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Journal of Physics Conference Series

Growth of a single vortex line of3He-A in a narrow cylinder under rotation

R. Ishiguro, Ken Izumina, Yutaka Sasaki, Mitsuru Kubota, Osamu Ishikawa, T Takagi

Published Feb 1, 2009• 2 citations
Publisher

Abstract

We have studied a single vortex in superfluid 3 He-A in a single narrow cylinder under rotation. The diameter of the cylinder is 230 μm. We observed the growth of a single vortex line in the cylinder by rotation. The vortex line grows along the cylinder when the rotation speeds are linearly accelerated above a critical velocity, which are about 4 (rad/sec).

DOI
10.1088/1742-6596/150/3/032033

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We have studied a single vortex in superfluid 3 He-A in a single narrow cylinder under rotation. The diameter of the cylinder is 230 μm. We observed the growth of a single vortex line in the cylinder by rotation. The vortex line grows along the cylinder when the rotation speeds are linearly accelerated above a critical velocity, which are about 4 (rad/sec).
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Vortex-free states have been observed in 3B^{3}\mathit{B}3B at rotation speeds up to 0.9 rad/s in a cylinder of 5-mm diameter. The measured cw NMR spectra, reflecting the order-parameter structure, respond very differently to rotation in opposite directions. The sign of this asymmetry is not linked to the direction of the applied magnetic field, as expected for a gyromagnetic effect, but varies randomly from one cooldown to another.
This paper reports the discovery of a new vortex phenomenon in superfluid 3B^{3}\mathit{B}3B. A single filament of quantized vortex line precesses as a solid body around a wire extending along the axis of a cylinder. The precession frequency equals the angular velocity of the apparatus at which the presence of a single quantum of circulation minimizes the system's free energy. The period of precession is related to the circulation quantum and the dimensions of the apparatus. Thus a measurement of the precession period is an accurate determination of the quantum unit. We find \ensuremath{\kappa}=(1.020\ifmmode\pm\else\textpm\fi{}0.03)h/2m3{\mathit{m}}_{3}m3​, where m3{\mathit{m}}_{3}m3​ is the mass of the 3He^{3}\mathrm{He}3He atom.
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Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}/(2MR)$, with MMM the mass of the superfluid particles and RRR the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\ensuremath{\chi}({\mathbit{r}}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\mathbit{r}}_{12}$ becomes larger than the cylinder radius. An appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.