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Persistent-current experiments on superfluid 3He-B and 3He-A

02 Jul 1984-Physical Review Letters (American Physical Society)-Vol. 53, Iss: 1, pp 70-73
TL;DR: In this paper, the authors investigated persistent flow of superfluid with an ac gyroscope filled with 20-ensuremath{mu}m powder, and the observed critical velocity in $^{3}mathrm{He}$-$B$ at $Pl~12$ bars is independent of temperature.
Abstract: We have investigated persistent flow of superfluid $^{3}\mathrm{He}$ with an ac gyroscope filled with 20-\ensuremath{\mu}m powder. In $^{3}\mathrm{He}$-$B$, currents circulate undiminished for 48 h at least; this implies a viscosity 12 orders of magnitude lower than in the normal fluid. In $^{3}\mathrm{He}$-$A$, the current does not persist. The observed critical velocity in $^{3}\mathrm{He}$-$B$ at $Pl~12$ bars is independent of temperature. At $Pg12$ bars there are two regimes in the $B$ phase: For example, at 29.3 bars the ultimate critical velocities are 5.4 and 7.8 mm/s, respectively.

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Pekola, J. P.; Simola, J. T.; Nummila, K. K.; Lounasmaa, O. V.; Packard, R. E.
Persistent-current experiments on superfluid 3He-B and 3He-A
Published in:
Physical Review Letters
DOI:
10.1103/PhysRevLett.53.70
Published: 02/07/1984
Document Version
Publisher's PDF, also known as Version of record
Please cite the original version:
Pekola, J. P., Simola, J. T., Nummila, K. K., Lounasmaa, O. V., & Packard, R. E. (1984). Persistent-current
experiments on superfluid 3He-B and 3He-A. Physical Review Letters, 53(1-2), 70-73.
https://doi.org/10.1103/PhysRevLett.53.70

VOLUME
53,
NUMBER 1
2 JULY 1984
Persistent-Current Experiments
on
Superfluid
3He-B
and
3He-A
J.
P.
Pekola,
J.
T.
Simola,
K.
K.
Nummila,
and O.
V.
Lounasmaa
Low Temperature Laboratory,
Helsinki
University
of
TechnologyS,
F-02750
Espoo
15,
Finland
and
R. E. Packard
Department
of
Physics,
University
of
California,
berkeley,
California
94720
(Received
20
April
1984)
We
have investigated
persistent
flow
of
superfluid
'He
with an
ac
gyroscope
filled
with
20-
p,
m
powder,
In
He-8, currents
circulate
undiminished for
48 h at
least;
this
implies
a
viscosity
12
orders of
magnitude
lower than in
the
normal fluid.
In
'He-A,
the
current does
not
persist.
The
observed
critical
velocity
in
He-8
at
P
~
12 bars is
independent
of
tempera-
ture.
At
P
)
12 bars
there are two
regimes
in the 8
phase:
For
example,
at
29.3
bars
the
ul-
timate
critical
velocities are
5.4 and 7.8
mm/s,
respectively.
PACS numbers:
67.5Q.Fi
%e
present
in this
Letter
results of
persistent-
current experiments
in
He-8
and
He-3;
we
have
obtained
extensive
data at
eight
different
pressures.
A comparison
with the
recent results of
Gammel,
Hall,
and
Reppy,
'
at
P=29
bars,
reveals several
qualitative
differences.
For
example,
we
see a
re-
versible
response
of
the superfluid
to subcritical
speeds
of
rotation and have observed
two
regions
in
the 8
phase
with
clearly
different critical
velocities;
we
have
also extended
persistent-current
measure-
ments
from 1 to 48 h.
By
use
of finer
powder
in
the experimental
cell,
critical velocities became
larger
and the scatter of
the data was
thus
consider-
ably
reduced
over the results of
Ref.
1
~
Our
experiments
were
carried out
in
a
rotating
nuclear
refrigerator.
The
basic measuring
device,
an
ac
gyroscope,
is
illustrated in
Fig.
1.
A metal
torus, packed
with
20-p,
m plastic
powder,
pfrms
a
path
for the circulating
superfluid.
This
ring
(R
=
22
mm,
r
=
3
mm)
is supported
by
two
sets of
mutually perpendicular
hollow
copper
torsion
tubes,
also
used as
the
filling
capillaries
for the He
sam-
ple.
Torsional modes
about the
tubes are
deter-
mined
by
angles
8 and
ItI.
The device is
ac-driven
about
8
by
a superconducting
solenoid
inside
a
niobium
shield;
capacitive
detectors are used
for
monitoring
the
ItI
motion.
%hen the
ring
is driven about
0
at the
resonant
frequenCy
tog2Tr
Of
the
It
mOde,
the
reSpOnSe
due
to the
angular
momentum
L
=
z L of the circulating
superfluid
is ItIO=
Q&L8ofI&to&
,
here
8o
is the
am-.
plitude
of
the
drive
motion
and
I@
and
0~
are
respectively
the moment of
inertia of the
torus
and
the
quality
factor of
the
resonance about the
ItI
axis.
In our
apparatus,
0&=
20000,
I&
30
g
cm2,
and
0I~/2n
=
69.8
Hz;
typically
8II
10
s
rad
giving
TORSION
MEMBERS
~
CAPACITIVE
DETECTOR
TORUS
FILLED
WITH
He
AND
PLASTIC
POWDER
(-20
pm)
4-AXIS
Nb-SHIELD
p//
~SUPERCONDUCTING
SOLENOID
'r////////
Nb-PLATE
Ag
SINTER
1
CM
VX////////////////////////////////////////////A
Pt
NMR
THERMOMETER
FILLING
CAPILLARY
FIG.
1.
The ac
gyroscope.
The foot is thermally
con-
nected
to the
nuclear
refrigerator.
For
further
explana-
tions,
see
text.
Ito=10
rad.
In our
mode of
operation,
with
toe
))
co&,
/II
is
insensitive
to
changes
in
the
resonant
frequencies.
The
response
Qo
is
detected
capacitively
and the preamplifier output
is fed back
to
a
self-resonating
drive circuit. This
technique
ensures
a
constant-amplitude
drive,
strictly
at
the
resonant
frequency
of
the
ItI
mode.
The minimum
observable
change
in
L
is
0.
01
g
cm2/s
(
102it
)
using
12-s
integration
time.
Noise in the
system
is
mostly
of mechanical
origin.
The L
sensitivity
of the
device can be calibrated
by
means of
the
Coriolis effect:
This force
pro-
duces an
additional
torque
about the
It
axis while
1984
The
American
Physical
Society

VOLUME
53,
NUMBER
1
PHYSICAL
REVIEW
LETTERS
2
JULY 1984
the
ring
is
b
'
being
rotated. Th
0,
where
is
the
cryostat's
e
n is
the
calib
'
ration constan
t
t flo
s
angular
veloci
w,
with
the
cr
In t
i
p
ases
n the
superfluid
phases
m
met
r
The
fr
e
qy
al to the
superfl
'"
isak
r uid fraction
perature
and
p
e
T
serve
as
calibration
fill
d
ihf'
there
is
a
spatially
ran
d bth
h
p
es. An ind
P=
=293
b b
th f t th
b
y
reversible
d
ea so
1
In
our ex eri
mo
omentum L
=
MR
(
periments
we
observe the an
h'" M
ang
is the mass of He in
is
the
average velocity
of
the
the
"lu
in
the
rin
as
n a
'g
io o
0
wh'
'
n
=maxin1um
tain
ih
h
s
was rotated. T
ci
y
p
g
p
e
cry
fL
th tdb
enc
d'
'
n
going
Lt
}.
The
diffi
erence,
ur
basic datum
P
recise
0
~
m
4—
U
A~
j'
2Ac
,
/
0.2
0.
4
I
I
0
~
0
'1.
0 1.2
0.
6
0.
8
Ap
(r
ad/s}
1.
4
FIG.
2.
~ .
Persistent
an
ula
g
velocity
0
of t
vs
the
f
h
i
}1o h
st eide
a
ions,
see
text.
sis
oop.
For
signal
is
ta
measurements
of
L
eing
rotated because th
un1 is
100
se
t
e
Coriolis
Ot
1
th
ects.
av
r an
the
superfl
'd
r
r
uid
ef-
a t
e
hav
her-
angular
mom
ave
made
exteensive
measuremen
P=3
y
:
(I)
fo
oM
tMt
th
b
h"'"
w"h
0
=0
C
nd L
ibra-
}1
'
ra-
turn.
m
persistent
angular
m
dent
Our
m er
u
ar
momen-
d
ur results can
be
i
at
idealized
e
interpreted
in
h t i
loo,
ho
db do th
s
a
e
premise
that
the
re
„—,
=RI
never
exceeds
the
e
iso
a
th
e
ine ow
e at
0=—
(u
=—
cu„because
d o
1
hh fld
id.
flow i
r
ui
component ex
'
'
n-
powder
d
d b h Ke elvin
dra
ia
'1
d h
e
~
co differs
from
0
b-
„and
the true
v
=
R
'
es
extent
from t
v,
=
Rcuc
deViateS
the
measured
RA .
of
oop
have unit
slo
pe
and
corres
ra
ion
The
sides
of th
flo
b
,
----
Th
e
e
ysteresis
a
'
x
creation
tices
become
pinned
to the ow
arises
because th
e
vor-
oop
mea
e. Our
result
'
is in
marked
by
Rudnick
et
14
Q.
their
d
(
Fi. 3 fR
amrne},
Hall
i
t
e
absent.
o
ef.
I)
the
clast'
as
ic
regime
is
In
Fig.
3,
u,
=
L,
/[MR
(
e
p$p
M
o
the reduced
tern
P=
. .
bars. The data
o h
temperature
T/
T
c
at
man
' '
ot oseinFi .
'
e
ina
g
,
.
The data
angu-
are
included fo
p
~ ~
at
v,
is inde
ur
thi bo
t 10/
o. In
previous
wo
per
ature
ff'
'
su
icient tod
-
0-
'
d
A heck
for
possible
d
'
3H
8
P=
1
in
the
ri
u
ar
momentum was
Th
t
h
measured.
After
as
t en brou
ght
to
rest
and L
P
C'
~ er the
cryostat
had
be
was
a een
kept
in the

VOLUME
53,
NUMBER
1
PHYSICAL
REVIE% LETTERS 2 JULY 1984
0
6
00
0
0
000
~
0
0
0
0
0
0
~
~
0
0
T
„/T~
=
0.
5
0
/op
0
0
0
0
0
0
O0
0
04
I
0.5
I
0.6
I
0.7
I
0.
8
0.
9
A
B
og
~+
TRAN-
SITION
+P'
T/
TL.
FIG. 3.
Critical
velocity
u,
at
P
=
15.0
bars
(open
cir-
cles)
and 12.
0
bars
(filled
circles) as
a
function of the
re-
duced
temperature
T/
T,
.
Lozenges
are
the
data of
Gam-
mel, Hall,
and
Reppy
(Ref. 1)
at P
=
29
bars,
multiplied
by
5,
the
ratio
of
the
pore
sizes
[(100
p,
m)/(20
p,
m)];
this reduction factor
is
only
approximate
because
of
dif-
ferent
types
of
geometries
involved.
B
phase
continuously
for
48
h,
L was
again
mea-
sured.
This value
was then compared
with that
ob-
tained
after
the cryostat
was
again
rotated
at the
same
velocity
as
before
and then
stopped.
Within
our
experimental
accuracy
of
10% there was no
de-
cay
in
the signal.
This
gives
for
v,
the relaxation
time of the
superflow,
a
value in excess
of 450
h
and
implies
in the
8
phase
an
effective
viscosity,
q,
rr=
pd
/r,
which
is
at
least 12 orders of
magni-
tude
smaller than
for
the normal
liquid
at
the same
temperature.
Here d
=
20
p,
m is the
average
size
of
the
interstitial
pores.
Measurements
of L
made after thermal
cycling
in
the
region
below T
=
0.98
T,
showed
that the angu-
lar momentum is a
reversible
function of
tempera-
ture. In addition
to the
fact that
v,
is independent
of
temperature,
this
demonstrates
that,
because of
macroscopic
quantization,
circulation
is conserved
in
3He-8
as
in
He
II.
~
The temperature
reversibility
was
used
to
study
the stability
of persistent
currents
in
the
immediate
vicinity
of
T,
.
These experiments
showed that
above
T=0.
98T,
the
critical
velocity
decreases
markedly;
at
T=0.
989T„
for
example,
u,
is
(50
+
5)%
of its
Iow-temperature
value.
Figure
4 shows a
plot
of
L,
vs
p,
/p
at 29.3 and
12.
0
bars. The
slope
of
the linear
regime
between
T„=0.
56T,
and
Tzz
in
the
29.
3-bar
data
corre-
sponds
to
v,
=7.
8
mm/s. The
critical
velocity
is
different below
T„;
at low temperatures
v,
5.
4
mmls.
This
value
is close to that measured at
P
~
12 bars.
The
change
in
v,
at
T„was
not
seen
by
Gammel, Hall,
and Reppy' because
an
experi-
mental
artifact
prevented
accurate
observations
near
T=0.
57T,
.
72
I
0.2
I
I
0.
4
0.6
ps
p
I
0.8
FIG. 4.
Saturated
angular
momentum
I.
,
as a function
of
p,
/p
at
P=
29.3 bars
(open
circles)
and
P
=
12.
0
bars
(filled
circles, crosses,
two
different
experiments). The
straight
line corresponds
to
v,
=
7.
8
and 5.
6
mm/s for the
29.
3-
and 12.
0-bar
data,
respectively
(to
compare
the two
critical velocities one should divide the
slopes
by
the
den-
sity
of
'He
at each
pressure).
The nonzero
L,
in 2
phase
is
an
experimental
artifact that was removed in later runs
(see
Fig.
5).
Experiments are
in
progress
to test
the
possible
relation
of
the
change
in
~,
at
T=0.
56T,
with
the
vortex-core
transition
observed in
NMR
experi-
ments at
T=0.
6T,
.
6
Data
in
Fig.
5
illustrate
that
currents in
He-A
do
not
persist,
at least under
zero
magnetic field.
This
conclusion
is
supported
by
an
experiment in which
the
maximum L
=
L,
was first
created
and
mea-
sured in He-B,
whereafter
the torus
was
thermally
cycled
to
the
3
phase
and
then
back
to the
8
liquid
again:
The
signal
had
completely
disappeared
dur-
ing
this
sequence.
The
upper
limit for the super-
flow
decay
in
He-3
is less than 1
min,
which
was
the transient time for
the
signal
to recover from
the
Coriolis
shift after
the
cryostat
had been
stopped.
Because of
the
anisotropic
nature
of
He-A,
the
su-
percurrent
might persist
in some
geometry
different
from
our
packed
powder.
Critical
velocities
of the order of
a few
millime-
ters
per
second seem
to
be associated with
vorticity
in
confined geometries
from 10
to
100
p,
m. For
the
emission of a vortex
ring
with
diameter
do,
u,
(t/m3de) ln(da/(a),
where
m3
is the
bare mass
of the
3He
atom and
(e=
20 nm
is the
coherence
length.
If the vortex
rings
have
a diameter
equal
to
the
pore
size,
the
calculated
critical
velocity is 7

VOLUME
53,
NUMBER
1
PHYSICAL
REVIE%
LETTERS
2
JULY 1984
0.
5
0.
1
I
t-T/Tc
0.
2
yo
ro
0
~
o
oe
~r'O
0
~
y
A~9
T
RANSIT ION
0.
3
I
p
pressure dependence
is
due
to
(o
in
the
logarithmic
factor.
The authors wish to
express
their
gratitude to
Professor J. D.
Reppy's
group
at Cornell for
useful
discussions. We thank Matti
Krusius and
Pertti
Hakonen for
experimental
advice,
and
Sandy
Fetter
and David Judd
for
theoretical
help.
Two
of
us
(O.
V.
L. and
R.
E.P.
)
thank,
respectively,
members
of
the
Berkeley
Physics
and
Chemistry
Depart-
ments
and of
the
Otaniemi Low
Temperature
Laboratory
for their
hospitality during
the evolution
of
this
experiment.
Our
work
was
supported
by
the
Academy
of
Finland,
by
the
Wihuri
Foundation,
and
by
the U. S.
National Science
Foundation
under
Grant No.
DMR-81-19542.
0
+
+
q
~
PS/P
I
0.2
0.3
mm/s in
our
experimental
setup,
quite
close
to the
observed
values 4.7
7.
8
mm/s. Additional
confir-
mation of this model is
provided
by
the
tempera-
ture
independence
of the measured
v,
. The weak
FIG. 5.
L,
vs
p,
/p
around
the 8
A
transition at
P
=
29.3 bars. Different
symbols correspond
to different
preparation angular
velocities:
open
circles,
O,
~
=
1.
16
rad/s;
filled
circles,
0.86
rad/s; plusses,
0.
57
rad/s.
Note
that the reduced
temperature
scale at the
top
is
non-
linear.
~P.
L.
Gammel,
H.
E.
Hall,
and
J. D.
Reppy,
Phys.
Rev. Lett.
52,
121
(1984).
2P.
J.
Hakonen,
O. T.
Ikkala,
S. T.
Islander,
T. K.
Markkula,
P. M.
Roubeau,
K.
M.
Saloheimo,
D. I.
Gari-
bashvili, and
J.
S.Tsakadze, Cryogenics
23,
243
(1983).
3C.
N.
Archie,
T.
A.
Alvesalo,
J.
D.
Reppy,
and R. C.
Richardson,
Phys.
Rev. Lett.
43,
139 (1979).
I.
Rudnick,
H.
Kojima,
%.
Veith,
and R. S.
Kagiwada,
Phys.
Rev. Lett.
23,
1220
(1969).
sJ.
D.
Reppy,
Phys.
Rev.
Lett.
14,
733
(1965).
6P.
J. Hakonen,
M.
Krusius,
M. M.
Salomaa,
J.
T.
Simola,
Yu. M.
Bunkov,
V.
P.
Mineev,
and
G.
E.
Volo-
vik, Phys.
Rev.
Lett.
51,
1362
(1983).
7See
for
example
A.
L.
Fetter,
in
The
Physics
of
Liquid
and
Solid
Helium,
Part
I,
edited
by
K. H,
Bennemann
and
J. B. Ketterson
(Wiley,
New
York,
1976),
p.
207.
73
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Journal ArticleDOI
TL;DR: In this paper, the concept of broken symmetry is applied to investigate the quantized vortex lines in rotating superfluid vortices, and it is shown that vortex-core structures exhibit an experimentally observed first-order phase transition.
Abstract: The first measurements on vortices in rotating superfluid $^{3}\mathrm{He}$ have been conducted in the Low Temperature Laboratory at Helsinki University of Technology during the past five years. These experiments have revealed unique vortex phenomena that are not observed in any other known superfluids. In this review, the concept of broken symmetry is applied to investigate the quantized vortex lines in superfluid $^{3}\mathrm{He}$. In the superfluid $A$ phase, vorticity can be supported by a continuous winding of the order parameter; this gives rise to continuous "coreless" vortices with two flow quanta. Novel vortices with a half-integer number of circulation quanta may also exist in $^{3}\mathrm{He}$-$A$ due to a combined symmetry of the superfluid state. In the superfluid $B$ phase, the vortices have a complicated core structure. The vortex-core matter is ferromagnetic and superfluid, and it displays broken parity. The ferromagnetism of the core is observed in NMR experiments due to a gyromagnetic effect. The calculated core structures exhibit an experimentally observed first-order phase transition. This vortex-core transition in rotating $^{3}\mathrm{He}$-$B$ may be understood in terms of a change in the topology for flaring-out of the vortex singularity into higher dimensions; the topological identification further suggests that the phase transition manifests a spontaneous bifurcation of vorticity---involving half-quantum vortices in $^{3}\mathrm{He}$-$B$. These recent advances of interest in quantum liquids are also of general relevance to a wide range of fields beyond low-temperature physics.

363 citations

Journal ArticleDOI
TL;DR: A review of the theoretical and experimental work that has addressed the question of Bose-Einstein condensation in solid 4He can be found in this paper, where potential future extensions of the experiments are discussed.
Abstract: This paper reviews the theoretical and experimental work that has addressed the question of the possibility of Bose-Einstein condensation in solid 4He. Due to its expected superfluid-like properties, this state of matter is called a supersolid. To date, no unambiguous supersolid 4He state has been observed. Potential future extensions of the experiments are discussed.

76 citations

Journal ArticleDOI
TL;DR: In this paper, the structure of vortices in fermionic superfluids and superconductors which break chiral symmetry is discussed, i.e. combined broken time inversion and 2D parity.
Abstract: Superconductors exhibit unconventional electronic and magnetic properties if the Cooper pair wave function breaks additional symmetries of the normal phase. Rotational symmetries in spin and orbital spaces, as well as discrete symmetries such as space and time inversion, may be spontaneously broken. When this occurs in conjunction with broken global U(1) gauge symmetry, new physical phenomena are exhibited below the superconducting transition that are characteristic of the broken symmetries of the pair condensate. This is particularly true of vortices and related defects. Superconductors with a multi-component order parameter exhibit a variety of different vortex structures and closely related defects that are not possible in condensates belonging to a one-dimensional (1D) representation. In this paper, we discuss the structure of vortices in fermionic superfluids and superconductors which break chiral symmetry, i.e. combined broken time inversion and 2D parity. In particular, we consider the structure of vortices and defects that might be realized in thin films of 3He-A and the layered superconductor Sr2RuO4, and identify some of the characteristic signatures of broken chiral symmetry that should be revealed by these defects.

64 citations

Journal ArticleDOI
TL;DR: An introduction to 3He and to the ROTA collaboration under which most of the knowledge on vortices in superfluid 3He has been obtained is presented and the possible applications of experiments and theory of 3He to particle physics and cosmology are discussed.
Abstract: In this review we first present an introduction to 3He and to the ROTA collaboration under which most of the knowledge on vortices in superfluid 3He has been obtained. In the physics part, we start from the exceptional properties of helium at millikelvin temperatures. The dilemma of rotating superfluids is presented. In 4He and in 3He-B the problem is solved by nucleating an array of singular vortex lines. Their experimental detection in 3He by NMR is described next. The vortex cores in 3He-B have two different structures, both of which have spontaneously broken symmetry. A spin-mass vortex has been identified as well. This object is characterized by a flow of spins around the vortex line, in addition to the usual mass current. A great variety of vortices exist in the A phase of 3He; they are either singular or continuous, and their structure can be a line or a sheet or fill the whole liquid. Altogether seven different types of vortices have been detected in 3He by NMR. We also describe briefly other experimental methods that have been used by ROTA scientists in studying vortices in 3He and some important results thus obtained. Finally, we discuss the possible applications of experiments and theory of 3He to particle physics and cosmology. In particular, we report on experiments where superfluid 3He-B was heated locally by absorption of single neutrons. The resulting events can be used to test theoretical models of the Big Bang at the beginning of our universe.

62 citations

Journal ArticleDOI
TL;DR: In this paper, a review of the experiments described in this paper shows that, when the 3He superfluids are rotated, many different vortex structures can be created and the vortex cores are large enough so that several details in their structure can be observed experimentally.
Abstract: The experiments described in this review show that, when the 3He superfluids are rotated, many different vortex structures can be created. The vortex cores are large enough so that several details in their structure can be observed experimentally. When probed with NMR, the vortices in 3He-B display both spontaneous and induced magnetization; their large magnetic moments reveal the existence of non-trivial vortex cores, consisting of magnetic superfluids. A first order phase change in the core structure, along a well defined transition line on the P-T-plane, appears a discontinuity in the magnetization of the rotating 3He-B. A similar transition, marked by a jump in the critical velocity for vortex creation, is also observed in hydrodynamic experiments. The most easily created vortices in 3He-A are doubly quantized and continuous. This identification is compatible with the results of NMR and negative ion experiments. The latter work reveals a focusing interaction between the ions and the vortex textures. Another, presumably singular vortex was also found in 3He-A by the ion technique in high magnetic fields. Gyroscopic measurements have demonstrated persistent currents in both superfluid phases of 3He. In addition, experimental data on vortex-free counterflow states, on critical velocities, on vortex states of 3He-A in restricted geometries and on mutual friction between the vortex lattice and the normal fluid are discussed.

46 citations