Vortex layer on the interface between theAandBphases in superfluidHe3

Abstract

Using NMR techniques we monitor the structure and number of vortices in a cylindrical container, rotating at constant angular velocity Q, before and after the passage of the A-B interface. The initial A phase contains the equilibrium number of vortices. The final B phase is found to have a deficit of vortices which depends nonmonotonically on the measured time £AB of the A -• B transition. We argue that a vortex layer is formed in front of the moving A-B interface. The measured vortex deficit can be understood by analyzing the stability of the layer.PACS numbers: 67.57.Fg, 67.57.Np The superfluid phases of 3 He support a rich variety of topological objects [1], The interface between the A and B phases offers a unique possibility to study the continuity of linear objects through a first order phase boundary. Consider the quantized vortices shown in Fig. 1. The prevailing vortex in the A phase is continuous, which means that the vorticity is distributed over a large crosssectional area (shaded tubes). In the B phase, the vortices are singular; i.e., the vorticity is concentrated into a core of the size of the superfluid coherence length (« 10 nm), which is « 10~3 of the length characterizing the core of a continuous vortex. We may ask what happens when the £?-phase volume grows at the expense of the A phase: Are A-phase vortices compressed and transformed to B-phase vortices or are they pushed aside in front of the interface? We find experimentally that both processes take place. Part of the A-phase vortices form a layer, which is pushed in front of the moving inter-FIG. 1. The continuous ^4-phase vortex (shaded tube on the right) and its two possible fates when the B phase expands to the right: (a) The ^4-phase vortex is pushed in front of the A-B interface (shaded surface) and eventually a layer of vortices will accumulate to cover the interface, (b) The continuous vortex is compressed so that it can penetrate through the interface and forms two singular S-phase vortices (lines), as required by the conservation of circulation. The continuous vortex terminates in a singular point on the wall, which may lower the energy barrier for the alternative (b) [1].face. The stability of the vortex layer seems to control the fraction of the vortices that leaks through the A-B interface.Experiment-Our NMR cell is a cylinder of radius R = 3.5 mm and height L = 7 mm. It is connected via an orifice of 1 mm in diameter to the rest of the 3 He volume, which contains a Pt thermometer and a sintered heat exchanger. The vortices are stabilized by continuous rotation around the axis of the cylinder. Measurements were performed at 29.3 bars pressure in magnetic fields of 14.2 or 28.4 mT. Initially the 3 He sample in the NMR cell was prepared to contain the equilibrium number of vortices in the A phase. This was done by accelerating the cryostat from rest to high speed and then decelerating to the desired angular velocity Q. The A-B interface was next allowed to pass through the cell at constant fl, and subsequently the number of vor...

Vortex formation and dynamics in superfluid 3He and analogies in quantum field theory

“…Thus here it is the A-phase shell within which the boundary instability has to occur. Such a situation is complicated (see Blaauwgeers et al 2002;Parts et al 1993) and possibly one where the escape of vorticity from the A-phase shell into B-phase is reduced. In first order these considerations suggest that v cn increases with increasing pressure and magnetic field, when the range of the stable A-phase regime increases over the length of the quench trajectory as a function of temperature.…”

“…In this experiment the initial A-phase state is one with the equilibrium number of doubly quantized singularity-free vortex lines while the final state is found to contain less than the equilibrium number of singly quantized B-phase vortex lines plus some number of spin-mass vortices. This means that A-phase vortex lines interact with the moving AB interface, they are not easily converted to B-phase vorticity, a critical value of bias flow velocity has to be exceeded before the conversion becomes possible, and even then some fraction of the conversion leads to vorticity with the additional defect in R αj ( n, θ) (Parts et al 1993;Krusius et al 1994). In neutron measurements the spinmass vortex was not observed at 2.0 bar, but at 18.0 bar.…”

Structure of the Surface Vortex Sheet between Two RotatingHe3Superfluids

“…These questions also appear in liquid crystals [1] and in the cosmos [2,3]. Here we provide an answer in the context of superfluid 3 He, where detailed results can be achieved by combining experimental and theoretical analysis [4,5].…”

“…In contrast, the phase field φ(y, z) on the B phase side has to be properly included, via f B = 1 2 ρ s (v sB − v n ) 2 and v sB = ( /2m)∇φ. Otherwise a surface vortex sheet is not stable, as is the case for a sheet which would coat a solid container wall [4].…”

What Can Superconductivity Learn from Quantized Vorticity in 3He Superfluids?

“…These interfaces include the free surface of the superfluid bath (i.e. the gas -liquid interface) [83], the superfluid -solid 3 He interface [84], the interfaces between 3 He and 4 He superfluids [76,85], and interfaces between the A and B phases in superfluid 3 He [86].…”