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Bose-Einstein Сondensation – Superfluids

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    “As we shall see, it is generally believed that the phenomenon ofsuperfluidity is directly connected with the fact that the atoms of helium-4obey Bose statistics, and that the lambda-transition is due to the onset of thepeculiar 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 quantumstate. 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-Einsteincondensates is that the many parts that make up the ordered system not onlybehave as a whole, they become whole. Their identities merge or overlap in sucha way that they lose their individuality entirely. A good analogy would be themany voices of a choir, merging to become ‘one voice’ at certain levels ofharmony. HISTORY The phenomenon of superfluidity was discovered in 1937 by aRussian physicist, Peter Kapitza, and then studied independently in 1938 by JohnFrank Allen, a British physicist, and his coworkers. It wasnt until the1970s however, that the useful properties of superfluids were discovered.

    Thanks to the work of David Lee, Douglas Osheroff and Robert Richardson atCornell University, we have gained valuable information on the effects and usesof superfluids. These three scientists jointly received a Nobel Prize in Physicsin 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 themelting curve of solid helium-3 (small structures in the curve of pressure vs.

    time). Normally, small deviations, like this one, are usually considered to bepeculiarities of the equipment, but the three physicists were convinced thatthere was a real effect. They werent looking for superfluidity in particular,but rather an antiferromagnetic phase in solid helium-3. According to theirpredictions, this phase appeared to occur at a temperature below 2mK. In theirfirst publication in 1972, they interpreted this effect as a phase transition.

    They did not completely agree with this hypothesis, but by further developingtheir technique they could, just a few months later, pinpoint the effect. Theyfound there were actually two phase transitions in the liquid phase, one at2.7mK and the second at 1.8mK. This discovery became the starting point ofintense activity among low temperature physicists. The experimental andtheoretical developments went hand-in-hand in an unusually fruitful way. Thefield was rapidly mapped out, but fundamental discoveries are still being made.

    SUPERFLUID HELIUM Superfluidity is a state of matter characterized by thecomplete absence of viscosity, or resistance to flow. This term is usedprimarily when involving liquid helium at very low temperatures. It was foundthat liquid helium (4He), when cooled below 2.17K (-271O C or -456 O F, couldflow with no difficulty through extremely small holes, which liquid helium at ahigher temperature cannot do. It was also noted that the walls of its containerwere 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 Thistemperature of 2.17K is called the lambda ( ) point because the graph of thespecific heat of liquid helium exhibits a lamda-shaped maximum at thattemperature. Under normal pressure, helium will liquefy at a temperature of4.2K. As the temperature is still lowered, helium behaves as a normal liquiduntil it reaches the lamda point. Before reaching the lamda point, it can becalled helium I. Helium II refers to the liquid state of helium below the lamdapoint. Superfluidity is found in helium II but it has limited uses. When thetemperature is dropped still lower, it was found that the stable isotopehelium-3 is formed. This liquid exhibits superfluid characteristics, but only attemperatures lower than 0.0025 K. Nuclei of helium-3 contain two protons and oneneutron, rather than the two protons and two neutrons found in the more commonisotope, helium-4. Superfluid helium-4 forms at approximately 2.17 K. Thissuperfluid moves without friction, squeezes through impossibly small holes, andit can even flow uphill. Superfluid helium-3 can do all these things, howevernot so spectacularly. The weird thing about helium-3 is that it can havedifferent properties in different directions, similar to the well-defined grainin a piece of wood. The difference between helium-3 and helium-4 is ratherdifficult to explain. The main difference comes from different quantumspins of the nuclei. This spin can be thought of as the angular momentum,although the particle is not actually spinning. Neutrons have been designated aspin 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 spinis an integer. Helium-3, having a spin of +1/2 belongs to a different group ofparticles, called fermions. The nuclei of bosons may pass through each other andcan occupy the same quantum state simultaneously therefore behaving as a singleentity. This is the essential requirement for superfluids. Bosons follow Bose-Einsteinstatistics but fermions can have at most one particle in each one-particlequantum state. Fermions cannot undergo Bose-Einstein condensation, but thenuclei in helium-3 can disguise itself as bosons by pairing up to formCooper pairs, which behave as bosons. When this happens however, the spin valueis one, rather than the zero spin on helium-4. This is the key difference and isused to understand superfluid helium-3. As a result of this, all the spins ofcomposite particles in superfluid helium-3 can be lined up by placing a magneticfield around the liquid. This alignment of spins can explain why properties ofsuperfluid helium-3 are different in different orientations. For example, soundtravels through it at different speeds in different directions, and it will flowfaster in one direction than in another. High-temperature superconductors alsohave different properties in different directions. It is believed that thecomplex pairing of spins, as seen in superfluid helium-3, will help explainhigh-temperature superconductivity. Recently, phase transitions have beenstudied as a model for those transitions that are thought to have occurred afraction of a second after the Big Bang. The critical points of these phasetransitions are used to define temperature scales at values extremely close tothe absolute zero. (Leggett, 1989) TECHNIQUES FOR STUDYING SUPERFLUIDS Helium isan inert gas, and it is present in ordinary air (about one part in 200 000). Thefraction of the isotope helium-3 is about on million times smaller, and it wouldbe 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 byneutrons from a nuclear reactor. After the nuclear reaction and beta decay, agas 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 atthe same time. Scientists increased the pressure slightly as the temperaturedropped and some of the helium crystallized (became a solid). In order for thesolid helium to turn back into a liquid, heat is required. This heat is absorbedfrom the surrounding liquid helium-3, decreasing the temperature of the heliumeven further. CONCLUSION Superfluidity in helium-3 only appears at very lowtemperatures, below about 2mK, and has found practical applications only forspecialists working with extreme low temperature techniques. Its main importancehas been to develop our understanding of the complicated behavior of stronglyinteracting many-particle systems, and for the development of theoreticalconcepts in the field of macroscopic quantum phenomena. The understanding ofhigh superconductors has gained from concepts developed for helium-3, givingexamples of interactions that lead to the pairing of particles, and contributinginfo on the symmetry of the wave function for such pairs. Another practicalapplication is using the fixed-point (2.17 K) to define temperature scales atvery low temperatures.

    BibliographyM. Beau, H. Gnther, G. zu Putlitz, B. Tabbert. 1996. Atoms and ions insuperfluid 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. Lowtemperature physics, superconductivity, and superfluidity. In The New Physics.

    Davies, ed., Cambridge Tilley R, Tilley J. 1974. Superfluidity andSuperconductivity, Halsted Press Tilley, R., Tilley, J. 1990. Superfluidity andsuperconductivity, 3rd. edn. Hilger, Bristol, New York. Soley, F.J.,Fitzsimmons, W.A. 1974. Physics Revolution. Simmons, New York.

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