FREE ESSAY ON SUPERFLUIDS

SUPERFLUIDS

SUPERFLUIDS
As we shall see, 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. (Leggett, 1989)
BOSE-EINSTEIN CONDENSATION
This is the phenomenon wherein the bosons (a type of particle) making up a substance
merge into the lowest energy level, into a shared quantum state. In general, it refers to
the tendancy of bosons to occupy the same state. This state, formed when a gas undergoes
Bose-Einstein condensation, is called a "Bose-Einstein condensate." 
The distinguishing feature of Bose-Einstein condensates is that the many parts that make
up the ordered system not only behave as a whole, they become whole. Their identities
merge or overlap in such a way that they lose their individuality entirely. A good
analogy would be the many voices of a choir, merging to become 'one voice' at certain
levels of harmony. 
HISTORY
The phenomenon of superfluidity was discovered in 1937 by a Russian physicist, Peter
Kapitza, and then studied independently in 1938 by John Frank Allen, a British physicist,
and his coworkers. It wasn't until the 1970's however, that the useful properties of
superfluids were discovered. Thanks to the work of David Lee, Douglas Osheroff and Robert
Richardson at Cornell University, we have gained valuable information on the effects and
uses of superfluids. These three scientists jointly received a Nobel Prize in Physics in
1996 for their discovery of superfluidity in helium-3. It took a while, however, before
they actually figured out what this phase in helium was. 
Superfluidity in helium-3 first manifested itself as small anomalies in the melting curve
of solid helium-3 (small structures in the curve of pressure vs. time). Normally, small
deviations, like this one, are usually considered to be peculiarities of the equipment,
but the three physicists were convinced that there was a real effect. They weren't
looking for superfluidity in particular, but rather an antiferromagnetic phase in solid
helium-3. 
According to their predictions, this phase appeared to occur at a temperature below 2mK.
In their first publication in 1972, they interpreted this effect as a phase transition.
They did not completely agree with this hypothesis, but by further developing their
technique they could, just a few months later, pinpoint the effect. They found there were
actually two phase transitions in the liquid phase, one at 2.7mK and the second at 1.8mK.

This discovery became the starting point of intense activity among low temperature
physicists. The experimental and theoretical developments went hand-in-hand in an
unusually fruitful way. The field was rapidly mapped out, but fundamental discoveries are
still being made. 
SUPERFLUID HELIUM
Superfluidity is a state of matter characterized by the complete absence of viscosity, or
resistance to flow. This term is used primarily when involving liquid helium at very low
temperatures. It was found that liquid helium (4He), when cooled below 2.17K (-271O C or
-456 O F, could flow with no difficulty through extremely small holes, which liquid
helium at a higher temperature cannot do. It was also noted that the walls of its
container were somehow coated with a thin film of helium (approximately 100 atoms thick).
This film flowed against gravity up and over the rim of the container
This temperature of 2.17K is called the lambda ( ) point because the graph of the
specific heat of liquid helium exhibits a lamda-shaped maximum at that temperature. Under
normal pressure, helium will liquefy at a temperature of 4.2K. As the temperature is
still lowered, helium behaves as a normal liquid until it reaches the lamda point. Before
reaching the lamda point, it can be called helium I. Helium II refers to the liquid state
of helium below the lamda point. Superfluidity is found in helium II but it has limited
uses. 
When the temperature is dropped still lower, it was found that the stable isotope
helium-3 is formed. This liquid exhibits superfluid characteristics, but only at
temperatures lower than 0.0025 K. Nuclei of helium-3 contain two protons and one neutron,
rather than the two protons and two neutrons found in the more common isotope, helium-4.
Superfluid helium-4 forms at approximately 2.17 K. This superfluid moves without
friction, squeezes through impossibly small holes, and it can even flow uphill.
Superfluid helium-3 can do all these things, however not so spectacularly. The weird
thing about helium-3 is that it can have different properties in different directions,
similar to the well-defined grain in a piece of wood. 
The difference between helium-3 and helium-4 is rather difficult to explain. The main
difference comes from different quantum 'spins' of the nuclei. This spin can be thought
of as the angular momentum, although the particle is not actually spinning. Neutrons have
been designated a spin of +1/2, and protons -1/2, therefore helium-4 has a net spin of
zero. This characterizes helium-4 as a boson, which means that the value of the spin is
an integer. Helium-3, having a spin of +1/2 belongs to a different group of particles,
called fermions. The nuclei of bosons may pass through each other and can occupy the same
quantum state simultaneously therefore behaving as a single entity. This is the essential
requirement for superfluids.
Bosons follow Bose-Einstein statistics but fermions can have at most one particle in each
one-particle quantum state. Fermions cannot undergo Bose-Einstein condensation, but the
nuclei in helium-3 can 'disguise' itself as bosons by pairing up to form Cooper pairs,
which behave as bosons. When this happens however, the spin value is one, rather than the
zero spin on helium-4. This is the key difference and is used to understand superfluid
helium-3. As a result of this, all the spins of composite particles in superfluid
helium-3 can be lined up by placing a magnetic field around the liquid. This alignment of
spins can explain why properties of superfluid helium-3 are different in different
orientations. For example, sound travels through it at different speeds in different
directions, and it will flow faster in one direction than in another. 
High-temperature superconductors also have different properties in different directions.
It is believed that the complex pairing of spins, as seen in superfluid helium-3, will
help explain high-temperature superconductivity. Recently, phase transitions have been
studied as a model for those transitions that are thought to have occurred a fraction of
a second after the Big Bang. The critical points of these phase transitions are used to
define temperature scales at values extremely close to the absolute zero. (Leggett,
1989)
TECHNIQUES FOR STUDYING SUPERFLUIDS
Helium is an inert gas, and it is present in ordinary air (about one part in 200 000).
The fraction of the isotope helium-3 is about on million times smaller, and it would be
extremely costly to extract it out of air or out of ordinary helium gas. Instead,
scientist found that it could be produced by irradiation of lithium by neutrons from a
nuclear reactor. After the nuclear reaction and beta decay, a gas rich in helium-3 is
left, which can be sold at a high price. (Fitzsimmons, 1974)
In order to cool the helium-3, several techniques were established. Helium-3, when cooled
will remain a liquid unless the pressure is increased at the same time. Scientists
increased the pressure slightly as the temperature dropped and some of the helium
crystallized (became a solid). In order for the solid helium to turn back into a liquid,
heat is required. This heat is absorbed from the surrounding liquid helium-3, decreasing
the temperature of the helium even further. 
CONCLUSION
Superfluidity in helium-3 only appears at very low temperatures, below about 2mK, and has
found practical applications only for specialists working with extreme low temperature
techniques. Its main importance has been to develop our understanding of the complicated
behavior of strongly interacting many-particle systems, and for the development of
theoretical concepts in the field of macroscopic quantum phenomena. The understanding of
high superconductors has gained from concepts developed for helium-3, giving examples of
interactions that lead to the pairing of particles, and contributing info on the symmetry
of the wave function for such pairs. Another practical application is using the
fixed-point (2.17 K) to define temperature scales at very low temperatures. 
Bibliography
M. Beau, H. Gunther, G. zu Putlitz, B. Tabbert. 1996. Atoms and ions in superfluid helium
II. Theoretical considerations. Zeitschrift fur Physik, Germany.
Fetter, A.L. 1974. The Physics Of Liquid And Solid Helium. Bennemann, K.H., Ketterson,
J.B. (eds.). Wiley, New York
M. Foerste, H. Guenther, O. Riediger, J. Wiebe, G. zu Putlitz. 1997. Ions And Atoms In
Superfluid Helium (4He)-IV. Zeitschrift fur Physik, Germany.
Leggett, Anthony. 1989. Low temperature physics, superconductivity, and superfluidity. In
The New Physics. Davies, ed., Cambridge 
Tilley R, Tilley J. 1974. Superfluidity and Superconductivity, Halsted Press
Tilley, R., Tilley, J. 1990. Superfluidity and superconductivity, 3rd. edn. Hilger,
Bristol, New York.
Soley, F.J., Fitzsimmons, W.A. 1974. Physics Revolution. Simmons, New York.