Cooling a "Macroscopic" Object to Its Quantum Ground State

ResearchBlogging.orgSeveral people have sent me links to news stories about last week's Nature paper, "Quantum ground state and single-phonon control of a mechanical resonator." (It was also presented at the March Meeting, but I didn't go to that session). This is billed as the first observation of quantum phenomena with a "macroscopic" or "naked eye visible" object.

Of course, there's a nice bit of irony in a story about quantum effects in a "naked eye visible" object that is accompanied by an image of the object in question taken with a scanning electron microscope. The longest dimension of the object in question is about the thickness of a human hair, which means it technically is naked-eye visible, provided you have pretty good eyes. In a different context, though, something this size would probably be billed as "nanotechnology" (as its smallest dimension is about one micron, or 1000 nanometers).

Still, this is unquestionably the largest thing ever observed in its quantum ground state, so it's big news. As you can tell by the fact that it's in Nature. So, what, exactly, have they done, and why is it cool? To vary things up a little, I'll do this one in Q&A format.

What, exactly, have they done? A group at UCSB has cooled a microfabricated resonator to its quantum ground state. This means that they have removed all the energy that it's possible to remove from the oscillating mode of the resonator-- the only motion left is the zero-point energy that's impossible to remove. They have also demonstrated the ability to make small excitations of this oscillating mode, both by directly driving it with microwaves, and also by coupling it to a "qubit" fabricated on the same chip.

In quantum mechanics, oscillating objects can only have discrete amounts of energy-- the zero-point energy plus 1, 2, 3,... times the energy associated with the oscillation frequency-- so the behavior they see is very much unlike a classical oscillator, which has energy that can be continuously varied from zero to whatever you like. What they see here shows signs of the discrete energy values you expect for a quantum oscillator, not a classical one.

So, they, like, took pictures of it moving, or something? I mean, it's visible, right? Not exactly.

The mode in question is an expansion and contraction of the thickness of a microfabricated multilayer structure of aluminum and aluminum nitride. The vibration is along the thin dimension of the object, and would be nearly impossible to see even if it weren't on a chip in the middle of a complicated apparatus.

So how do they measure it, then? They fabricated the resonator on a chip, and connected it electrically to a superconducting qubit, a loop of wire with a small gap in it, that can sustain an oscillating electric current in one of two states, which acts like an artificial two-level "atom." They can measure the state of this "atom" very well, and treat it as a qubit, a two-state quantum object that can be manipulated with applied electromagnetic pulses and magnetic fields.

In its normal state, the qubit is not sensitive to what's going on with the resonator, but if they apply a magnetic field of the right amplitude, they can arrange for the qubit and the resonator to oscillate at (very nearly) the same frequency. When that happens, energy in one of the two can pass into the other. So, they can measure the amount of energy in the resonator by preparing their qubit in its lowest energy state, putting on the magnetic field, waiting a while, and then looking at the state of their qubit. If there's any energy at all in the resonator, a little of it can leak over to the qubit, giving it a slightly greater chance of being in its excited state.

So, what do they see? Nothing at all. If they prepare their qubit in its low-energy state then couple it to their oscillator, they see absolutely no change in the probability of finding it in the excited state, which suggests that there's no energy to be extracted from the oscillator. That is, that it's in the quantum ground state.

Wow. So, they must do some really tricky cooling scheme, right? Nope. They just built the resonator and qubit on a chip, and cooled it to 0.025 K (25 one-thousandths of a degree above absolute zero) using liquid helium in a dilution refrigerator. It's nothing fancy at all on the cooling side, just some clever manufaturing of the resonator and qubit.

OK. So, you said something about exciting the resonator, and the news stories talk about putting the thing in two places at once. What's up with that? They can make the coupling go the other way, by putting some energy into their qubit, and transferring it to the resonator. They use microwaves to put the qubit in its excited state, and then couple it to the resonator. The energy in the qubit can then move over into the resonator, starting it oscillating, and then shift back to the qubit, like you get when you couple two pendula together (YouTube video)-- first one oscillates, then the other, then the one, and so on back and forth.

When they start their qubit in the excited state, then couple it to the resonator for some time, then decouple them and measure the qubit, they find that the probability of finding the qubit in the excited state drops down to zero in about 3.8 ns (around 23 oscillations of the resonator), indicating that the energy has moved over into the resonator. The excited state probability increases again over roughly the same amount of time, as the energy comes back, and they see four or five oscillations before it damps out, showing that this is really a quantum transfer of energy, and not just some sort of loss.

They can also do two-pulse experiments showing the same sort of thing-- energy is resonantly coupled from one one system to the other, and maintains coherence for about 20 ns (100+ oscillations of the resonator, which isn't too shabby for a first demonstration). Everything hangs together very nicely.

So, they can only dump in as much energy as they have in the qubit? No. They can also directly excite the oscillations in the resonator by pulsing in microwaves, and then use the qubit to measure the state. When they do this, they see oscillations indicating the same sort of energy transfer, starting with energy in the resonator.

Another nifty quantum angle on this is that the frequency at which energy transfers back and forth between the resonator and the qubit increases as they increase the amount of energy they put in-- they don't have a precise calibration of the energy dumped into the resonator by the microwaves, but they show some simulations that suggest it ranges up to maybe 20 times the fundamental energy of the resonator. The frequency increase is consistent with a simple theory, and shows that, in a particle-based picture of things, the "phonons" (one quantum worth of vibration energy, analogous to a photon of light) are bosons, as they should be.

What about the "two states at once" part, though? How did they do that?. I'm not entirely sure what they're referring to there-- this may be a case of journalists overreaching.

I suspect that what that's referring to is an intermediate state of the coupled oscillators. When they have energy sloshing back and forth between the resonator and the qubit, there are points in the oscillation when they two exist in an entangled quantum state-- that is, if one is excited, the other is not, and vice versa, but neither has a definite state until the measurement is made. In such a state, the state of either system can be viewed as a superposition of the "0" and "1" energy states at the same time.

The data they have strongly suggest that they've made just such a state, but they aren't able to provide the absolute smoking-gun proof. Proving entanglement beyond a shadow of a doubt would require them to do some complicated operations on the state ("full Wigner tomography") to demonstrate that it's really an entangled state of the two, and not some funny semi-classical thing that happens to look superficially like an entangled state. The operations involved are a little time-consuming, though, and would take longer than the 20ns that their states last before random noise swamps their signal.

You can bet that they're in the lab right now working on ways to extend that coherence time, and do the necessary state tomography. You can also bet that at least some sticklers will claim that they haven't really demonstrated entanglement until they do.

So, when are they going to put a cat in a superposition state, anyway? Not for a good long time. This is technically visible to the naked eye, but we're still talking about something with dimensions measured in microns, with a mass of around 10-12 kg. That's nowhere near the scale at which some people (Roger Penrose, say) claim that mass effects would cut off quantum superpositions, let alone the scale of a cat.

Still, this is way cool, and a nice demonstration of the quantum nature of everything, not just single atoms or electrons.

O'Connell, A., Hofheinz, M., Ansmann, M., Bialczak, R., Lenander, M., Lucero, E., Neeley, M., Sank, D., Wang, H., Weides, M., Wenner, J., Martinis, J., & Cleland, A. (2010). Quantum ground state and single-phonon control of a mechanical resonator Nature DOI: 10.1038/nature08967

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I suspect that for a cat that < dead|cool to 0.025K|x > = 1, so the experiment is a little moot.

By Blaise Pascal (not verified) on 24 Mar 2010 #permalink

Let's try that again...

I suspect that for a cat, = 1, making the experiment a little moot

By Blaise Pascal (not verified) on 24 Mar 2010 #permalink

So, an engineer would tend to ask two questions about this:

1) What's it good for, and
2) If it's good for something, how hard is it to do more?

I'm curious about 2). As the size of the thing they're cooling and measuring increases, what is it about the problem and solution that gets harder, and how fast does it get harder?

Meaning, if they chose to do this to a resonator twice as big, what's the metric for "big"? The length dimmensions? Mass dimensions? Number of atoms in the resonator? Something else?

And given that, if they're doing something "twice as big" by whatever is the right metric of big, what gets more difficult (and how fast) in the experimental setup? More refrigeration? More manufacturing precision? Twice as much? Four times as much?

By John Novak (not verified) on 24 Mar 2010 #permalink

I tried to fix the brackets in that comment (#2), but I can't get it to show up. The gist is that cooling a cat to 0.025 K creates a state that is indistinguishable from "dead cat."

1) What's it good for, and

Mostly, for learning more about quantum mechanics. People who do this sometimes talk about making devices to do really sensitive measurements of other things, but it's not entirely clear to me what those things might be, or whether this really adds anything.

2) If it's good for something, how hard is it to do more?

Hard. The tricky part is cooling an object down to the point where its thermal energy is significantly lower than the energy needed to excite a vibrational mode. That requires really cold temperatures, or really high vibration frequencies-- the resonator in these experiments oscillates at around 6 GHz, which is a little tough to arrange.

The folks at LIGO think they have a cooling scheme that could get the vibration mode of a gram- or even kilogram-scale mirror down to its quantum ground state. That would be pretty amazing.

In that case, you're talking about something really strange, in that the mirror itself would not be at cryogenic temperatures-- only one vibration mode of the mirror surface would be cooled to the ground state, while the mirror itself and the atoms making it up would still be at considerably higher temperatures. I expect that, if they pull it off, some people will object that it doesn't really count because it's not cooling of all of the mirror's vibration modes.

in Hilbert Space, no one can hear you laugh.

Fantastic post! I had been wondering about that article because I saw it reported everywhere. I just have a couple of quick points:

"Proving entanglement beyond a shadow of a doubt would require them to do some complicated operations on the state ("full Wigner tomography")"

I've no idea why they would need to do full tomography, although it is nice if you can manage it. Most people would accept that a violation of a Bell inequality or some other entanglement witness test would be sufficient. If you know what the state *should* be then it is not too hard to devise an entanglement witness with far fewer measurements than full tomography. Of course, I imagine that the hard part here would be "freezing" the system in its entangled state for long enough to do the measurement.

"That's nowhere near the scale at which some people (Roger Penrose, say) claim that mass effects would cut off quantum superpositions, let alone the scale of a cat."

There is another issue in Penrose's proposal, which is that the two states need to have significantly different mass distribution, so that they couple to the gravitational field differently. If I had a lead weight in a superposition of two states that only differed by a nanometer then that probably wouldn't be good enough. Usually, one requires a significant difference in the mass density distribution of the two states, e.g. centre of mass differs by mghffxhg (I can't be bothered to get Penrose's book of the shelf) meters. A superposition of ground and first-excited states is very unlikely to satisfy this, so I don't think this sort of experiment is relevant to collapse theories regardless of the mass of the object. This is the same reason why earlier experiments on macroscopic SQUID currents are not relevant to Penrose. Similar remarks apply to GRW and other spontaneous collapse theories, even though gravitation is not taken to be the collapsing agent, because the collapse is still taken to depend on spatial displacement.

Cleland (and collaborators) are the shiznit.

In addition to the cool nanomechanical devices, the dilution refrigerators, the low-noise SQUID electronics, etc. etc., he and his collaborators have built fantastic custom data-acquisition systems that let them take and process data at massive rates. In past talks I've seen him show beautiful plots of the evolution of a qubit (not the nanomechanical resonator) on the Bloch sphere, and the signal-to-noise was incredible. I was blown away because it was the kind of textbook illustration stuff that atomic folks are always tooting their own horn about. In some sense the quick decoherence times are actually an advantage for getting that kind of data, since the full experiment every microsecond or so.

By Anonymous Coward (not verified) on 24 Mar 2010 #permalink