Superfluid

Superfluid

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Superfluidity is a state of matter
State of matter
States of matter are the distinct forms that different phases of matter take on. Solid, liquid and gas are the most common states of matter on Earth. However, much of the baryonic matter of the universe is in the form of hot plasma, both as rarefied interstellar medium and as dense...

 in which the matter behaves like a fluid without viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 and with extremely high thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....

. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own inertia. Since even gasses have viscosity, superfluids have less resistance to shear than a gas does.

Despite its lack of viscosity, the liquid still has surface tension, which allows it to rise up the sides of its containers without any normal frictional restrictions to flow. This allows the liquid to flow up the sides of containers, over the top, and down to the same level as the surface of the liquid inside the container, in a siphon effect.

These unusual effects are observed when liquids, typically helium-4
Helium-4
Helium-4 is a non-radioactive isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth. Its nucleus is the same as an alpha particle, consisting of two protons and two neutrons. Alpha decay of heavy...

, overcome friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

 in surface interaction at a stage known as the "lambda point
Lambda point
The Lambda point is the temperature below which normal fluid helium transitions to superfluid helium II. More precisely, there is a lower lambda point at 2.172 K, 0.0497 atm, and an upper one at 1.76 K, 29.8 atm....

". This is the temperature and pressure at which the liquid's viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 becomes zero. Although liquid helium forms at 4.2 Kelvin at 1 atmosphere, it does not become a superfluid until it is cooled below its lambda point at 2.18 Kelvin.

Known as a major facet in the study of quantum hydrodynamics
Quantum hydrodynamics
Quantum hydrodynamics is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems . They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the Wigner-Boltzmann equation...

, the superfluidity effect was discovered by Pyotr Kapitsa
Pyotr Kapitsa
Pyotr Leonidovich Kapitsa was a prominent Soviet/Russian physicist and Nobel laureate.-Biography:Kapitsa was born in the city of Kronstadt and graduated from the Petrograd Polytechnical Institute in 1918. He worked for over ten years with Ernest Rutherford in the Cavendish Laboratory in Cambridge...

, John F. Allen, and Don Misener
Don Misener
Don Misener was a physicist. Along with Pyotr Leonidovich Kapitsa and John F. Allen, Misener discovered the superfluid phase of matter in 1937....

 in 1937. It has since been described through phenomenological
Phenomenology (science)
The term phenomenology in science is used to describe a body of knowledge that relates empirical observations of phenomena to each other, in a way that is consistent with fundamental theory, but is not directly derived from theory. For example, we find the following definition in the Concise...

 and microscopic theories. The formation of the superfluid is known to be related to the formation of a Bose-Einstein condensate. This is made obvious by the fact that superfluidity occurs in liquid helium-4 at far higher temperatures than it does in helium-3. Each molecule of helium-4 is a boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....

 particle, by virtue of its zero spin. Helium-3, however, is a fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

 particle, which can form bosons only by pairing with itself at much lower temperatures, in a process similar to the electron pairing in superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...

.

In the 1950s, Hall and Vinen performed experiments establishing the existence of quantized vortex lines in superfluid helium. 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
Josephson effect
The Josephson effect is the phenomenon of supercurrent across two superconductors coupled by a weak link...

 in superfluid helium-4.

Theories


L. D. Landau's
Lev Landau
Lev Davidovich Landau was a prominent Soviet physicist who made fundamental contributions to many areas of theoretical physics...

 phenomenological and semi-microscopic theory of superfluidity of helium 4- earned him the Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

 in physics, in 1962. Assuming that sound waves are the most important excitations in helium-4 at low temperatures, he showed that helium-4 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. (Helium-4 actually 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 helium-4, which is known as the "condensate".

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 helium-4 is no longer superfluid.

To explain the early specific heat data on superfluid helium-4, Landau posited the existence of a type of excitation he called a "roton
Roton
A roton is an elementary excitation, or quasiparticle, in superfluid Helium-4. The dispersion relation of elementary excitations in this superfluid shows a linear increase from the origin, but exhibits first a maximum and then a minimum in energy as the momentum increases...

", 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
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

 around 1955,
developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky.

Landau thought that vorticity entered superfluid helium-4 by vortex sheets, but such sheets have since been shown to be unstable.

Lars Onsager
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....

 and, later independently, Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

 showed that vorticity enters by quantized vortex lines. They also developed the idea of quantum vortex
Quantum vortex
In physics, a quantum vortex is a topological defect exhibited in superfluids and superconductors. Superfluids and superconductors are states of matter without friction. They exist only at very low temperatures. The existence of these quantum vortices was independently predicted by Richard Feynman...

 rings.

Background


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 atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s are boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....

s, and their superfluidity can be understood in terms of the Bose–Einstein statistics
Bose–Einstein statistics
In statistical mechanics, Bose–Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium.-Concept:...

 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 fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s, and the superfluid transition in this system is described by a generalization of the BCS theory
BCS theory
BCS theory — proposed by Bardeen, Cooper, and Schrieffer in 1957 — is the first microscopic theory of superconductivity since its discovery in 1911. The theory describes superconductivity as a microscopic effect caused by a "condensation" of pairs of electrons into a boson-like state...

 of superconductivity. In it, Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...

ing takes place between atoms rather than electrons, and the attractive interaction between them is mediated by spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

 fluctuations rather than phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...

s. (See fermion condensate.) A unified description of superconductivity and superfluidity is possible in terms of gauge symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....

.

Superfluids, such as supercooled helium-4, exhibit many unusual properties. (See Helium#Helium II state). 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
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, zero entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. 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
Second sound
Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to a very high thermal conductivity...

.

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
Clausius-Clapeyron relation
The Clausius–Clapeyron relation, named after Rudolf Clausius and Benoît Paul Émile Clapeyron, who defined it sometime after 1834, is a way of characterizing a discontinuous phase transition between two phases of matter. On a pressure–temperature diagram, the line separating the two phases is known...

. 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. See Rollin film
Rollin film
A Rollin film, named after Bernard V. Rollin, is a 30 nm-thick liquid film of helium in the helium II state. It exhibits a "creeping" effect in response to surfaces extending past the film's level...

.

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
Quantum vortex
In physics, a quantum vortex is a topological defect exhibited in superfluids and superconductors. Superfluids and superconductors are states of matter without friction. They exist only at very low temperatures. The existence of these quantum vortices was independently predicted by Richard Feynman...

. 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.

Properties


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).

Practical application


Recently in the field of chemistry, superfluid helium-4 has been successfully used in spectroscopic techniques as a quantum solvent
Quantum solvent
A quantum solvent is essentially a superfluid used to dissolve another chemical species. Any superfluid can theoretically act as a quantum solvent, however in practice the only viable superfluid medium that can currently be used is helium-4, and it has been successfully accomplished in controlled...

. 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 (for an example, see the Gravity Probe B
Gravity Probe B
Gravity Probe B is a satellite-based mission which launched on 20 April 2004 on a Delta II rocket. The spaceflight phase lasted until 2005; its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor in and near Earth...

 article).

In 1999, one type of superfluid was used to trap light and greatly reduce its speed
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. In an experiment performed by Lene Hau
Lene Hau
Lene Vestergaard Hau is a Danish physicist. In 1999, she led a Harvard University team who, by use of a superfluid, succeeded in slowing a beam of light to about 17 metres per second, and, in 2001, was able to momentarily stop a beam.In 1989, Hau accepted a two-year appointment as a postdoctoral...

, 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, 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
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

. 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
IRAS
The Infrared Astronomical Satellite was the first-ever space-based observatory to perform a survey of the entire sky at infrared wavelengths....

, launched in January 1983 to gather infrared data was cooled by 73 kilograms of superfluid helium, maintaining a temperature of 1.6 K (-271.4 °C). Furthermore, when used in conjunction with helium-3, temperatures as low as 40 mK are routinely achieved in extreme low temperature experiments. The helium-3, in liquid state at 3.2 K, can be evaporated into the superfluid helium-4, where it acts as a gas due to the latter's properties as a Bose-Einstein condensate. This evaporation pulls energy from the overall system, which can be pumped out in a way completely analogous to normal refrigeration techniques.

21st century developments


In the early 2000s, physicists created a Fermionic condensate
Fermionic condensate
A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar conditions. Unlike the Bose–Einstein condensates, fermionic condensates are formed using...

 from pairs of ultra-cold fermionic atoms. Under certain conditions, fermion pairs form diatomic molecules and undergo Bose–Einstein condensation
Bose–Einstein condensate
A Bose–Einstein condensate is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero . Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at...

. 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
Supersolid
A supersolid is a spatially ordered material with superfluid properties. Superfluidity is a special quantum state of matter in which a substance flows with zero viscosity.-Background:...

 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
Annealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...

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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