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.
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.