Bouncing Neutrons for Fun and Science: "Realization of a gravity-resonance-spectroscopy technique"

Several people blogged about a new measurement of gravitational states of neutrons done by physicists using ultracold neutrons from the Institut Laue-Langevin in France. I had to resort to Twitter to get access to the paper (we don't get Nature Physics here, and it's way faster than Inter-Library Loan), but this is a nice topic for a ResearchBlogging post, in the now-standard Q&A form:

OK, why was this worth begging people on Twitter to send you a copy? The paper is a demonstration of a sort of spectroscopy of neutrons bouncing in a gravitational field. They showed they could drive neutrons bouncing on a "mirror" between two of the discrete quantum states of the system, and measure the energy difference between those states very accurately.

Wait, neutrons bouncing on a mirror have discrete states? Why doesn't anybody tell me these things? Well, you didn't ask. Anyway, yes, neutrons bouncing on a mirror have discrete states, just like any other quantum system. Quantum mechanics tells us that confined systems will always exist only in special discrete states-- that's what puts the "quantum" in "quantum mechanics," after all.

But how are these confined? They're confined by gravity. To do the experiments, they send a beam of extremely slow-moving neutrons above a polished glass surface. When the neutrons fall under the influence of gravity, they hit the surface and bounce back upward. On the high side, the neutrons have only a limited amount of energy, and once all the kinetic energy of their vertical motion has been turned into gravitational potential energy, they turn around and fall back down, just like a tennis ball thrown up into the air for a dog to chase after.

Yeah, but tennis balls don't have discrete states. They do, you just can't tell the difference between them very easily, because they're so close together in energy, and the wavelength is so small. A sample of slow-moving neutrons, though, can clearly show these different states, which are described by wavefunctions that look like this:

The solid lines show the probability of finding the neutron at a given height (probability increasing to the left) for the first four states of a neutron bouncing on their mirror. It's taken from an older paper (from 2002) where they demonstrated the existence of these quantized states.

How did they do that? The basic technique is the same one they used for the detection in this experiment: they put an absorber above their mirror at a set height, to block any neutrons in states that extended up too high.

You can see from that figure that as you go up from one state to the next, the probability of finding the neutron at higher elevations increases. Neutrons in the lowest state will basically never be found more than 20 microns above the surface, while neutrons in the third state (from the left) have a pretty good probability of turning up that high.

So, how does an absorber help demonstrate the existence of these states? I mean, as you move it closer to the mirror, it'll block the higher states, but you expect the number making it through to decrease anyway, because there's less space to squeeze through. Right, but in a classical system, no matter how narrow you make the gap, some neutrons can always sneak through. In a quantum system, if the gap is too small, the neutrons will always be absorbed, so there should be a minimum height below which nothing makes it through.

And that's what they saw? Yep. It looked like this:

The solid line is the classical prediction, the points are the data for various heights of the absorber. You can clearly see the cut-off: below about 15 microns, nothing makes it through, even though classically there should be some transmission.

OK, so you can see the lowest-energy state. So, for the current paper, they did what, raised the absorber higher and looked for steps in the transmission? Better than that. They demonstrated a way to drive the neutrons from one state to another by shaking the mirror on the bottom. They picked out the lowest-energy state with a narrow mirror-absorber gap in the first stage of their apparatus, then used a vibrating mirror to put the neutrons into the third energy state.

So, instead of pushing the absorber down, they brought the bottom mirror up? No, they used the shaking on the mirror to pump energy into the system, and resonantly transfer the neutrons from the lowest energy state to the third state. When they shake the bottom mirror at exactly the right frequency, the neutrons pick up energy from the shaking, and move to the third state; at frequencies a little higher or lower, they just stay in the lowest energy state where they were all along.

Wait, how does that work? Well, you can think of it as being a little bit like when I take SteelyKid to the playground, and put her on the swings. If I push the swing at just the right rate-- basically, once per swing, as she comes back to where I'm standing-- she quickly starts swinging higher and higher (and yelling "Faster!" and giggling). If I were to push at a frequency a little higher or lower, I would sometimes increase her swing, but a few swings later, I'd be pushing her before she got to the end of her oscillation, and that would interrupt her swinging and bring her to a stop.

And she wouldn't like that. No. Not one little bit. That ideal frequency of pushing for a swing is set by the length of the chains on the swing, which determine the time needed for it to go through one full oscillations.

In the case of the bouncing neutron, the ideal frequency of pushing is set by the energy difference between states. If they shake their bottom mirror up and down at a frequency equal to the energy difference between the first and third states divided by Planck's constant h, they will take atoms from the lowest energy state and move them to the third energy state.

Wait, why the third state? Don't they have to go through the second state? No, because quantum states are discrete and independent. You can go directly from state 1 to state 3 or state 5 or state 137, without passing through the intervening states, so long as the frequency of the shaking is at the right frequency.

The probability of making that transition goes down as you go to higher states, because higher states spend most of their time at higher elevations than the lowest energy state can possibly reach, so it's not that easy to go directly from a low to a high state. There's no fundamental reason why you can't go directly to any state you like, though.

So why did they pick state 3? I don't know. Probably because it gives a cleaner separation between the neutrons remaining in state 1 and those moved to state 3, since the maximum height difference is greater.

OK, so, let me see if I've got this: they send neutrons in, use an absorber to pick out only the lowest energy state, then use a shaking mirror to excite those neutrons to the third energy state. Then, what, they stick in another absorber and look at what makes it through? You've got it exactly. They use a third mirror section with an absorber placed at a height that picks out and blocks the third state, and they show a decrease in the number of neutrons making it through.

Shouldn't you show a graph at this point? Sure:

The top figure shows the transmission of neutrons through the absorber region as a function of the frequency of the shaking. The dip corresponds to two different amplitudes of the moving mirror, showing that you get more neutrons making the transition when you shake a little bit harder. The second graph is a combination of all their measurements into a single plot, with the horizontal axis being a sort of fractional difference between the frequency of the shaking and the resonant frequency.

Yeah, that looks like a clear dip, doesn't it? Yep. It's a pretty nice, clean signal, showing that they have some control over the states of their system. It's be nice if they could show Rabi oscillations clearly (that is, demonstrate the ability to drive the neutrons from state 1 to state 3 and then back to state 1), but given what they're working with, it's a little amazing they can do this at all.

OK, this is cool and all, but what is this good for? Well, the spacing between the states depends on the gravitational attraction between the neutrons and the Earth, so probing the difference between these states tells you something about gravity and the acceleration of gravity. This can be a test of the equivalence principle saying that the inertial mass in Newton's Second Law is the same as the gravitational mass, which is the cornerstone of general relativity.

The scale over which these things move is really small-- 10-20 microns-- so this might also provide a way to test the behavior of gravity on those kinds of separations. Since neutrons are, by definition, neutral, they're not strongly effected by electric charges and things like that, making them potentially a very good tool for testing theories that predict a dramatic strengthening of gravity at small distances.

There's a lot of cool fundamental physics stuff you can imagine doing with a system of slow bouncing neutrons. This paper demonstrates some ability to manipulate the states of these neutrons, which is one of the key prerequisites to doing any of the really cool stuff.

And, you have to admit, it's pretty cool in its own right.

Jenke, T., Geltenbort, P., Lemmel, H., & Abele, H. (2011). Realization of a gravity-resonance-spectroscopy technique Nature Physics DOI: 10.1038/nphys1970

Nesvizhevsky, V., Börner, H., Petukhov, A., Abele, H., BaeÃler, S., RueÃ, F., Stöferle, T., Westphal, A., Gagarski, A., Petrov, G., & Strelkov, A. (2002). Quantum states of neutrons in the Earth's gravitational field Nature, 415 (6869), 297-299 DOI: 10.1038/415297a