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ScienceWeek
ON SUPERSOLID HELIUM
The following points are made by John Beamish (Nature 2004 427:204):
1) At temperatures below 2.176 K, helium-4 enters a superfluid state and flows without friction. This "perpetual motion" makes superfluidity -- perhaps even more than its electronic counterpart, superconductivity -- the most dramatic manifestation of quantum mechanics on a macroscopic scale. Despite its appeal, and despite many searches for superfluidity in other systems, it remains an uncommon phenomenon. From 1938, when superfluidity was discovered(1,2), helium-4 was the only known example until 1972 when the phenomenon was seen(3), at much lower temperatures, in helium-3. That temperature difference between the behavior of the two isotopes reflects the intimate connection of superfluidity to Bose-Einstein condensation -- the transition that occurs when "bosons" collect in a single quantum mechanical state. Atoms of helium-4 are bosons, but helium-3 atoms are "fermions" and must pair up before they can condense into a single state.
2) In 1995, advances in laser-cooling and magnetic-trapping techniques led to the achievement(4) of Bose-Einstein condensation in rubidium vapour, adding to the list of superfluid systems. That list now includes other gases, such as spin-polarized hydrogen gas(5), and, most recently, molecular gases of paired fermions. Kim and Chan (Nature 2004 427:225) claim the first observation of superfluid behavior in a solid. A sample of solid helium-4, confined in the nano-scale pores of Vycor glass and rotated in a torsional oscillator, underwent a transition below about 175 mK that indicated the onset of "supersolid" behavior. If it can be confirmed that superflow is occurring in the solid helium, this is a remarkable result indeed.
3) Despite their rarity, superfluids are fundamental to, for example, statistical mechanics and fluid dynamics, and they are a valuable test bed in fields as diverse as turbulence and cosmology. So it is not surprising that superfluidity has been sought in new systems. Solids, with their atoms localized on a periodic lattice, are certainly the most unexpected phase of matter in which to find superfluidity. However, the low atomic mass and the weak interatomic forces in solid helium make it very different from conventional solids. A quantum mechanical effect known as "zero-point motion" dominates its properties, to the extent that it does not freeze at all unless external pressure (of at least 25 bar) is applied. At higher pressures helium does crystallize, but zero-point motion remains important and produces a very compressible low-density solid. In such a "quantum solid", defects such as vacancies on the atomic lattice are easily created and can be very mobile. They might even exist in finite concentrations at absolute zero. Although such zero-point vacancies have not been directly observed, they would be expected to condense into a coherent state at low temperatures. And because mass flow accompanies the movement of vacancies, such a state could exhibit superfluid flow.
References (abridged):
1. Kapitza, P. Nature 141, 74 (1938)
2. Allen, J. F. & Misener, A. D. Nature 141, 75 (1938)
3. Osheroff, D. D., Richardson, R. C. & Lee, D. M. Phys. Rev. Lett. 28, 885-888 (1972)
4. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Science 269, 198-201 (1995)
5. Fried, D. G. et al. Phys. Rev. Lett. 81, 3811-3814 (1998)
Nature http://www.nature.com/nature
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ON HELIUM SUPERFLUIDITY AND BOSE-EINSTEIN CONDENSATION
The following points are made by Anthony Leggett (citation below):
1) If we put a large number of helium atoms, of isotopic mass 4, in a box, then at temperatures above about 4 K they will form a gas. As we cool below this temperature they form a liquid (with, of course, a few atoms left as a gas above the liquid), but this liquid does not have any particularly spectacular properties; in this phase it is called helium-I (He-1). However, if we cool it further, below a specific temperature close to 2 K, conventionally called T-lambda (because the graph of specific heat near there, when plotted against temperature, has a shape resembling the Greek letter lambda), the liquid suddenly starts to display quite abnormal and spectacular properties: it flows through tiny capillaries without apparent friction, climbs, in the form of a film, over the edge of vessels containing it ('film creep'), spouts in a spectacular way when heated under certain conditions ('fountain effect') and displays a host of other abnormal properties
2) This complex of effects is generally lumped together under the name of superfluidity, and the liquid in its superfluid phase is known as helium-II (He-11). The transition between the two phases is called the lambda-transition.
3) It is generally believed that the phenomenon of superfluidity is directly connected with the fact that the atoms of helium-4 obey Bose statistics, and that the lambda-transition is due to the onset of the peculiar phenomenon called Bose condensation...
4) The phenomenon of Bose condensation, and the closely related phenomena which occur in some Fermi systems, are absolutely crucial to our modern understanding of the anomalous phenomena which occur in superfluids and superconductors, and particularly of the way in which they display the effects of quantum mechanics on a macroscopic scale.
5) Imagine that you are on a mountain-top looking down at a distant city square on market day. The crowd is milling around at random, and each individual is doing something different; from that distance it is very difficult to make out precisely what. Now suppose, however, that it is not market day but the day of a military parade, and the crowd is replaced by a battalion of well drilled soldiers. Now every soldier is doing the same thing at the same time, and it is very much easier to see (or hear) from a distance what that is. The physics analogy is that a normal system is like the market day crowd -- every atom is doing something different -- whereas in a Bose condensed system the atoms (or, more accurately, the fraction of them which is condensed at the temperature in question) are all forced to be in the same quantum state, and therefore resemble the well drilled soldiers: every atom must do exactly the same thing at the same time!
6) This means, among other things, that effects which are far too small to be detectable at the level of single atoms may be quite easily observable in a Bose condensed (or similar) system; this is one feature which makes such systems so unique and exciting.
Adapted from: Anthony Leggett: in P. Davies (ed.): The New Physics. Cambridge University Press 1989, p.275. More information at: http://www.amazon.com/exec/obidos/ASIN/0521438314/scienceweek
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ON ROTATING SUPERFLUID HELIUM-3
In general, a "superfluid" is a fluid that flows without any resistance. "Superconductivity" is sometimes considered as a special case of superfluidity in which the "fluid" components (electrons) are charged. But more conventionally, superfluidity is considered a property of liquid helium at extremely low temperatures, a property that enables liquid helium to flow without friction.
Both helium isotopes (sup4)He (the common isotope, often denoted as helium-4) and (sup3)He (the rare isotope, often denoted as helium-3) possess superfluidity under special circumstances: helium-4 becomes a superfluid below 2.172 degrees kelvin, while helium-3 becomes a superfluid only below 0.00093 degrees kelvin.
The superfluidity of liquid helium is apparently due to the weakness of the attractive force between two helium atoms and to the small atomic mass, which according to laws of quantum mechanics make the atoms difficult to *localize. One interesting difference between helium-4 and helium-3 is that the helium-4 atom, with two protons, two neutrons, two electrons, and an *intrinsic spin of 0, is subject to *Bose-Einstein statistics, while the helium-3 atom, with two protons, one neutron, two electrons, and an intrinsic spin of 1/2, is subject to *Fermi-Dirac statistics.
There are at least two distinct superfluid states in helium-3, the two most common denoted as helium-3A and helium-3B. Aside from the fascinating macroscopic behaviors of superfluid liquid helium, it is a system that provides a window for the understanding of certain important quantum behaviors, including microscopic quantum vortices (which are also displayed by electrons in superconductors). A quantum vortex is a type of flow pattern exhibited by superfluids under certain experimental conditions, e.g., liquid helium in a rotating container.
The term "vortex" designates the familiar whirlpool pattern where the fluid moves circularly around a central line and the velocity decreases in inverse proportion to the distance from the center. A superfluid is considered to be characterized by a macroscopic quantum-mechanical wave function that locks the superfluid into a *coherent state. This forces certain mathematical constraints on the wave function, so that for a superfluid in a rotating container, the system (the wave equation for the system) produces a lattice of quantized vortex lines, each line the axis of a microscopic vortex, with the entire array of vortex lines rotating rigidly with the container. The essential idea is that when superfluid helium is in a rotating container, the mathematics of the system wave function are such that a set of discrete microscopic vortex states are produced by each particular set of boundary conditions, and these microscopic vortex states are experimentally observable [*Note #1]. In short, the result is a system where the "quantum world" becomes visible on a macroscopic scale.
The superfluidity of liquid helium was first discovered in 1938, and the quantized vortex lines were first detected in the mid-1950s. Experimentally, quantized vortex lines are usually produced by rotating a vessel containing superfluid helium, but other methods for producing vortex lines have been used.
The following points are made by O.V. Lounasmaa et al ((Proc. Natl. Acad. Sci. 1999 96:7760):
1) Superfluid helium-3 exhibits a multitude of different types of topological defects, such as point singularities, vortex lines, *domain walls, and 3-dimensional textures. This behavior allows investigation of general principles, such as topological stability and confinement, nucleation of singularities (i.e., seeded growth of the number of singularities), and interactions between objects (localized discrete patterns; a vortex is an "object" in this context) of different topologies. There are promising analogies to *quantum field theory, elementary particle physics, and cosmology.
2) Superfluid helium-3 exhibits the most complicated vortex states that exist in nature. Experiments have revealed 7 different kinds of vortices in the two superfluid phases helium-3A and helium-3B. Many interesting properties of the vortex structures have been discovered, and frequently these are understood in detail because quasi-classical quantum theory forms a reliable foundation for theoretical studies.
3) Most of the knowledge of quantum vorticity in helium-3 originated from the Finnish-Soviet ROTA project started in 1978. These studies have concentrated on identifying the topology and structure of the different objects in the rotating superfluid helium-3. Work using the first ROTA machine quickly resulted in the discovery of vortices both in the A and B phases, which was expected, but the great variety of vortex phenomena was a surprise.
4) The ROTA experimental method typically involves a cylindrical container 7 millimeters long and 5 millimeters in diameter, which is rotated around its axis up to 3 radians per second. To study the superfluid state, the liquid must be cooled to a temperature of a few millikelvins or less. In addition to the ROTA apparatus in Helsinki, rotating cryostats for investigation of superfluid helium-3 have been used at the University of Manchester (UK), Cornell University (US), and University of California Berkeley (US).
5) Concerning analogy applications to cosmology, the authors report experiments in which superfluid helium-3 was heated locally by absorption of single neutrons, and the authors suggest the resulting events can be used to test theoretical models of the Big Bang at the beginning of our Universe.
6) The authors suggest that helium-3 provides a well-understood model for analyzing other systems where theory and/or experiments are less developed: superfluid helium-3 is the most complex coherent many-body system available that can be described by quasi-classical quantum theory, a theory which has been highly successful in explaining laboratory observations.
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Notes:
localize: In this context, a "localized" atom is an atom that has a greater probability of being in some region of space than in others.
intrinsic spin: In this context, the term "intrinsic spin" refers to the intrinsic (virtual) angular momentum of an atom. In general, angular momentum is a property of any rotating or revolving system, its value dependent on the distribution of mass and velocity about the axis of rotation or revolution.
Bose-Einstein statistics: Bose-Einstein statistics is the statistical mechanics of a system of indistinguishable particles for which there is no restriction on the number of particles that may simultaneously exist in the same quantum energy state. Bosons are particles that obey Bose-Einstein statistics, and they include photons, pi mesons, all nuclei having an even number of particles, and all particles with integer spin.
Fermi-Dirac statistics: The statistics of an assembly of identical half-integer spin particles. Such particles satisfy the Pauli exclusion principle, i.e., no two particles of the same kind in the system may simultaneously occupy the same quantum state.
coherent state: In quantum physics, coherence is matter of locking of phase differences between wave functions. The wave functions of two or more particles are said to be coherent if the phase difference between their wave functions remains constant. In general, a perfectly coherent system of particles can be described by a single macroscopic wave function.
Note #1: Below a certain rotation speed threshold, no vortices exist, and the superfluid remains at rest while the container rotates (the Landau state). At the threshold speed, the first vortex appears and corresponds to the first excited rotational state of the system. If the container continues to accelerate, additional quantized vortices appear, and at any given speed the vortices form a regular array that rotates with the vessel.
domain walls: (Bloch walls) In general, a Bloch wall is a transition layer, with a finite thickness of a few hundred lattice constants, between adjacent ferromagnetic domains with opposite spin directions. A "lattice constant" is any one of several possible parameters defining the unit cell of a lattice. A "ferromagnetic domain" is a region of a ferromagnetic material (e.g., various forms of iron, steel, cobalt, nickel, and their alloys) within which atomic or molecular magnetic moments are aligned parallel.
quantum field theory: In general, a quantum field theory is a theory that describes the quantum effects of a classical system of fields defined on space-time and satisfying various partial differential equations.
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