How big is it by a truly quantum measurement?

I am thinking of comparing Science magazines "Breakthrough of the Year" (BYOT) with the Zeilinger buckyball. The BYOT is a piezoelectric mechanical oscillator (PO) the size of the cross section of a human hair. It is placed in a superposition of its ground state and its first excited state. The well known buckyball experiment is a two slit experiment using buckyballs. (A third candidate might be a macroscopic Josephson junction oscillator conducting both ways at once.)

I have made some basic calculations. For instance, the BYOT contains about 10^14 atoms compared to 60 or 72 atoms in the buckyball. By this measure the BYOT is bigger by a factor of about 10^12.

On the other hand, the two slits are separated by 50 to 100 nanometers, or 10^-7 meters. In its first excited state, the top of the BYOT PO moves about 10^-15 meters per cycle, according to my calculations. By this measure the buckyball wins by a factor of about 10^8.

Calculating energy of the moving parts, I find a much closer horserace, but the buckyball is about 100 times bigger.

However, none of these calculations is at all quantum mechanical (QM). ArXiv lists at least five papers proposing truly quantum mechanical measures of the size of a macroscopic Schrodinger cat. The most recent is Lee and Jeong http://arxiv.org/abs/1101.1209 which references the other four. Can someone competent (or expert) in QM apply one or more of these quantum measures to the BYOT and the buckyball and tell me which is larger? TIA. Jim Graber

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The question sounds interesting, could you link to more information and to references on both BYOT and the BB? – Bruce Connor Jan 19 '11 at 14:12
References: 1.)As already listed by Chad Orzel, the BYOT reference is Nature 464:697-703 (17 March 2010). Also interesting is the News and Views article by Markus Aspelmeyer on pp 685-686, which does refer to the Schroedinger cat issue and states that “the actual displacement between the two motional states of the prepared superposition is on the order of 10^–16 metres — that is, six orders of magnitude smaller than the size of the unit cells of the resonator’s structural lattice.” 2.) The buckyball reference is Am. J. Phys., Vol. 71, No. 4, April 2003. – Jim Graber Jan 19 '11 at 23:29
Define "larger". Number of particles? Physical size? More publicity? Greater scientific impact? One could argue endlessly about what would constitute the "largest" cat. Ferinstance, the superconducting junction paper Chad Orzel referenced has a large number of particles, but - if I remember correctly - the superposition still evolves phase like it was just 2 electrons (a single Cooper pair). As opposed to some ion-trap-quantum-computer cats, which may have only a dozen particles, but the superpostion evolves phase like a dozen-particle object. – Anonymous Coward Feb 18 '11 at 19:05
@Anonymous coward: A interesting question in current research is to find a meaningful definition of larger in this context... – Frédéric Grosshans Feb 25 '11 at 11:21
Schrödinger did not define the special nature of that cat, so feel free to assume a lion or a tiger, what ever my be bigger. – Georg Mar 4 '11 at 18:36
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The largest genuine "cat state" sort of experiment I could find, measured by number of particles, was a couple of experiments on superconducting junctions which involved a few billion electrons. I have, of course, misplaced the references, but I believe this arxiv paper is one of them. (Though looking around for the reference also turns up this recent paper arguing the number is far smaller, at most a few thousand.

Note also that the "Breakthrough of the Year" paper (this Nature article) does not actually claim to have made a Schroedinger cat state. They have cooled a mechanical resonator to its ground state, and demonstrated some control over its state, but they haven't done all the work that would need to be done to demonstrate that what they have is a cat state (which would probably involve some sort of interference effects, that being the usual way to demonstrate something being in more than one state). Given what they have done, it's not a big stretch to think that they will eventually do the cat state experiment, but they haven't published that yet.

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From the Nature paper midway between figure 5 and figure 6: “After one-quarter of the first Rabi oscillation, at τ ≈ 1.9 ns, the qubit and the mechanical resonator are entangled in the state |g1  + |e0 .” This is what I took to be the claim for a Schrodinger cat state. I think the arguable part is how macroscopic it is. – Jim Graber Jan 19 '11 at 23:55
Korsbakken et. al <arxiv.org/abs/1003.5294>; Marquardt et. al. <arxiv.org/abs/quant-ph/0609007>; These two references also argue that the size of the cat in the superconducting junctions is much smaller than it naively appears. – Jim Graber Jan 20 '11 at 0:06
The link in my original answer is to the Korsbakken paper in what I thought was an open-access IOP journal, but turns out to be one of the pay ones (bastards). I'm not certain I would call the sentence you quote a claim to have made a cat state-- what they've got is a pair of systems with one quantum of energy between them-- but even if it is, I don't think what they have is conclusive on that count. They really need to do something more to demonstrate that it's a cat state, either some state tomography or some kind of interferometry. – Chad Orzel Jan 20 '11 at 0:56
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OK, I concede, and I think the original authors also concede that they haven't (yet) fully characterized the quantum state--or in my oversimplification proved that it is a cat state. But I remain under the impression that it is very likely to actually be one. Do you disagree? – Jim Graber Jan 20 '11 at 4:25
I actually expected more controversy about the buckyball experiment: Is it fair to call a two slit experiment a cat state? – Jim Graber Jan 20 '11 at 4:27
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Recall that the LIGO noise limit in some frequency bands is given by the Heisenberg position uncertainty of the two multi kg single crystal sapphire mirrors, apparently about 10^-18m. In other words, to lower the noise, the designers are planning to increase the mass of the mirrors from 10 to 40 kg apiece! This is different from the radiation pressure uncertainties which apparently dominate the error budget in other frequency bands. See e.g. elmer.tapir.caltech.edu/cajagwr/pdf/chen.pdf, for several examples of entanglement, squeezing, etc. Check out the first slide for a photo of one of the 10 kg mirrors. To see Heisenberg position uncertainty in an object of this scale is, to me, somehow truly inspiring.

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The Dec 17 2011 Science has in its breakthrough of the year a discussion of “The first Quantum Machine.” It is a vibrating device which has some superposition of vibrational states. It is a maybe a sort of Schrodinger cat state.

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