A Quantum Kind of Order

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thesis A quantum kind of order

Order versus chaos — it is one of the Oliver Penrose in the 1950s, but was first oldest themes in human history. For The ordinary and described in something like its current Plato, the highest kind of reality was that form by Chen Ning Yang in 1962. In the of the ‘forms’ — the pure conceptual not-so-ordinary kinds quantum description of matter, Yang noted, order existing behind the messy details of long-range order can the ordinary long-range order of a simple of physical substance, revealed only solid shows up in the diagonal elements through mathematics and logic. In science, exist at the same time. of the density matrix — the quantum progress has often come through an analogy of the classical material density. In appreciation of ever finer and lesser shades a superfluid, these elements show no long- of order, measured steps on the path to Apparently. However, it turns out range order, reflecting the disorganization disorder. The pure spatial periodicity of that the experiment may have other of the liquid. a perfect crystal gives way to that of a interpretations. A solid helium-4 But Yang showed that the onset of liquid crystal, for example, with order crystal, for example, has many highly superfluidity involves long-range order in only in molecular orientation, not in mobile, extended defects. In principle, the non-diagonal elements of the density spatial arrangement. the decrease in inertia might reflect a matrix. In the abstract, these elements The categories of order are not always reorganization of such defects, leading depend on two positions, r and rʹ, and so tidy, however. The forces supporting to a ‘quantum plasticity’ and softening of take nonzero values even as r − rʹ tends to periodic order, and maintaining that the material. The jury is still out on the infinity (away from the diagonalr = rʹ). order in the face of noise, also imply that a proper interpretation of this experiment, Less abstractly, this nonzero value reflects crystalline solid will resist external forces as physicists Massimo Boninsegni and the appearance of a macroscopic fraction and will not flow, although a liquid can. Yet Nikolay Prokof’ev point out (Rev. Mod. of particles in one quantum state — the glassy materials such as window glass both Phys.; in the press). superfluid condensate. resist forces and flow, at least slowly. Even so, no one seems to doubt that the This is the second kind of long-range With quantum theory, this blurring idea itself is sound, and will certainly be order — an inherently quantum kind of of categories becomes more ominous: detected somewhere, somehow. A quantum order — that makes it possible for a system ‘supersolids’, or more accurately ‘superfluid solid can be partly fluid, which seems to to be both solid and superfluid at once. solids’, flow like superfluids even though defy logic. But quantum theory makes it Everything depends on the identical nature they remain solid. How can that be? Here possible — in a typically non-intuitive way. of the particles, and their character as the nuance allowing the mingling of The defining character of a crystalline indistinguishable bosons. In a supersolid, distinct orders isn’t a matter of timescales, solid in three dimensions is long-range off-diagonal long-range order implies but something far more delicate — testing order — that is, the existence of periodic delocalization of these identical particles; the limits of our current conceptions regularities in material density and other they occupy the entire space, leading to of order. local properties extending out across the odd phenomena. In 2004, Eun-Seong Kim and sample. A crystal may have defects, yet As Boninsegni and Prokof’ev note, Moses Chan created a torsional oscillator the basic periodic arrangements of atoms for example, although a supersolid is by placing some solid helium-4 (at low otherwise repeat throughout the crystal. solid, hard and rigid, nevertheless a fluid temperature and high pressure) into a This kind of order immediately implies that can in principle flow directly through a small chamber suspended from a fine wire. the material has rigidity — a solid resists sample of it. Some helium-4 ice blocking a Twisted and released, the mass oscillated shear forces that would make adjacent pipe — like ice in a frozen pipe — wouldn’t back and forth, with the frequency offering parts slide past one another, and this is actually block the pipe. It would present a a sensitive measure of the moment of what distinguishes a solid from a liquid, solid block to the passage of non-helium-4 inertia of the material about the wire axis. which cannot resist such forces. In a solid, particles, but superfluid helium-4 would On lowering the temperature, they noticed the resistance comes from the same thing easily flow right through the solid. Atoms an abrupt decrease in the inertia at a producing the long-range order — forces entering one side, being delocalized, temperature of 250 mK. locking the atoms into a periodic pattern. could exchange positions with others on the Kim and Chan weren’t experimenting Fluids lack such long-range order, at far side of the solid, afterwards flowing out. at random. This kind of transition was least of the normal kind. But this clean But solid helium-4 ice would still remain a predicted some 34 years earlier by ‘either or’ doesn’t survive the conceptual hard normal solid — easily supporting any Anthony Leggett, who suggested that solid onslaught of quantum theory. Quantum heavy steel object, for example. helium-4 might well develop a superfluid theory allows a totally different kind of The notion of superfluidity is one of component at low temperatures, part of the long-range order, and it’s possible that the more peculiar additions to the zoo of solid becoming fluid-like and able to flow. the ordinary and not-so-ordinary kinds different kinds of order. It hasn’t yet been This is apparently what the experiment of long-range order can exist at the same pinned down experimentally, but probably showed — part of the solid material time, making a system at once both solid will be soon — demonstrating yet again the apparently becoming ‘decoupled’ from the and superfluid. sharp limitations of our familiar intuitions. ❐ motion below 250 mK. Hence, a solid that What is this kind of order? The original flows, and supersolidity. idea goes back to Lars Onsager and MARK BUCHANAN

NATURE PHYSICS | VOL 8 | MARCH 2012 | www.nature.com/naturephysics 175