Fig. 6. Cross section of a rotating 3He container (a) in the equilibrium vortex state, (b) in the vortex-bundle state, (c) during the A -> B transition, and (d) a magnified picture of the vortex layer at the A - B interface. The bottom parts show the corresponding distributions of the superfluid (red) and normal fluid velocity (blue). In the equilibrium state, as well as inside the vortex bundle, the average superfluid velocity < vs> equals the uniform rotation vn =
The macroscopic properties of superfluids can often be understood using two-fluid hydrodynamics. In this model the liquid is assumed to consist of a normal and a superfluid component. When the liquid is placed in a rotating vessel, the normal fraction soon starts to move with the container. Uniform rotation of the superfluid component, however, is prohibited because the superfluid velocity vs must be curl-free. Instead, the rotational state is realized by the formation of quantized vortex lines: the superfluid becomes strongly modified near these singularities. In equilibrium, the density of vortices is such that, on the average, the superfluid also rotates uniformly with the container. The number of vortices in a typical sample cell of 10 mm diameter is over 2000 at a rotation speed of 1 rad/s. The major part of the experimental work on quantized vortices in superfluid 3He has been carried out at the LTL. Many striking discoveries have been made, which were totally unexpected on the basis of previous knowledge about quantized vorticity. For example, it is possible to have several types of singularities, which differ in the structure of their cores. In 3He-B, a transition was observed between two kinds of vortices, one (V1) having rotational symmetry around its axis and the other (V2) with spontaneously broken symmetry. In 3He-A a vortex transition can be provoked by changing the magnetic field.
In 3He-B metastable states with a deficit of vortices can be
created. In such a case, all the singularities are packed, at the equilibrium
density, to a vortex bundle in the center of the rotating container. Outside
the bundle there is macroscopic counterflow, = vn - vs of the
normal and superfluid components. The deficit is limited by the critical
flow velocity for nucleation of vortices, which is on the order of 1 cm/s. The
hydrodynamic mode associated with the broken symmetry in the V2 vortex has
been detected in measurements.
New properties of vortices have been discovered by studying transitions between the A and B phases. Consider an equilibrium vortex state in 3He-A when the A - B interface is driven through the experimental cell. Because of coherence between the two phases, vortices in 3He-A either transform to B-phase vortices or they are pushed ahead in front of the interface until they annihilate at the container wall. It has been ascertained experimentally that both processes take place: a vortex deficit is observed in 3He-B after the transition is finished. These vortices which do not penetrate through the phase boundary are removed as a layer just in front of the interface. The amount of the deficit in 3He-B is determined by the stability of the vortex layer.
Besides the vortex bundle, some unexpected features were often seen after the A -> B transition. Detailed experiments and careful theoretical analyses revealed that these are caused by spin-mass vortices (SMV), which have, in addition to mass flow, a quantized spin flow around the vortex line. For some reason, a small fraction of vortices transform to this unusual structure during penetration through the A - B interface.
Most of our theoretical research on 3He is closely related to experiments. Matters studied recently include critical velocities for vortex nucleation, hydrodynamic modes of vortices, structure of the vortex core in 3He-A (high and low field type vortices) and in 3He-B (V1, V2, and SMV), stability and penetration of vortices at the A - B interface, friction between vortices and the normal fluid, and an analysis of various NMR modes. Several experimental results can be understood in detail because the so-called quasiclassical theory of Fermi liquids gives a reliable foundation for the theoretical calculations.
