No abstract

Parts, Ü.; Karimäki, J.; Koivuniemi, J.; Krusius, M.; Ruutu, V.; Thuneberg, E.; Volovik, Grigory Phase diagram of vortices in superfluid 3He-A

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 ...

We report on the first comprehensive measurements of critical superJlow velocities in ~He-B which allow diJferent mechanisms of vortex Jormation to be identifi'ed. As a Jimction of temperature T and pressure P, we measure the critical anguhw velocity ~(" T, P) at which vortices start to Jbrm in slowly accelerating rotation in a cylindrical conta#wr fi'llcd with ~He-B. Owing to the long coherence length ~(T, P) ~ 10-100 nm, either trapped remanent vortici O' or #ztrinsie nucleation me O, dominate vortex Jbrmation, depending on the roughness of the contahwr wall and the presence of loaded traps. NMR measurement with a resohztion of one single vortex line allows us to distinguish between diJferent processes: ( 1 ) Three extrinsic mechanisms of vortex Jormation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit Jor intrinsic nuch, ation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a criticalvelocity vJT, P)= g2~(T, P) R, where R is the radius of the container. We find v~(T, P) to be related to the calculated intrinsic stability limit Vcb(T, P) of homogeneous superJlow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.

Nucleation of vortices in units of one quantum has been observed with C.W. NMR in a rotating cylinder filled with 3He-B. During acceleration a new vortex is created each time the counterflow velocity at the perimeter reaches a critical value v,(T, p ) . The measured v, resembles the calculated velocity v,b (T, p ) of the bulk superflow instability, but is smaller by a factor with power law dependence on the superfluid coherence length. This indicates that a nucleation event takes place whenever the flow exceeds v,b locally at the nucleation site and the nucleation barrier vanishes.

No abstract

No abstract

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Powered by TCPDF (www.tcpdf.org)This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. VOLUME 80, NUMBER 7 P H Y S I C A L R E V I E W L E T T E R S 16 FEBRUARY 1998Defect Formation in Quench-Cooled Superfluid Phase Transition We use neutron absorption in rotating 3 He-B to heat locally a ϳ100-mm-size volume into normal phase. When the heated region cools back in microseconds, vortex lines are formed. We record with NMR the number of lines vs the applied superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and indicate that the superfluid state itself forms as a patchwork of competing A-and B-phase blobs. The consequences to the A ! B transition in supercooled 3 He-A are discussed. [S0031-9007(98)