Barely Excited

By Sean Carroll | July 31, 2009 9:10 am

The purpose of the LIGO experiment is to search for gravitational waves in the universe. They haven’t found any yet, but no good big-science experiment would be complete without a few cool spinoffs. They LIGO folks have an especially cool one: they’ve put a kilogram-sized pendulum and “cooled” it so effectively that it’s almost in its quantum-mechanical ground state. To be honest, I’m not exactly sure what this is good for, but it’s really cool. Ha ha, little physics humor there, get it? “Cool.”

LIGO works by bouncing lasers down a pair of evacuated tubes four kilometers in length. The laser beams bounce off a mirror suspended from a pendulum, and then recombine back at the source, where you look for tiny changes in the phase of the light wave. If a gravitational wave passes by, it will gently disturb the pendulums, and the length the laser has to travel down one or the other tube will be slightly changed, leading to a detectable shift in the phase. But obviously they’re looking for an extremely tiny shift, so it’s important that those mirrors not be jiggling around just due to random noise. Thus, they need to be kept cool; a warm mirror will be jiggling just from its thermal motion, even before we start worrying about noisy trucks passing by the observatory.

Physicists are pretty good at getting things to be cold; they can cool down collections of atoms to under a billionth of a Kelvin (room temperature is about 300 Kelvin). But there we’re talking about relatively small collections of atoms, maybe a million at a time. Here we’re talking about a kilogram, which is a honking big number of atoms, something like 1025. And the LIGO folks have cooled the oscillator down to about a millionth of a Kelvin, which is pretty cold.

The secret is that they don’t cool the entire mirror down to that low temperature. That would mean taking all of those 1025 atoms and putting them close to their quantum-mechanical ground state. But instead of thinking of the mirror as a collection of individual atoms, you can think of it as a single “center of mass,” plus a bunch of individual displacements from that center for each of the atoms. Then forget about the individual atoms, and just worry about that center of mass. That’s what we do all the time in the real world; when you tell someone where you are, you give them a single position — you don’t individually specify the location of every atom in your body.

harmonicoscillator.jpg We can think of the center of mass as an isolated “degree of freedom,” and talk about its quantum state apart from that of all the other atoms. Ordinarily, if a big collection of atoms is in thermal equilibrium, each of its degrees of freedom is “excited” above its ground state by a similar amount. Every physicist learns about the simple harmonic oscillator, which is one of the most basic physical systems we can study — it’s just a pendulum. In quantum mechanics, the nice thing about such an oscillator is that it has discrete energy levels, equally spaced, that depend only on the frequency of the pendulum. There is a ground state with just a tiny bit of energy (the “zero-point energy”), then a bunch of higher energy levels, from the first excited state all the way up to infinity. The energy of the Nth excited state is just (N+1/2) times Planck’s constant, times the frequency of the oscillator.

What the LIGO folks have done is to isolate that single degree of freedom, the center of mass of the oscillator, and gently coax it into a very low quantum state: N is about 200, whereas at room temperature N would be about 40 billion. An amazing feat, for a collection of that many atoms.

So what can you do with it? Don’t ask me. But the LIGO scientists know they have something interesting on their hands, and are thinking of ways they can take advantage of this approach to the quantum realm. It’s different, but complementary, to the strategy of putting entire macroscopic objects in a coherent quantum state. (Notice that the linked article is still talking about 1010 atoms, not 1025 atoms.) The LIGO mirror as a whole is still resolutely classical, even if the center-of-mass degree of freedom is near its quantum ground state. But taking big things and pushing them toward the quantum realm is a growth industry these days, and I’m sure we’ll be hearing more about clever applications of the process.

  • James

    Of course, as you well know, the pendulum is not a simple harmonic oscillator. However there will be non-physicists reading your postings, so I think it’s a good idea to be accurate so as not to misinform.

    For small displacements the restoring force – proportional to the sine of the angle – approximates the linear force of a true harmonic oscillator. This is true of many systems for small displacements.

    Every undergraduate physicist learns how to quantise the harmonic oscillator – few, if any, quantise the pendulum.

  • Chris W.

    Speaking of centers of mass, see this article that appears in the August issue of Scientific American. (Although mostly off-topic, but it describes some fascinating and little-known manifestations of spacetime curvature, recently investigated by Jack Wisdom of MIT.)

  • Chris W.

    PS: While I gnash my teeth over an editing oversight in my previous comment, I’ll add the abstract of Wisdom’s article (from Science, 2003):

    Cyclic changes in the shape of a quasi-rigid body on a curved manifold can lead to net translation and/or rotation of the body. The amount of translation depends on the intrinsic curvature of the manifold. Presuming spacetime is a curved manifold as portrayed by general relativity, translation in space can be accomplished simply by cyclic changes in the shape of a body, without any external forces.

    ..and the concluding paragraph of the article:

    The curvature of spacetime is very slight, so the ability to swim in spacetime is unlikely to lead to new propulsion devices. For a meter-sized object performing meter-sized deformations at the surface of the Earth, the displacement is of order 10-23 m (17). Nevertheless, the effect is interesting as a matter of principle. You cannot lift yourself by pulling on your bootstraps, but you can lift yourself by kicking your heels.

  • gopher65

    Not exactly on topic, but I’ve read that some recent results from… somewhere (my mind is like a sieve :P ) are starting to suggest that we may indeed live in a holographic universe. And if this is true, the “resolution” of our universe might be too low for us to directly observe (reasonably weak) gravitational waves on a setup like LIGO or LISA. For some reason that bums me out:(.

    Do you have any thoughts on whether or not that is a giant load of crap?

  • Lab Lemming

    How do they correct for earthquakes?

  • Serge

    I’m wondering how long before somebody freeze the cat to ground state and solve Schrödinger box mystery once and for all.

  • Jeff


    I seem to remember recently discussing the paper I think you’re referring to and concluding that the arguments of the author would put the “resolution” of the universe significantly larger than the scale we’ve already probed down to, presumably ruling out such reasoning.

  • Gray Gaffer

    It occurred to me that a Gravity Wave is essentially a flexure of space-time. If this is the case, would not the laser beam be equally affected? The ruler would change in the same way as the ruled, hence no change would be measured? They have been running long enough for cataclysmic waves to have passed us by, surely, yet no positive signal measured to date. I thought the length change they are seeking was a space-time distortion effect, not a pure space gravitational force compression of matter with no space-time geometry distortions. But the experimental setup seems to be assuming the latter is what will happen.

  • gopher65

    Gray Gaffer: LIGO’s sensitivity during its last run was so low that only a truly unbelievably ginormous event would have triggered a positive result. Each time they upgrade it the distance from which they can detect those ginormous events increases, and their ability to detect weak(er) nearby events increases, increasing the likelihood of a detectable event.

    So far, because of the low sensitivity, the calculated probability of a detectable event happening within detection range has been very, very low. They haven’t actually expected to find anything yet. They’re currently “just” trying to upgrade their experimental setup to the point where they have a decent chance of occasionally catching something big happening.

    I put “just” in quotes because their current task is no mean feat, but people seem to dismiss it as worthless because they aren’t yet to the point where they are producing usable observations.

    It’ll be really cool when they “see first light” though:). Then we’ll have an entirely new type of telescope to play with :D . And this one won’t even be reliant on EM. Woot!

  • Lab Lemming

    “And this one won’t even be reliant on EM. Woot!”
    So what sort of laser beam are they using?

  • gopher65

    I obviously meant that the thing that they were detecting wasn’t EM radiation, unlike almost every other type of telescope we have:P.

    Don’t be unnecessarily obstinate.

  • Gray Gaffer

    gpher65: so it is just a G force on the tubes changing their length, without affecting the space-time through which the laser beam is traveling and therefore not the beam? Or not as much? I thought gravity was equivalent to space-time distortion?

  • Serge

    @Gray Gaffer It’s not changing the length of tubes or pendulums inside the tubes. The noticeable change of length would require something unimaginable, like black holes collision nearby. The pendulum just swing tiniest amount, so the length which laser beam should travel before reflection change.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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