OBSERVATION OF QUANTUM STEPS IN THE SUPERFLUID CIRCULATION AROUND A FINE WIRE IN LIQUID 4He II IN ROTATION

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OBSERVATION OF QUANTUM STEPS IN THE SUPERFLUID CIRCULATION AROUND A FINE

WIRE IN LIQUID 4He II IN ROTATION

P. Karn, D. Starks, W. Zimmermann, Jr

To cite this version:

P. Karn, D. Starks, W. Zimmermann, Jr. OBSERVATION OF QUANTUM STEPS IN THE SU-

PERFLUID CIRCULATION AROUND A FINE WIRE IN LIQUID 4He II IN ROTATION. Journal

de Physique Colloques, 1978, 39 (C6), pp.C6-170-C6-171. �10.1051/jphyscol:1978675�. �jpa-00218355�

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JOURNAL D E PHYSIQUE Colloque C6, suppliment au no 8, Tome 39, aoiit 1978, page C6-170

OBSERVATION O F QUANTUM STEPS I N T H E S U P E R F L U I D C I R C U L A T I O N AROUND A F I N E W I R E I N L I Q U I D 4 ~ e 1 1 I N R O T A T I O N

P.W. Karn, D.R. Starks and W W. Zimmermann, Jr.

T a t e Laboratory o f Physics, University o f Minnesota Minneapolis, W 55455, U.S.A.

Rdsum6.- Nous avons mesurd par la mdthode de Vinen la circulation superfluide autour d'un fil fin dans l'hdlium I1 P % 0,4 K en fonction de la vitesse angulaire de rotation de l'appareil. Ces rdsul- tats prdsentent l'dvidence ddfinitive d'dtapes de circulation quantique. Cependant, la grandeur de 1'Etape observge a varid d'une expdrience P l'autre.

Abstract.- Measurements by the Vinen method of the superfluid circulation aroud a 25 um diameter wire in liquid helium I1 at % 0.4 K as a function of angular velocity of rotation of the apparatus show clear evidence for quantum steps in the range of ? 4 quantum units. However, the observed size of the circulation step has varied from run to run.

Measurements of the superfluid circulation around a fine wire in liquid helium I1 by the Vinen method have had a qualified success in providing direct evidence for the existence of quantization of superfluid circulation. While in the original experiments of Vinen /I/ and in those of Whitmore and .2j%mmemann /2/ clear preferences for stable circulations at the expected quantum levels were seen, nanquantum circulations and spontaneous, continuous changes of circulation were also often observed. In the experiments of Kral and Zimmermann 131, which studied the circulation K as a function of angular velocity wr of rotation of the apparatus, any direct evidence for quantum steps was almost completely masked by metastability of K. Their experiments used wirkfrom 66 to 83 vm in diameter. In this re- port we describe an extension of their work to wi- res 25 vm in diameter which has yielded the clea- rest quantum step structure yet observed. However, rather than equaling the expected value h/m4, where h is Planck's constant and m4 the mass of the helium atom, the size of the circulation step observed has varied from run to run.

In the Vinen method, the superfluid circulation around a fine wire is measured by measuring the angular frequency difference Awt between the two nearly-degenerate elliptically-polarized lowest- frequency modes of transverse vibration of the wire. This Awt is given to godapproximation by the expression

~w~~ = ~w~~ + (AwK

-

^2wr)* (1)

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X Present address : Control Data Corp. Arden Hills, MN 55112, U.S.A.

where Awo is the angular frequency difference between the perpendicular plane-polarized modes observed in the absence of circulation and Aw is the

K

angular frequency difference due to circulation ale ne given by the expression

AwK = P,K/V (2)

where ps is the superfluid density andpis the ef- fective mass of the wire per unit length 131. The wire is situated in a transverse magnetic field and is pulsed into vibration by passing a current pulse through it. The ensuing decaying vibrations are then observed by detecting the emf induced a- long the wire.

In these measurements the "wire", a gold- plated quartz fiber 'L 50 nun long, was stretched along the vertical axis of a 5 mm diameter quartz tube filled with liquid helium. The cell containing wire and surrounding tube was attached to the lower end of a 3 ~ e refrigerator which could be operated in rotation at cd values up to % 4 rad/s 131.

Figure 1 shows our best data, obtained at a cell temperature of % 0.4 K by varying slowly at a uniform rate from 0 to +3.7 rad/s, then from +3.7 to -3.7 rad/s and finally from -3.7 to +I. I rad/s, the entire sequence of events requiring 10h.

The wire was pulsed and a measurement of Awt made every 10 s. The quantity Amo was determined by ob- serving the minimum value assumed by Awt, corres- ponding to a cancellation of Aw by 2w in eq. ( 1 ) . The points plotted in figure 1 which represent cir- culatiorsin units of himl, versus wr, are one-minu- te averages of our determinations of K using eqs.

(1) and (2)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978675

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1 1 1 1 1 1 1 1 ~ 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1

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CIRCULATION vs ANGULAR V E L O C I T Y O F ROTATION

-

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-

4 - 4 II.

. ^-

-

3 -

- 7 j - - - - ¹

-

2- ^*rc s

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_{I - .}

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_{0 -}

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0

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- . - ^-

^{- I}

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FIRST CYCLE (COMPLETE)

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_{- 4} SECOND CYCLE (PARTIAL)

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_RESCALED

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^LEVELS

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1 1 1 1 l 1 1 1 1 I 1 1 1 I 1 1 1 I 1 I I I I I I I I I I I I l l 1

ANGULAR VELOCITY OF ROTATION w, (rod/$)

Fig. 1 : Circulation K in units of h/m4 versus angular velocity of rotation w r e The hysteresis loop in figure 1, which was

traversed in the counter-clockwise direction, shows the existence of metastability of K versus w

.

^Ne-

vertheless, there are four well-defined magnitudes of circulation which are particularly stable and persistent and which appear with both signs in a roughly symmetrical fashion in the figure. While these circulations do not coincide with the expected integer multiples of h/m4, their magnitudes are in the ratio of 1:2:3:4, so that when the expected levels are multiplied by a scale factor of 0.76 as shown in figure 1, they are brought into agreement with the observed levels.

While we believe that the observed level- structure provides convincing evidence for quantization of circulation, we do not understand the scale discrepancy. An earlier run with a different wire having the same dimensions yielded similar re- sults with a scale factor of 0.91 141. Thus the scale discrepancy appears to be some artifact of our measurement procedure.

There are at least two possible events which may account for the observation of a continuum of nonquantum levels of circulation. One is the termi- nation along the wire of free vortex lines in the superfluid /I/. The other is the presence of free vortex lines in the superfluid lying parallel to an close to the wire. One of us (D.R.S.) has shown that a single such vortex has an effect on the wire's vibration identical to that of circulation

around the wire, except that its magnitude dimini- shes continuously to zero with increasing distance between vortex and wire / 4 / . However, neither of these effects appears to offer a likely explana- tion for an apparent overall circulation scale chan- ge. These experiments are being continued in an at- tempt to understand the scale discrepancy.

We acknowledge support of this work by the United States Energy Research and Development Administration.

References

/ 2 / Whitmore,S.C. and Zimermann,W.Jr.,Phys.Rev.

166 (1968) 181

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/3/ Kra1,S.F. and Zimnermann,W.Jr.,Phys. Rev.

(1975) 3334