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Two fascinating superfluids. Historic discoveries. The multifarious superfluid
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Two fascinating superfluids
The lightest rare gas, helium, exists in nature in two forms, two isotopes. The usual form is represented as 4He, where the figure 4 stands for the number of nucleons in the atomic nucleus (two protons and two neutrons). In the unusual form, 3He, the atomic nucleus has only one neutron, so it is lighter. In helium that occurs naturally the heavier isotope is more frequent than the lighter one by a factor of about 10 million. That is why it is only in the last 50 years that it has been possible to produce large amounts of 3He, at nuclear power stations, for example. At normal temperatures the gases of the two isotopes differ only in their atomic weights.
If helium gas is cooled to low temperatures, approximately 4 degrees above absolute zero (-273. 15°C), the gas passes into liquid form, it condenses. This happens in the same way as when steam condenses into water. Provided the temperature is not too low, the liquids of the two isotopes have similar properties. Liquid helium is used widely as a coolant, in superconducting magnets, for example. In this case naturally-occurring helium is used, of course, that is, the usual and cheaper form of helium, 4He.
If liquid helium is cooled to even lower temperatures, dramatic differences arise between the liquids of the two isotopes; quantum physical effects appear that cause the liquids to lose all their resistance to internal movement, they become superfluid. This occurs at quite different temperatures for the two superfluids and they exhibit a wide range of fascinating properties, such as flowing freely from openings in the vessel they are kept in. These effects can be explained only by means of quantum physics.
Historic discoveries
The fact that 4He becomes superfluid was discovered by Pyotr Kapitsa, among others, already in the late 1930s. This phenomenon was explained almost immediately by the young theoretician Lev Landau, who was awarded the Nobel Prize in Physics in 1962 for this discovery. (Kapitsa was also awarded the Nobel Prize in Physics, but not until 1978. ) The transformation from normal to superconducting liquid, which for 4He occurs at approximately 2 degrees above absolute zero, is an example of Bose-Einstein condensation, a process that has also been observed more recently in gases (cf. the Nobel Prize in Physics awarded in 2001 to Eric Cornell, Wolfgang Ketterle and Carl Wieman).
For the 3He isotope the transformation into the superfluid state was not discovered until the early 1970s by David Lee, Douglas Osheroff and Robert Richardson (Nobel Laureates in Physics in 1996). One reason why this discovery came so much later is that the transformation occurs at a very much lower temperature, approximately 1, 000 times lower than for 4He. Even though 3He differs in quantum physical respects from 4He and cannot directly undergo Bose-Einstein condensation, this discovery was not unexpected. Thanks to the microscopic theory of superconductivity presented in the 1950s (see above) by Bardeen, Cooper and Schrieffer, there was a mechanism, the formation of Cooper pairs, that ought to have been paralleled in 3He (fig. 4).
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| Fig. 4. The pair formation that occurs in superfluid 3He differs from that which occurs between electrons in a superconductor (Cooper pairs). The magnetic properties of the helium atoms act together, whereas those of the electrons counteract each other | 
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The multifarious superfluid
The theoretician who first succeeded in explaining the properties of the new superfluid in a decisive way was Anthony Leggett, who in the 1970s was working at the University of Sussex in England. His theory helped experimentalists to interpret their results and provided a framework for a systematic explanation. Leggett's theory, which was first formulated for superfluidity in 3He, has also proved useful in other fields of physics, e. g. particle physics and cosmology.
As superfluid, 3He consists of pairs of atoms, its properties are much more complicated than those of the 4He superfluid. In particular the pairs of atoms of the superfluid have magnetic properties, which means that the liquid is anisotropic, it has different properties in different directions. This fact was used in experiments in which studies were made of the liquid immediately after its discovery. By means of magnetic measurements it was revealed that the superfluid has very complex properties, exhibiting a mixture of three different phases. These three phases have different properties and the proportions in the mixture are dependent on temperature, pressure and external magnetic fields (fig. 5).
| Fig. 5. Superfluid 3He can exist in three phases called A, A1, and B. The type of phase is determined by pressure, temperature and magnetic field according to the figure's phase diagram | 
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Superfluid 3He is a tool that researchers can use in the laboratory to study other phenomena as well. In particular the formation of turbulence in the superfluid has recently been used to study how order can turn into chaos (fig. 6). This research may lead to a better understanding of the ways in which turbulence arises — one of the last unsolved problems of classical physics.
Fig. 6. It has recently been shown that if a vortex is created in a rotating vessel containing superfluid 3He (a), the result can critically depend on the temperature. Above a critical temperature the vortex lines up along the axis of rotation (b). Below the critical temperature a confusion of vortices occurs (c)
(http: //www. nobelprize. org/nobel_prizes/physics/laureates/2003/public. html)
Exercises
1) The outline of the history of discoveries concerning superconductivity and superfluids contains a number of names. Can you remember what the achievements of these people are? Consult the text if necessary
Heike Kamerlingh Onnes, John Bardeen, Leon Cooper, Robert Schreiffer, Pyotr Kapitsa, Lev Landau, Georg Bednorz, Alex Mü ller, Eric Cornell, Wolfgang Ketterle, Carl Wieman, David Lee, Douglas Osheroff, Robert Richardson, Alexei Abrikosov, Vitaly Ginzburg, Anthony Leggett
2) Translate the terms into Russian and explain what they mean in English
type-I superconductors, type-II superconductors, BCS theory, Cooper pairs, the Meissner effect, order parameter, wave function, vortex core, strong superconducting magnet, Bose-Einstein condensation, microscopic theory of superconductivity, anisotropic liquid, external magnetic field, confusion of vortices
o) Answer the questions.
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a) What does the phenomenon of superconductivity imply?
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b) What is the difference between type-I and type-II superconductors?
c) Can the BCS theory describe the specific properties of type-II superconductors?
d) What was Alexei Abrikosov’s starting point in investigating superconductivity?
e) What breakthrough did Abrikosov make in his research in the late 1950s?
f) Why was it necessary to introduce an order parameter describing the density of the superconductive material?
g) What revolutionary applications has the knowledge of superconductivity led to?
h) What forms can helium take and what is the difference between them?
i) Why was it crucial to turn to quantum physical effects in explaining the properties of liquid helium?
j) How did Pyotr Kapitsa, Lev Landau and Richard Feynman contribute to the study of liquid helium?
k) What three different phases does the superfluid (³ He) exhibit?
l) How does turbulence form in the superfluid?
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