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

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superfluid helium II. Theoretical considerations. Zeitschrift für 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 für 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

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superconductivity, 3rd. edn. Hilger, Bristol, New York. Soley, F.J.,

Fitzsimmons, W.A. 1974. Physics Revolution. Simmons, New York.