actually hit them with one more laser pulse, tuned to interact with only one of the internal states, that separates the two, then they take a picture (cold-atom physics is all about taking pictures...). The number of atoms in the two clouds varies as you change the "phase" the atoms accumulate in the interferometer, which is related to the maximum separation of the two pieces at the top, and the time of flight, etc.

Yes, and this is especially sensitive because they spend such a long time going up and coming back, I get that part. What's new, here? Well, the picture above is for an imaginary bunch of atoms that goes perfectly straight up and falls perfectly straight back down. But you never really have that-- individual atoms each have some initial velocity that's pointed in a random direction. So one atom may be going up and moving a bit to the right, while another is going up and to the left, and a third is up and out of the screen, and so on.

The key to the new analysis they do here is that if your atoms are moving to the left or to the right, the phase they see going through the interferometer can be slightly different than the phase for atoms that go straight up and down. The fraction of atoms moving from one state to the other after a pass through the interferometer going up-and-right is slightly different than for atoms that went straight up, or up-and-left.

So, that screws up your interference pattern? Ordinarily, yes. If you have a short interferometer, and cold atoms, the atoms moving up-and-right that started on the left side of the initial cloud fall in the same place as the atoms moving straight up that started on the right side of the cloud, and you just get some loss of contrast. It tends not to be a huge effect, but it's there.

In this case, however, the atoms they're using spend so much time in the interferometer that the up-and-right atoms are cleanly separated from those that went straight up. The atoms they use are very cold-- 50 nanokelvin or less-- but over a period of seconds, that small velocity difference still expands the cloud to 30 times its initial size.

That's the "point source" part of this. The final measurement is made on a cloud that's so much bigger than the original that you can think of it as a tiny point, and get velocity resolution from the side-to-side position of the atoms. Each atom interferes with itself, in some sense, so you've got a huge array of interferometers in parallel, each with its own value of the sideways velocity that you can determine from its position. The left edge is all atoms that were moving up-and-left, the middle is atoms that went straight up, and the right edge is atoms that were moving up-and-right. And the same is true going in and out of the screen.

So you've got arrays of interferometers spread out over two axes? And they're measuring the acceleration along the vertical direction, yes. Hence "Multiaxis Inertial Sensing."

So, what is it that they sense? Well, they can sense anything that makes the phase of the interferometer depend on the sideways velocity of the atoms. Such as the rate of rotation of the interferometer.

Whoa. You mean they spin their interferometer around? That's a big centrifuge, dude. It'd be pretty amazing if they did that, but it turns out to be much easier. In fact, they get the rotation for free.

How? Well, they're on the surface of the Earth, after all, and the Earth is rotating. After all, the sun doesn't really go down, it's just an illusion caused by the world spinning around.

Thank you for the earworm, you bastard. But how does the rotation of the Earth matter? Isn't their whole apparatus spinning? It is, but the top is moving at a very slightly greater speed than the bottom. In an ordinary interferometer, this wouldn't matter much, but for this gigantic one, the difference is significant. In fact, they have to mount the mirror for the bottom laser doing their interferometer pulses on a tilting stage, and correct for the rotation of the Earth.

So, they get rotation for free, and to look at a controlled rotation, they just change how much they correct the mirror tilt. Which gets you this lovely series of images:

Interference patterns for different rotation rates, Figure 2 from the paper discussed in the text.

Oooh, pretty colors That's artificial, to make the figure look clearer. But it gets you the right idea: when they do the full rotation correction, they see a single blob, that doesn't show any effect of the velocity difference, but as they increase the rotation rate (by not correcting the inevitable rotation of the Earth fully), they see more and more interference fringes. These show that the phase of the interferometer depends on the sideways velocity of the atoms, and that velocity-dependent shift is a measure of the rotation rate. They go through a bunch of cross-checks and sensitivity measurements, and determine that the interferometer is measuring the rotation rate of the Earth at the level of 200 nano-radians per second.

Wow. I have no idea what a radian is, but "nano" sounds cool. A radian is a measurement of angle, and the Earth by definition rotates through 2π radians every 24 hours, which is a rate of about 73 microradians per second. So it's not quite as mind-blowing as the "nano" makes it sound, but still pretty impressive. And some further number crunching shows that, in principle, they can measure accelerations of about 0.000000000007 times the acceleration of gravity in a single show of their interferometer, which is about a factor of 100 times better than the previous best.

Pretty amazing what you can do with BEC, huh? Actually, these aren't Bose condensed atoms, they're just very cold. Probably because they didn't want to throw away as many atoms as they would need to to make a condensate, but also possibly because they didn't want to have to worry about collisional shifts. I'm not actually sure.

They also point out that the general technique doesn't absolutely require cold atoms. You can get the same "point source" effect from starting with a small beam of hot atoms. All you need is for them to spread out by much more than the initial size of the sample.

So, really, this whole thing is just driven by the unavoidable expansion of their cloud? It's really just making a virtue of necessity? Well, yeah. But it's very, very virtuous.

Are you sure this isn't just the sort of annoying reinterpretation that's going to annoy people, like that clock business a while back? Am I 100% sure? No. There's no telling what will upset some people. But Mark's got a pretty impeccable reputation in the interferometry business, and doesn't usually publish stuff that isn't rock solid. So I wouldn't expect this to upset many people.

If he started claiming that this actually tested the gravitational redshift at some absurd precision, then things might get ugly. But that's really not his style.

So, at heart, this is really a fairly technical advance in precision measurement, no? Do you have anything inspiring and mind-blowing to close with? Well, if you wanted me to point to a single "Wow!" image out of the whole thing--

That's exactly what I want --it would be the upper right insert in the "featured image," which I'll reproduce here:

Schematic of the interferometer measurement, Fig. 1 from the paper discussed in the text.

That little 3-d plot is an image of the density distribution of the atoms as seen on the camera at the very top of the interferometer. The separation between those two peaks is almost a centimeter and a half.

So? You've got two clouds of atoms a centimeter and a half apart. Big deal. Ah, but remember what I said about the key to this whole business: while when you make the measurement, what you find is two clouds of atoms each in a definite position, prior to the measurement, you have several million atoms each in a superposition of two states. Since each atom ultimately interferes with itself, what you're seeing here is several million atoms, each in two positions at the same time, separated by a centimetter and a half.

Wow. Exactly.