The Towering Interferometer: “Testing General Relativity with Atom Interferometry”

In which we look at a slightly crazy-sounding proposal from my former boss, the experimental realization of which is getting close to completion.

————

I spent more or less the entire first day of DAMOP a couple of weeks ago going to precision measurement talks. Most of these were relatively sedate (at least by the standards of a sub-field that routinely involves people proposing incredibly difficult experiments), but my boss when I was at Yale, Mark Kasevich, provided the bold proposals I usually expect, in this case suggesting an experiment using an atom interferometer to measure gravitational effects on the scale of something like 10^-17 times the normal acceleration of gravity.

That sounds completely crazy, but he showed pictures of the apparatus under construction, and some preliminary data indicating that they’re close to getting this to work. Better yet, when I was in the Bay Area for my signing last week, I swung by their lab to look at it, and they are, in fact, doing amazing things. In honor of that, then, here’s a ResearchBlogging post about the proposed experiment and what it hopes to measure.

Wait, you’re just blogging their proposal? Not the actual experiment? Well, yeah, because they only have preliminary data at this point. Nothing on the experimental results is available yet. They do, however, have two proposal papers, one in Physical Review Letters (arXiv version) and one in Physical Review D (arXiv version). The Phys. Rev. D is talking about more or less the same idea, but goes into much more detail about the calculations (and also provides the color figure used as the “Featured image” above. So, I’ll blog about those.

Didn’t you at least take pictures of the lab when you visited? Sadly, no, because my cell phone battery was just about shot from spending the early part of the afternoon live-tweeting soccer games. Sorry.

Oh, all right. So, what’s the deal, here? Well, the title pretty much says it all: they’re proposing to use an atom interferometer to measure the effects of general relativity at extremely high precision.

An atom what? Interferometer. Meaning, a device that uses the interference of waves to measure something. The classic example is a Michelson interferometer, used in the Michelson-Morley experiment: a beam of light from some source is split into two parts, which separate and then are brought back together. When the light waves are recombined, you get a pattern of bright and dark spots that depends on the difference between lengths of the two different light paths, which is sensitive to changes of a small fraction of the wavelength of the light.

Yeah, but how do you do that with atoms, which are solid objects? Ah, you’re forgetting about quantum mechanics, which tells us that material objects have wave-like properties. You can perfectly well make an interferometer using atom waves in place of light waves, and use it to measure stuff. Mark’s group has been doing this for years, and they used atom interferometry to measure Newton’s gravitational constant a while back.

Isn’t that kind of difficult? Yes, but there are some advantages to using atoms. For one thing, the wavelength associated with a moving atom is much, much shorter than the wavelength of light. For a rubidium atom moving at 10m/s (about the speed of an Olympic sprinter), the wavelength is around 0.5 nanometers. To get that same wavelength with light, you’d need to be well into the x-ray range of the spectrum, and the technology to build an x-ray interferometer just isn’t there yet.

Plus, since the atoms have mass, they interact with gravity? Well, sort of. It’s not like light doesn’t interact with gravity– the gravitational redshift has been measured, after all– but it’s a little easier to do gravity experiments with atoms than with light, because the velocities involved are lower, allowing for much greater deflections.

OK, so what is it that they propose doing? Well, they want to make an atom interferometer to measure the effects of general relativity, by starting with ultra-cold rubidium atoms and manipulating them with light pulses. The basic scheme, drawn like a spacetime diagram in general relativistic terms, looks like this:

The squiggly lines in this picture represent light pulses from the control lasers, while the smooth lines represent the atoms. Time moves from left to right in the diagram, while the height of the atoms is shown in the vertical direction. The diagram isn’t really to scale– the left-to-right travel of the light pulses has been exaggerated to make the separation between events clearer.

What’s the difference between the solid and dashed lines for the atoms? The solid lines are atoms whose vertical velocity has only been affected by gravity, while the dashed lines are atoms that have received a large velocity “kick” in the upward direction. You can provide this “kick” through the interaction of two lasers– the atom absorbs light from one, and is stimulated to emit light into the other, giving it a “kick” equal to twice the momentum of one of the photons from the laser.

So, how does this give you an interferometer? The picture looks a little complex, but if you follow along the worldline of the atoms, you’ll see that there are three places where the atom line intersects the squiggly light lines. Whenever that happens, the atoms get a “kick,” changing the velocity.

The first time they intersect, at the lower left, the time and intensity of the light pulses are chosen to give a 50% chance of an atom getting the two-photon momentum kick, which is called a π/2-pulse (“pi-over-two-pulse”) for technical reasons. This splits the atom worldline into one dashed line (atoms heading up rapidly) and one solid line (atoms heading up more slowly). As they move upward, gravity acts on the atoms slowing them down and eventually turning them around, so the two atom lines follow curved trajectories.

The second interaction, where the atom lines are crossed by the light pulse starting at T on the bottom, involves pulses whose duration and intensity are chosen to flip 100% of the atoms from the solid line to the dashed line (a “π-pulse”). This brings the two atom lines back together for the third interaction, on the right side of the diagram, where they get a second π/2-pulse. This mixes the dashed line from the top path with the solid line from the bottom path, and produces an interference pattern.

So the atoms that went along the high path are messing with the ones that went on the low path? Actually, they’re the same atoms. The splitting is “coherent” in physics jargon– because you don’t follow the path of individual atoms, each atom follows both the upper and lower paths at the same time, and they interfere with themselves. Quantum physics is weird like that.

And how does this interference tell you anything about gravity? The key feature here is that the two paths aren’t perfectly identical (you can see that from the fact that the curves don’t quite match), and that difference leads to a shift in the phase of the waves that went one way when compared to the waves that went the other way– there are slightly more oscillations along the upper path than the lower, or vice versa. That phase difference shows up as a shift in the interference pattern when the two paths are recombined.

And this has to do with gravity? Exactly. There are a number of things that contribute to the shift– things like the gradient in gravity due to the fact that the force decreases with distance, so the upper path feels a slightly different force than the lower– some of which are due to effects of general relativity. If you do this experiment carefully, with the parameters chosen appropriately, you can make a measurement of these effects that’s comparable to the best limits from looking at astrophysical. And you can do it in a laboratory, where you have better control over the conditions, and more ability to change things than in the astrophysical situations where you have to take what nature gives you.

So, what are the parameters? Well, they consider the case of a 10-meter separation between the top and bottom paths, and–

TEN METERS?!?! That’s crazy! You’re talking about pulling each atom apart into bits separated by ten meters? Yeah, that’s the part that seems a little crazy. They’ve almost got the apparatus to do it, though. In their basement lab, they have a 10-meter deep pit left over from an older experiment, and they’ve built a laser cooling apparatus at the bottom of that to produce Bose-Einstein condensates of rubidium. Above that, they’ve got a ten-meter aluminum tube under vacuum, inside three layers of magnetic shields, where they can toss the atoms.

And this works? Believe it or not, yes. They’ve got the system all pumped out and have tested the basic components. They’ve launched rubidium atoms 8.5m into the air, and observed them coming back down. They see plenty of atoms on the return to resolve an interference signal, almost three seconds later. They’ve even demonstrated a beamsplitter of sorts, using their lasers to launch the atoms upward at some average velocity plus or minus one photon momentum. They see two bunches of atoms falling back down, separated by a centimeter or so, as they should be.

Wow. That’s pretty amazing. Which is why I’m writing about this. If it were just a couple of theory papers, I’d be half inclined to laugh it off, but they’ve actually built the machine to do it, and the preliminary data look fairly promising.

So, what are the parameters? Using a 10-m launch with ten photon momenta between the two paths (readily achievable with the lasers they have), they’re potentially sensitive to accelerations as small as 10^-15 times the acceleration of gravity (the 9.8 m/s/s that you use in intro physics, but with more digits), and can potentially test the Equivalence Principle (which says that all masses experience the same gravitational acceleration) at the level of a few parts in 10¹⁵ by using two different isootpes of rubidum. That’s better than any current test, by a couple of orders of magnitude.

Measurements of non-Newtonian gravity are trickier, but they can tease out relativistic effects by varying parameters like the launch height and the momentum difference between the paths. The constraints they can place on the relevant parameters aren’t as good as the astrophysical measurements, but with a few upgrades (bigger momentum differences, bigger launches) they could be competitive. And, again, there’s the possibility of doing something clever in the lab to test new things, and the fact that systematic effects would be completely different, making it worthwhile to look at.

So, is this, like, going to produce a theory of quantum gravity? It doesn’t look like it would be sensitive at that kind of scale, no. But it’s pretty darn cool in its own right– for the kinds of momentum separation they’re talking about, the peak separation between the atom paths could be almost a meter, which is kind of mind-boggling.

And you think this will really work? Had I not seen it myself, I’d be really skeptical. But it does look like they’ve got the hardware they need, and the preliminary tests look surprisingly promising.

Now, that doesn’t mean there won’t be some technical issue that will throw them off– the gravitational force between two 70kg people separated by 1m is about 5×10^-10 times the gravitational force between one of those people and the Earth, so at some point on the way to 10^-17, they’ll be sensitive to noise caused by students walking to class, and that sort of thing. But as crazy as it sounds, they look like they might be able to do it.

Savas Dimopoulos, Peter W. Graham, Jason M. Hogan, & Mark A. Kasevich (2007). Testing General Relativity with Atom Interferometry Physical Review Letters, 98 DOI: 10.1103/PhysRevLett.98.111102

Savas Dimopoulos, Peter W. Graham, Jason M. Hogan, & Mark A. Kasevich (2008). General relativistic effects in atom interferometry Physical Review D, 78 DOI: 10.1103/PhysRevD.78.042003