Single-Vortex Nucleation in Rotating Superfluid
                    <sup>3</sup>
                    He-B

Parts, Ü.; Ruutu, V. M. H.; Koivuniemi, J.H.; Bunkov, Yu. M.; Дмитриев, В. В.; Fogelström, Mikael; Huebner, M.; Kondo, Yasushi; Kopnin, N. B.; Korhonen, J. S.; Krusius, M.; Lounasmaa, O. V.; Soininen, P. I.; Volovik, G. E.

doi:10.1209/0295-5075/31/8/005

Cited by 85 publications

(58 citation statements)

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“…Such a "soft-core" structure carries continuous vorticity with two circulation quanta and is three orders of magnitude larger than the core of the B-phase vortex. Thus converting an A-phase vortex into a B-phase vortex requires large concentration of the flow energy.The large difference in core radii is the origin for the much lower rotation at which vortices start forming in A phase at the outer sample circumference, compared to B phase [9]. If the sample consists of only B phase then the 1…”

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“…The large difference in core radii is the origin for the much lower rotation at which vortices start forming in A phase at the outer sample circumference, compared to B phase [9]. If the sample consists of only B phase then the Vortex lines are thus easily created at low rotation in the A-phase section of the sample, while no vortices are detected in the B phase section.…”

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Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Blaauwgeers¹,

et al. 2002

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The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3 He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with a modified Kelvin-Helmholtz theory.Instabilities in the shear flow between two layers of fluids [1] belong to a class of interfacial hydrodynamics which is attributed to many natural phenomena. Examples are wave generation by wind blowing over water [2], the flapping of a sail or flag in the wind [3,4], and even flow in granular beds [5]. In the hydrodynamics of inviscid and incompressible fluids the transition from calm to wavy interfaces is known as the Kelvin-Helmholtz (KH) instability [6,2]. Since Lord Kelvin's treatise in 1871, difficulties have plagued its description in ordinary fluids, which are viscous and dissipative. They also display a shear-flow instability, but its correspondence with that in the ideal limit is not straightforward. The tangential velocity discontinuity in the shear-flow instability is created by a vortex sheet. In a viscous fluid a planar vortex sheet is not a stable equilibrium state and not a solution of the hydrodynamic equations [7].Superfluids provide a close variation of the ideal inviscid limit considered by Lord Kelvin and thus an environment where the KH theory can be tested. The initial state is a non-dissipative vortex sheet -the interface between two superfluids brought into a state of relative shear flow. So far the only experimentally accessible case where this can be studied in stationary conditions, is the interface between 3 He-A and 3 He-B [8], where the order parameter changes symmetry and magnitude, but is continuous on the scale of the superfluid coherence length ξ ∼ 10 nm. We discuss an experiment, where the two phases slide with respect to each other in a rotating cryostat:3 He-A performs solid-body-like rotation while 3 He-B is in the vortex-free state and thus stationary in the laboratory frame. While increasing the rotation velocity Ω, we record the events when the AB phase boundary becomes unstable -when some circulation from the A-phase crosses the AB interface and vortex lines are introduced into the initially vortex-free B phase. On increasing the rotation further, the instability occurs repeatedly. Such a succession of instability events can be understood as a spin-up of 3 He-B by rotating 3 He-A. Our experimental setup is shown in Fig. 1. The AB boundary is forced against a magnetic barrier in a smooth-walled quartz container, by cooling the sample below T AB at constant pressure in a rotating refrigerator. The number of vortices in both phases is indepe...

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Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Blaauwgeers¹,

et al. 2002

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“…Except for a tiny region near T c (Fig. 2), v d is much smaller than is needed to nucleate usual "singular vortices", such as one encounters in other superfluids [1,6]. Let us drive the current by applying a normal fluid velocity v n .…”

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“…Three different sample cylinders have been used, which were fabricated from epoxy or fused quartz with radii R = 2 -2.5 mm, heights L = 6 -7 mm, and different surface roughness [6]. No systematic dependence of v c on the container was found.…”

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Critical Velocity of Vortex Nucleation in Rotating Superfluid3He-A

Ruutu¹,

Kopu²,

Krusius³

et al. 1997

Phys. Rev. Lett.

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We have measured the critical velocity vc at which 3 He-A in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that vc is distributed between a maximum and minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentuml(r) in the cylinder. Slow cool down through Tc in rotation yieldsl(r) textures for which the measured vc's are in good agreement with the calculated instability of the expectedl texture.PACS numbers: 67.57. Fg, 05.70Fh A first order transition from one phase to another is associated with hysteresis because of the difficulty of nucleating the new phase. Two effects generally reduce the hysteresis. Firstly, thermal or quantum fluctuations cause the new phase to appear before the energy barrier separating the two energy minima vanishes. Secondly, surfaces, impurities, or other external agents reduce the energy barrier from its intrinsic value. Both phenomena are of crucial importance for the long standing problem of critical velocities and vortex nucleation in superfluids [1], but occur also in more usual phenomena like formation of water droplets or gas bubbles [2]. The purpose of the present work is to study an exceptional case of vortex nucleation where neither fluctuations nor external surfaces should play a role: superfluid 3 He-A.In usual superfluids and superconductors the phase slip takes place by creation and motion of zeros in the order parameter [3]. The A phase of 3 He is exceptional because the phase slip arises from the motion of the local angular momentum axisl(r). The characteristic length scale of thel(r) texture is macroscopic ∼ 10 µm. Therefore all thermal and quantum fluctuations are negligible. Moreover, a rigid boundary condition fixesl perpendicular to the wall of the experimental container. Thus the processes responsible for the critical velocity take place further than 10 µm from the wall, beyond the reach of surface roughness. Instead, the critical velocity v c for the phase slip depends on the initiall texture. We measure the critical velocity in a rotating cylinder, and find that it may vary within a factor of 6. However, by cooling slowly through the superfluid transition temperature T c in rotation, the equilibrium texture is created and the measured v c is in agreement with theoretical calculations.Anisotropic superflow.-In ordinary superconductors and superfluids, the order parameter has a phase factor exp[iφ(r)], and the superfluid velocity is defined as the gradient of the phase, v s ∝ ∇φ. In 3 He-A there is an additional phase factor exp[iφ l (p)], which depends on the azimuthal angle φ l of the quasiparticle momentum p with respect to the angular momentum axisl. Instead of resolving the two phases separately, one may only define the total phase factor, which can be expressed as (m + in) ·p. Herel,m, andn form an orthonormal triad, which generally depends on the location r. The superfluid velocity is defined as v s =h 2m km k ∇n k , where ...

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Fischer

2000

Ann. Phys.

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The geometric theory of vortex tunnelling in superfluid liquids is developed. Geometry rules the tunnelling process in the approximation of an incompressible superfluid, which yields the identity of phase and configuration space in the vortex collective co‐ordinate. To exemplify the implications of this approach to tunnelling, we solve explicitly for the two‐dimensional motion of a point vortex in the presence of an ellipse, showing that the hydrodynamic collective co‐ordinate description limits the constant energy paths allowed for the vortex in configuration space. We outline the experimental procedure used in helium II to observe tunnelling events, and compare the conclusions we draw to the experimental results obtained so far. Tunnelling in Fermi superfluids is discussed, where it is assumed that the low energy quasiparticle excitations localised in the vortex core govern the vortex dynamical equations. The tunnelling process can be dominated by Hall or dissipative terms, respectively be under the influence of both, with a possible realization of this last intermediate case in unconventional, high‐temperature superconductors.

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Single-Vortex Nucleation in Rotating Superfluid ³ He-B

Cited by 85 publications

References 17 publications

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Critical Velocity of Vortex Nucleation in Rotating Superfluid3He-A

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Single-Vortex Nucleation in Rotating Superfluid 3 He-B

Cited by 85 publications

References 17 publications

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Shear Flow and Kelvin-Helmholtz Instability in Superfluids

Critical Velocity of Vortex Nucleation in Rotating Superfluid3He-A

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Single-Vortex Nucleation in Rotating Superfluid ³ He-B