Observation of quantized circulation in superfluid helium

Abstract

OBSERVATION OF QUANTIZED CIRCULATION IN SUPERFLUID HELIUM Circulation of the superfluid component of liquid-helium II around a fine wire has been measured by means of the influence that the circulation exerts on the transverse vibrations of the wire. The work is a repetition and extension of an experiment performed earlier by Vinen. It gives new evidence in support of the Onsager-Feynman hypothesis that circulation of superfluid helium is quantized in units of h/m, where h is Planck's constant and m is the mass of the helium atom. A fine wire is stretched down the center of a cylindrical vessel containing liquid helium, and the circulation is prepared by rotating the vessel around the axis of the wire while cooling from above T. Then the rotation of the vessel is stopped, and A. the wire is set into vibration by passing a current pulse through it in the presence of a transverse magnetic field. The free, slowly damped vibrations which follow can then be observed by means of the oscillatory e.m.f. induced along the wire. If circulation exists around the wire its influence on a cylindrically symmetric wire is to cause the plane of vibration of the wire to precess at a rate proportional to the circulation, in the same direction as the circulation. As the plane of 1. W. F. Vinen, Proc. Roy. Soc. (London) A260, 218 (1961). CONTENTS LIST OF FIGURES LIST OF TABLES I. INTRODUCTION A. The Two-Fluid Model B. Superfluid Flow C. The Vinen Experiment vii 19. Number of Observations vs Apparent Circulation for Runs C-l and C-4. Time in Stable Levels vs Apparent Circulation for Run C-4 20. Number of Observations vs Apparent Circulation for Runs D-l and D-6. Time in Stable Levels vs Apparent Circulation for Runs D-l and D-6 21. Time in Stable Levels vs Apparent Circulation for Run D-4 22. Time in Stable Levels vs Apparent Circulation for Run E-l 23. Time in Stable Levels vs Apparent Circulation for Runs E-3 and E-5 24. Time in Stable Levels vs Apparent Circulation for Run E-6 25. Time in Stable Levels vs Apparent Circulation for Run E-7 132 26. Time in Stable Levels vs Apparent Circulation for Run H-2 133 27. Au> vs P s /p, for Wire E 28. Signal Amplitude as a Function of Time with Normal Modes Excited Unequally vii LIST OF TABLES Experimental Parameters for Runs with Wire C. .. 112 Experimental Parameters for Runs with Wire D. . .

Smooth vortex precession in superfluid4He

“…However, as explained in detail in Ref. [9], the modes are actually linear and perpendicular. They differ in frequency by ∆ω 0 , probably because of imperfections in the wire's cross-section or mounting.…”

“…Our experimental setup is similar to that used in previous generations of vibrating wire experiments [8,9,13]. A brass cylinder of height 50 mm and inner radius about 1.5 mm is filled with helium.…”

“…Since the middle has a larger vibration amplitude than the ends, it contributes more heavily to the final beat frequency. If there is one quantum of circulation on the wire below an attachment point z, and zero circulation above z, then Equation 1 still holds, with κ replaced by an effective circulation < κ > defined by [9]…”

“…In the presence of fluid circulating around the wire, the normal modes of the wire's vibration are split, with the beat frequency revealing the circulation around the wire. This technique originated nearly forty years ago in early measurements of quantized circulation in superfluid 4 He [8,9], and was later used to measure circulation in superfluid 3 He [10].…”

Modelling of vorticity, sound and their interaction in two-dimensional superfluids

“…The quantization of the circulation then manifests as quantized values of the splitting experienced by third-sound modes confined to the surface of the resonator. This approach is in essence a two-dimensional analogue of Vinen's experimental technique for the first observation of circulation quanta in bulk helium [71,72], where circulation trapped around a vibrating wire lifted the degeneracy between the wire's normal modes of vibration. In Fig.…”