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Supercool Dude .. A chat with Anthony J. Leggett

December 16, 2009

Sir Anthony J. Leggett and Schroedinger's famous thought experiment Prof. Anthony J. Leggett of the University of Illinois at Urbana-Champaign shared the 2003 Nobel Prize in Physics "for pioneering contributions to the theory of superconductors and superfluids".

Superfluids can, in theory, be used in topological quantum computing .

Superconductors are materials which offer effectively zero resistance to current at nearly absolute zero temperatures. They have been in the news recently in the form of superconducting magnets for the Large Hadron Collider.

Superfluids exhibit fluid dynamics analogous to the electrical dynamics of superconductors: they will flow through the finest capillaries without friction. The connection between superfluids and superconductors is more than an analogy: the quantum theories of the two phenomena are intimately related.

Prof. Sir Anthony (he was knighted in 2004) spoke with me by phone from his office.

JW: Can you please describe the connection in nature between the twin phenomena of superconductivity and superfluidity?

AL: From a modern point of view, superconductivity is simply superfluidity occurring in an electrically charged system. Superfluidity is not a simple phenomenon; it's a complex of phenomena which generally seem to go together in real life, though I don't think anyone has any a priori guarantee that they will. The most dramatic manifestation clearly is the apparent ability of superfluids to sustain currents without any apparent friction.

An example of this is if I take a toroidal or annular geometry and I put helium in it and set it into annular rotation. At high temperatures helium behaves like water. Then when I cool it down to the superfluid transition and stop the annulus, the superfluid will basically go on rotating forever.

JW: Just as electrons in a superconducting circuit.

AL: That particular experiment offers a very obvious visible parallel between superfluidity and superconductivity.

JW: Well ... why the heck is that!?

AL: The general idea is that either single atoms, or in the case of superconductors, pairs of electrons, undergo Bose-Einstein condensation and that means basically that they have to all behave in exactly the same way at the same time. So once you've got the superfluid into rotation the individual atoms can't scatter out of that state. If they're going to make a transition, they have to do it collectively. One can give arguments to show that, under normal conditions, the process of getting out of the rotating state into a non-rotating one has a substantial free energy barrier that must be overcome.

JW: Something has to provide more energy into the system.

AL: Yes, and the only obvious way of doing that is to heat the thing back up above the superfluid transition. Without that, it's essentially impossible to stop the superfluid rotating.

JW: I first saw liquid helium at the 1964 World's Fair in New York. They poured it out of the beaker and its viscosity made it pour itself back in ... but this I think was before one could reach the millikelvin temperatures that are necessary for the phenomena you describe.

AL: For 4He, the common isotope of helium, it's not important to get it down to millikelvin temperatures. Everything that's going to happen happens around one or two degrees. 3He is the one that requires the lower temperatures.

JW: Is there an explanation for the difference?

AL: While there's some sense of the common principle underlying superfluidity of 4He and 3He, the detailed mechanism is different. In 4He the helium atoms are already bosons, so they can automatically undergo Bose-Einstein condensation at a low enough temperature. That temperature turns out to be, crudely speaking, when the de Broglie wavelength becomes comparable to the inter-particle space. That's quite a high temperature, about two degrees kelvin.

3He atoms are fermions. They would not naturally, as it were, undergo Bose-Einstein condensation. But if you can get two 3He atoms to form a sort of bound state, a complex - you can think of it somewhat like a diatomic molecule - in that case, since you have two spin-½ particles, they can form a spin-0 or spin-1 boson, effectively, then that boson can undergo Bose-Einstein condensation.

JW: This is a Cooper pair?

AL: Yes. For this purpose, one can rather qualitatively think of Cooper pairs as sort of giant diatomic molecules.

JW: But you can't get them into this state until they're quite cold?

AL: That's right, you don't get Cooper pairs until about two millikelvin.

JW: In your 2003 Nobel Lecture you wrote, "It occurred to me that a two-band superconductor should show a sort of internal Josephson effect corresponding to fluctuations of the relative number of electrons in the two bands and of the relative phase of the Cooper pairs in them." You go on to state that your ideas about two-band superconductors seemed unrealistic at the time, but that there was evidence by 2003 of this sort of mode in the material MgB2.

AL: It's claimed that such a mode has been seen with magnesium diboride. The evidence of that is rather indirect. My retired colleague Miles Klein has done some work on this and does believe the experiments are seeing this. As I say, it's a fairly indirect argument.

JW: Are there special properties of two-band superconductors that make this field of research attractive?

AL: Not really ... I don't think there's much you can do with a two-band superconductor you can't do with a straightforward one-band one. I think the main interest has been simply that they use this superconducting compound MgB2 which is important for certain applications. It's the highest-temperature "old-fashioned" superconductor, meaning, it seems to be of the class that existed back in the 1950's and '60's and which Bardeen and Cooper explained. It's more like those than like the modern cuprates.

JW: You were quoted in Wired Science as saying that a study of the work of John Martinis' team at UCSB “does seem to be rather unambiguous evidence for entanglement.” Did you mean that the study provides evidence that they have achieved the massive entanglement they claim or that it provides experimental evidence of the phenomenon of entanglement?

AL: If you are content to describe your system by quantum mechanics, then I believe they have fairly unambiguous evidence for an entangled state. However, that's rather different from saying that the raw data by themselves unambiguously establish the existence of an entangled state, because, for all one knows, quantum mechanics might be going wrong about this sort of thing!

JW: Have you banged your head much against this mystery in your career?

AL: Oh, yes! I've written numerous articles and tried to motivate experiments in this area, of which the Martinis experiment is a very good example. What has been interesting, even serendipitous, is that this whole enterprise, trying to demonstrate evidence for quantum superposition at the macroscopic level, has been able to piggyback on the idea using some of these Josephson devices as qubits for quantum computers.

However, the entangled states in the Martinis experiment are not macroscopically distinct. You could argue that there are currently no experiments which have unambiguously demonstrated the superposition of macroscopically distinct states. That depends a lot on how you define "macroscopically distinct" but ...

JW: How do you define that?

AL: Here's what I would regard as sufficient criteria to be macroscopically distinct: if they can be distinguished with the unaided human eye. In Martinis's experiment the device is macroscopic, but the two states in question are not macroscopically distinct, at least, not by my definition.

JW: Have you suggested something that would unambiguously resolve the nature of entanglement?

AL: Personally, I don't think that entanglement is the most mysterious thing. We've been a bit too much on the entanglement bandwagon the past few years. It's the idea of quantum superposition of macroscopically distinct states that is the real puzzle and mystery.

With my former post-doc Anupam Garg , we suggested in the mid-1980's an experiment which would at least test the predictions of quantum mechanics at the quasi-macroscopic level against the predictions of a whole class of alternative theories, what I call macro-realistic theories. I would not say that experiment has really yet been done, but people are working on it. There are a number of steps on the road that people have realized quite recently, in fact. Our 1985 paper was Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?

JW: What are you interested in today?

AL: I'm mostly interested in the questions related to topological quantum computing.

JW: I spoke with Michael Hermele and he gave me the layman's tour of non-abelian statistics and was quite frank that this might not be demonstrated experimentally for ten to fifteen years.

AL: That's a reasonable conjecture.

JW: I suppose it's only a few years since the temperatures necessary to demonstrate these effects could be reached practically.

AL: People actually took 4He down below what we now call the lambda point way back around 1920. It was only in 1938 with the experiments of Misener and Kapitsa it was clearly realized that something very peculiar was going on. Superfluidity in liquid helium must have existed before that, it's just that no one realized.

JW: Do things like superfluids exist if we don't make them?

AL: That's a very good question. At least as far as we know, if you except certain speculative scenarios of the early universe, the universe has never been cooler than it is right now, and right now it is not quite cool enough for superfluidity in liquid helium to exist except in labs on Earth.

JW: Maybe the comedian George Carlin was correct when he said that the reason humanity exists is that Mother Nature wanted styrofoam?

AL: [Laughing] I'm interested in a particular kind of alleged topological quantum computer based on P+IP Fermi superfluids. These include the A-phase of superfluid 3He and strontium ruthenate (Sr2RuO4).

JW: How would this compute?

AL: The idea is that if you can make a certain kind of vortex in such a system, then a pair of vortices carries a fermion exitation. Then the story is that by braiding these vortices around one another you can perform quantum computation.

JW: This is the same concept of braiding we encounter with quantum Hall liquids?

AL: That's right. The general belief is that there is a fairly close theoretical analogy between the P+IP Fermi superfluids and the possible quantum Hall states. That's something I'm trying to understand at a more fundamental level.

JW: Are you in that sort of profession where if you turn away for a moment and look back, you find your own field has become baffling to you?

AL: Yes, very much so! I missed out on the first few years of topological quantum computing and am trying to catch up. I was doing other things!

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