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Monday, January 21, 2013

The Superfluid.

Helium II will "creep" along surfaces in order to find its own level - after a short while, the levels in the two containers will equalize. The Rollin film also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape.

Superfluidity is a state of matter in which viscosity of a fluid vanishes, while thermal conductivity becomes infinite. These unusual effects are observed when liquids, typically of helium-4 or helium-3, overcome friction in surface interaction at a stage (known as the "lambda point", which is temperature and pressure, for helium-4) at which the liquid's viscosity becomes zero.
Also known as a major facet in the study of quantum hydrodynamics, it was discovered by Pyotr Kapitsa, John F. Allen, and Don Misener in 1937 and has been described through phenomenological and microscopic theories. In the 1950s Hall and Vinen performed experiments establishing the existence of quantized vortex lines. In the 1960s, Rayfield and Reif established the existence of quantized vortex rings. Packard has observed the intersection of vortex lines with the free surface of the fluid, and Avenel and Varoquaux have studied the Josephson effect in superfluid 4 He.


L. D. Landau's phenomenological and semi-microscopic theory of superfluidity of 4 He earned him the Nobel Prize in Physics in 1962. Assuming that sound waves are the most important excitations in 4 He at low temperatures, he showed that 4 He flowing past a wall would not spontaneously create excitations if the flow velocity was less than the sound velocity. In this model, the sound velocity is the "critical velocity" above which superfluidity is destroyed.

(4 He has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.) Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the 4 He called the "condensate".

The liquid helium is in the superfluid phase. As long as it remains superfluid,
it creeps up the inside wall of the cup as a thin film. It comes down on the
outside, forming a drop which will fall into the liquid below.
Another drop will form - and so on - until the cup is empty.
From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the 4 He is no longer superfluid.

To explain the early specific heat data on superfluid 4 He, Landau posited the existence of a type of excitation he called a "roton", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.

Bijl in the 1940s, and Feynman around 1955, developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky.

Landau thought that vorticity entered superfluid 4 He by vortex sheets, but such sheets were shown to be unstable.

Lars Onsager and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex rings.


Although the phenomenologies of the superfluid states of helium-4 and helium-3 are very similar, the microscopic details of the transitions are very different. Helium-4 atoms are bosons, and their superfluidity can be understood in terms of the Bose statistics that they obey. Specifically, the superfluidity of helium-4 can be regarded as a consequence of Bose-Einstein condensation in an interacting system. On the other hand, helium-3 atoms are fermions, and the superfluid transition in this system is described by a generalization of the BCS theory of superconductivity. In it, Cooper pairing takes place between atoms rather than electrons, and the attractive interaction between them is mediated by spin fluctuations rather than phonons. A unified description of superconductivity and superfluidity is possible in terms of gauge symmetry breaking.

Superfluids, such as supercooled helium-4, exhibit many unusual properties. Superfluid acts as if it were a mixture of a normal component, with all the properties associated with normal fluid, and a superfluid component. The superfluid component has zero viscosity, zero entropy, and infinite thermal conductivity. (It is thus impossible to set up a temperature gradient in a superfluid, much as it is impossible to set up a voltage difference in a superconductor.) Application of heat to a spot in superfluid helium results in a wave of heat conduction at the relatively high velocity of 20 m/s, called second sound.

One of the most spectacular results of these properties is known as the thermomechanical or "fountain effect". If a capillary tube is placed into a bath of superfluid helium and then heated, even by shining a light on it, the superfluid helium will flow up through the tube and out the top as a result of the Clausius-Clapeyron relation. A second unusual effect is that superfluid helium can form a layer, 30 nm thick, up the sides of any container in which it is placed.

A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity (the speed of sound in the superfluid) is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized, that is, a superfluid can only spin at certain "allowed" or critical speed values. In simplified terms, if the container is rotated to a certain allowed speed, the superfluid will rotate very quickly along with the container, otherwise, if the speed is too slow, then the superfluid will not move at all. Rotation in a normal fluid like water is not quantized.


Theoretically, a normal fluid phase of non-zero entropy can coexist with a superfluidic phase with zero entropy. This leads to the strange phenomenon of a two-fluid model, in which there can be a transfer of mass without a transfer of energy: when such a fluid/superfluid system is introduced in a setup that would normally trap a fluid, the superfluid can flow out due to its zero-viscosity property, leaving the normal fluid behind. Thus, part of the fluid system's mass is transferred without any energy transfer (since the superfluid has zero entropy).


Recently in the field of chemistry, superfluid helium-4 has been successfully used in spectroscopic techniques as a quantum solvent. Referred to as Superfluid Helium Droplet Spectroscopy (SHeDS), it is of great interest in studies of gas molecules, as a single molecule solvated in a superfluid medium allows a molecule to have effective rotational freedom, allowing it to behave exactly as it would in the "gas" phase.

Superfluids are also used in high-precision devices such as gyroscopes, which allow the measurement of some theoretically predicted gravitational effects.

In 1999, one type of superfluid was used to trap light and greatly reduce its speed. In an experiment performed by Lene Hau, light was passed through a Bose-Einstein condensed gas of sodium (analogous to a superfluid) and found to be slowed to 17 m/s (61.2 km/h) from its normal speed of 299,792,458 metres per second in vacuum. This does not change the absolute value of c, nor is it completely new: any medium other than vacuum, such as water or glass, also slows down the propagation of light to c/n where n is the material's refractive index. The very slow speed of light and high refractive index observed in this particular experiment, moreover, is not a general property of all superfluids.

The Infrared Astronomical Satellite IRAS, launched in January 1983 to gather infrared data was cooled by 720 litres of superfluid helium, maintaining a temperature of 1.6 K (-271.4 °C).

21st century developments

In the early 2000s, physicists created a Fermionic condensate from pairs of ultra-cold fermionic atoms. Under certain conditions, fermion pairs form diatomic molecules and undergo Bose–Einstein condensation. At the other limit, the fermions (most notably superconducting electrons) form Cooper pairs which also exhibit superfluidity. This work with ultra-cold atomic gases has allowed scientists to study the region in between these two extremes, known as the BEC-BCS crossover.

Additionally, supersolids may also have been discovered in 2004 by physicists at Penn State University. When helium-4 is cooled below about 200 mK under high pressures, a fraction (~1%) of the solid appears to become superfluid. By quench cooling or lengthening the annealing time, thus increasing or decreasing the defect density respectively, it was shown, via torsional oscillator experiment, that the supersolid fraction could be made to range from 20% to completely non-existent. This suggested that the supersolid nature of helium-4 is not intrinsic to helium-4 but a property of helium-4 and disorder. Some emerging theories posit that the supersolid signal observed in helium-4 was actually an observation of either a superglass state or intrinsically superfluid grain boundaries in the helium-4 crystal


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