Pair Correlations in Superfluid Helium 3

In 1996 Lee, Osheroff and Richardson received the Nobel Prize for their 1971 discovery of superfluid helium 3 – a discovery which opened the door to the most fascinating system known in condensed matter physics. The superfluid phases of helium 3, originating from pair condensation of helium 3 atoms, turned out to be the ideal test-system for many fundamental concepts of modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and their spontaneous breakdown, topological defects, etc. Thereby they enriched condensed matter physics enormously and contributed significantly to our understanding of various other physical systems, from heavy fermion and high-Tc superconductors all the way to neutron stars and the early universe. A pedagogical introduction is presented. 1 THE HELIUM LIQUIDS There are two stable isotopes of the chemical element helium: helium 3 and helium 4, conventionally denoted by He and He, respectively. From a microscopic point of view, helium atoms are structureless, spherical particles interacting via a two-body potential that is well understood. The attractive part of the potential, arising from weak van der Waals-type dipole (and higher multipole) forces, causes helium gas to condense into a liquid state at temperatures of 3.2 K and 4.2 K for He and He, respectively, at normal pressure. The pressure versus temperature phase diagrams of He and He are shown in Figs. 1.1 and 1.2. When the temperature is decreased even further one finds that the helium liquids, unlike all other liquids, do not solidify unless a pressure of around 30 bar is applied. This is the first remarkable indication of macroscopic quantum effects in these systems. The origin of this unusual behaviour lies in the quantum-mechanical uncertainty principle, which requires that a quantum particle can never be completely at rest at given position, but rather performs a zero-point motion about the average position. The smaller the mass of the particle and the weaker the binding force, the stronger these oscillations are. In most solids the zero-point motion is confined to a small volume of only a fraction of the lattice-cell volume. In the case of helium, however, two features combine to prevent the formation of a crystalline solid with a rigid lattice structure: (i) the strong zero-point motion arising from the small atomic mass (helium is the second-lightest element in the periodic table); and (ii) the weakness of the attractive interaction due to the high symmetry of these simple atoms. It is this very property of helium – of staying liquid – that makes it such a valuable system for observing quantum behaviour on a macroscopic scale. Quantum effects are also responsible for the strikingly different behaviours of He and He at even lower temperatures. Whereas He undergoes a second-order phase transition into a state later shown to be superfluid, i.e. where the liquid is capable of flowing through narrow capillaries or tiny pores without friction, no such transition is observed in liquid He in the same temperature range (see Figs. 1.1 and 1.2). The properties of liquid He below 1 K are nevertheless found to be increasingly different from those of a classical liquid. It is only at a temperature roughly one thousandth of the transition temperature of He that He also becomes superfluid, and in