Journalof Low TemperaturePhysics,Vol. 93, Nos. 5/6, 1993
T h e N u c l e a t i o n of Vortices in Superfluid 4He:
A n s w e r s and Questions
O. Avenel, G.G. ]:has t and E. Varoquaux*
Service de Physique de l'ffStat Condensg, Centre d'l~tudes de Saclay,
91191 Gif-sur- Yvette Cedex (France)
Laboratoire de Physique des Solides, Universitd Paris-Sud, Bdt. 510, 91405 Orsay
(France)
The velocity threshold for phase slips, vc, has been measured in ultra-pure 4He and
ultra-dilute 3He-4He mixtures, down to a temperature of 15 mK. These experiments
have revealed a crossover from a temperature-dependent rdgime above N 150 m K
to a plateau of vc below in ultra-pure 4He. Concentrations of 3He impurities as
low as a few parts in 10-9 greatly affect the plateau rdgime, causing v¢ to decrease
markedly at low temperature. These observations are interpreted in the framework
of the nucleation, either thermally activated or by quantum tunnelling, of vortices
in the approximate shape of half-rings. These vortices form on wall asperities at
local velocities us estimated to be ..~ 22 m / s in these experiments. The half-ring
model is shown to yield a critical velocity of the same magnitude but leaves many
basic questions unanswered.
PACS numbers: 57 40 Hf, 67.40 Vs.
The existence of vortices in superfluid 4He was postulated by Onsager, and
independently by Feynman1 who also suggested that they could account for the
phenomenon of a critical velocity in superfuid fows. A large body of work has been
devoted to their studies 2 as they constitute the archetypal defect of fluid dynamics.
None the less, the formation of vorticity in superfluids is one of the fundamental
remaining problems. Progress has been made in two directions in recent years. The
mechanism for the onset of self-sustaining tangles has been extensively studied,
both experimentally3 and by numerical simulations.4,5 The other direction which
t Permanent address: Center for Ultra-LowTemperature Research, WilliamsonHall, Universityof
Florida, Gainesville- FL 32611 - USA
1031
0022-2291/93/1200-1031507.00/0© 1993PlenumPublishingCorporation
,1032 O. Avenel, G.G. Ihas, and E. Varoquaux
has been explored lies in the observation of events involving single, or few, vortices
in the critical superfiuid flow through orifices of submicronic sizes. 6, 7
In this paper we report recent experiments on phase slippage in ultra-pure 4He
down to 15 mK from which we have inferred the existence of a quantum nucleation
r~gime for vortices. Also, the study of the effect of minute amounts of 3He impurities
has led to an estimate of the local superfluid velocity at the nucleation site in our
particular experiment.
The measurements are made using a two-hole, superfluid filled, hydro-
mechanical resonator which has been described in detail elsewhere (see ref. 6 for
references therein). One wall of this Helnaholtz-type resonator is a flexible mem-
brane which is driven to excite fluid flow through the resonator openings, one of
which is a microscopic orifice. Fluid motion is observed by monitoring the mem-
brane displacement with an ultra-sensitive superconducting sensor.
The validity of our observations relies on the absence of interferences from
mechanical vibrations. We therefore describe in the first section the improvements
in the experimental set-up and procedures that were carried out to decrease the
likelihood of instrumental artifacts. We then turn to the purification of 4He and
the manufacture of the ultradilute 3He-4tte samples, which play an important role
in the interpretation of the experiments.
The next section is devoted to the experimental observations, namely the ex-
istence of a low temperature plateau for the critical velocity and the profound
influence that minute traces of 3He impurities have on the low temperature end of
the plateau.
Then follows the description of a nucleation model, based on the formation of
microscopic vortex half-rings at the walls, which is shown to offer a framework for
the interpretation of these data.
We have not attempted here to review the field in a systematic way as other
contributions to these Proceedingss cover the same topic. The present paper is
basically a follow-up of the work presented at the Exeter meeting. 6 Some questions
raised then have now found answers owing to new experimental results. These
results have been reported previously.9-11
1. A P P A R A T U S a n d E X P E R I M E N T A L T E C H N I Q U E S
1.1. V i b r a t i o n I s o l a t i o n a n d Checks
For the quantum phase slips to be useful as a probe of vortex nucleation mech-
anisms, one must be able to observe slips which are due to intrinsic mechanisms.
Previous work 12,13,6,14,15 showed that above T = 150 mK thermally activated pro-
cesses dominated slip production. A deviation from this dependence was seen at
lower temperatures when large amounts of 3He impurities were present in the 4He
sample in the resonator. Various tests at both Orsay 16 and Berkeley Ir led to the
conclusion that mechanical vibrations impinging on the cryostat were very likely
causing phase slips at low temperature, imitating the thermal activation at higher
temperatures. In order to minimize the effect of vibrations, a unique apparatus
had to be designed and constructed in a new location at Saclay for the detection of
intrinsically triggered phase slips.
, The Nucleation of Vortices in Superfluid 4He 1033
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Fig. 1. Side projection view of apparatus. (1) Operation room floor; (2) Sound-
proofing and rf enclosure; (3) Aluminium casing imbedded in concrete table; (4)
Rotary seals for pumping lines; (5) 15-ton stainless steel reinforced concrete table;
(6) Composite plate to complete enclosure # 2; (7) Air mounts; (8) rf filter box for
electrical signals and power; (9) 45-ton concrete base; (10) Concrete pillar
attached to base # 9 for small plumbing and electrical cable anchors; (11) Access
tunnel to casing # 3; (12) Dewar surrounded by mixture of sand and visco-elastic
pebbles filling # 3; (13) Basement floor; (14) Experimental resonator; (15) Elbow
bellows for pumping lines; refrigerator plumbing cast into base # 9; (17)
Undisturbed, virgin soil; (18) Polyurethane foam surrounding base # 9.
