The extraordinary phases of liquid 3 He *

Modern low-temperature physics began with the liquefaction of helium by Kamerlingh Onnes (1908) and the discovery of superconductivity (Kamerlingh Onnes, 1911) at the University of Leiden in the early part of the 20th century. There were really two surprises that came out of this early work. One was that essentially all of the electrical resistance of metals like mercury, lead, and tin abruptly vanished at definite transition temperatures. This was the first evidence for superconductivity. The other surprise was that, in contrast to other known liquids, liquid helium never solidified under its own vapor pressure. Helium is an inert gas, so that the interactions between the helium atoms are very weak; thus the liquid phase itself is very weakly bound and the normal boiling point (4.2 K) is very low. The small atomic masses and the weak interaction lead to large-amplitude quantum mechanical zero-point vibrations which do not permit the liquid to freeze into the crystalline state. Only if a pressure of at least 25 atmospheres is applied will liquid 4He solidify (Simon, 1934). It is thus possible, in principle, to study liquid 4He all the way down to the neighborhood of absolute zero. Quantum mechanics is of great importance in determining the macroscopic properties of liquid 4He. Indeed, liquid helium belongs to a class of fluids known as quantum fluids, as distinct from classical fluids. In a quantum fluid the thermal de Broglie wavelength lT 5 h(2pmkT)21/2 is comparable to, or greater than, the mean interparticle distance. There is then a strong overlap between the wave functions of adjacent atoms, so quantum statistics will have important consequences. 4He atoms contain even numbers of elementary particles and thus obey Bose-Einstein statistics, which means that any number of atoms can aggregate in a single quantum state in the non-interacting particle approximation. In fact macroscopic numbers of atoms in a quantum fluid can fall into the lowest-energy state even at finite temperatures. This phenomenon is called BoseEinstein condensation. On the other hand 3He atoms, each of which contains an odd number of elementary particles, must obey Fermi-Dirac statistics: only one atom can occupy a given quantum state. Therefore one should expect a very large difference between the behavior of liquid 4He and that of liquid 3He for low tem-