“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). 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 tendency 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, but 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 1970s, 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 (-271°C or -456°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. The temperature of 2.17 K is called the lambda (λ) point because the graph of the specific heat of liquid helium exhibits a lambda-shaped maximum at that temperature. Under normal pressure, helium will liquefy at a temperature of 4.2 K. As the temperature is lowered, helium behaves as a normal liquid until it reaches the lambda point. Before reaching the lambda point, it can be called helium I. Helium II refers to the liquid state of helium below the lambda point. Superfluidity is found in helium II, but it has limited uses. When the temperature is dropped still lower, it is 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, squeeze through impossibly small holes, and 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 a designated 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 themselves 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 the 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 absolute zero (Leggett, 1989).
TECHNIQUES FOR STUDYING SUPERFLUIDS:
Helium is an inert gas and is present in ordinary air (about one part in 200,000). The fraction of the isotope helium-3 is about one million times smaller, and it would be extremely costly to extract it out of air or out of ordinary helium gas. Instead, scientists 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 extremely 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 been 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. Gnther, G. zu Putlitz, B. Tabbert. 1996. Atoms and ions in superfluid helium II. Theoretical considerations.
- Zeitschrift fr 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 fr 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.
