Our recent work has led to a number of novel problems which can be solved with techniques presently available in the LTL. An experiment is under way in which the methods introduced by D.D. Osheroff et al. (1992) for suppressing the nucleation of 3He-B have been put to use. It is crucial to avoid surface roughness on the scale of the superfluid coherence length. In a smooth-walled sample container, we can now investigate 3He-A in weak magnetic fields to temperatures as low as T = 0.3Tc. This allows measurements on vortices in 3He-A with much better resolution than before. Among the new problems to be studied are:
Nucleation at Tc: When 3He-A is cooled through Tc under continuous rotation, vortices of different structures may nucleate, depending on the experimental parameters such as the rotation velocity , the magnetic field H, and the rate of cooling dT/dt. Although the nucleation process is a complicated one it leads to a simple result at low cooling rates: the vortex structure of minimum energy is invariably formed at Tc. In contrast, when the 3He sample is first cooled into the superfluid state and then accelerated to rotation, the vortex structure of the lowest critical velocity is created, even if it energetically represents a metastable state. The nucleation process at Tc bears some analogy with the question whether and what kind of topological objects were created in the early universe while it was rapidly expanding through a series of phase transitions and when the seeds for the inhomogeneous mass distribution in the present universe were laid down. Our intention is to establish an understanding of this process in 3He-A.
Mixed vortex lattices: Under specific conditions both singly and doubly quantized vortex lines are simultanoeusly present in 3He-A. Measurements show that certain radial distributions of vortices in the rotating container are preferred. The mechanism for producing such ordering in the vortex lattice will be investigated.
Dynamic modes of the vortex sheet: The domain wall, which provides the back-bone for the vortex sheet, is best formed by changing rapidly and periodically the rotation velocity . By harmonic modulation of the rotation drive, an intermediate state can be created which is related to the vortex sheet and which displays much faster temporal response to rapid changes of than individual quantized vortex lines do. The structure and dynamics of this state will be investigated.
Nucleation of singular structures: We have shown that the nucleation threshold of a vortex line with a singular core corresponds in 3He-B to the Landau instability of the superflow. On rough surfaces this critical velocity is reached at a lower average speed. Therefore, the nucleation temperature of 3He-B and the measured critical velocity of vortex creation both depend on the quality of the boundaries and must bear some correlation with each other. Our new sample container allows for high critical velocities which, perhaps, can be lowered by gamma -rays, similarly to the enhancement of the B phase nucleation rate by ionizing radiation. This is called the 'baked Alaska effect', which was proposed by A.J. Leggett in 1984 and experimentally demonstrated by D.D. Osheroff in 1992.
Apart from relatively short calculations in response to immediate experimental needs, the following more extensive theoretical projects are under way:
Phase diagram of 3He-A vortices: Calculation of the phase diagram for continuous vortices of 3He-A in the - H plane. Nucleation of continuous structures: The experimental critical velocity for vortex nucleation in 3He-A is approximately one half of the value theoretically predicted from helical instability. We are studying whether this discrepancy can be accounted for by the presence of continuous 2-dimensional defects called dipole-locked solitons.
Identification of NMR signatures: At least 9 different absorption maxima have been observed in the NMR spectra of rotating 3He-A. In order to put their identification on a firm basis, the peaks for all possible types of defects should be calculated. Part of this project is to evaluate the microscopic parameters, which influence the order parameter texture, at all relevant temperatures and pressures.
A comprehensive review article on rotating superfluid 3He will be written.