Transcript pickettpresentationp..

Quantum Turbulence and (some of) the Cosmology of
Superfluid 3He
George Pickett
Symmetry
corresponding to all
forces together –
who knows?
Symmetry
corresponding to all
forces together –
who knows?
GUT symmetry 
Strong + weak +
EM together
Symmetry
corresponding to all
forces together –
who knows?
GUT symmetry 
Strong + weak +
EM together
Breaking this symmetry
to choosing a phase
angle f.
The two Higgs fields
give mass to the
leptons, quarks, W and
Z particles.
Symmetries Broken
Universe
SU(3)  SU(2)  U(1)
L = 1
S = 1
Superfluid 3He
SO(3)  SO(3)  U(1)
Universe
SU(3)  SU(2)  U(1)
Superfluid 3He is the most complex system for
which we already have “The Theory of
Everything”.
Outline
•Some Basics of Superfluid 3He
•The Cosmology Thereof
L = 1
S = 1
From of the number of L and S degrees of freedom there are several
possible superfluid phases.
The A phase has only and pairs
(all with the same L value).
The B phase has all three and pairs
(all giving J = 0, i.e. Sz + Lz= 0).
The B phase has  and spin pairs as well as and
pairs and thus has a lower magnetic susceptibility than
the A phase \the B phase can be depressed by a magnetic
field.
What are the excitations?
The excitations are broken Cooper pairs, i.e. a “pairs” with only one particle but still
coupled to the “missing particle” hole state.
Normal scattering
Venuswilliams-on
Quasiparticle
Normal scattering
Venuswilliams-on
Venuswilliams-on
Quasiparticle
Quasiparticle
Momentum of incoming and outgoing
quasiparticle not correlated
Andreev scattering
Cooper pair
Quasiparticle
Quasihole
Cooper pair has ~zero momentum, so incoming
and outgoing excitation have same momenta (but
opposite velocities).
Cooper pair
Normal scattering
Andreev scattering
Observer stationary
Or of liquid
Motion of observer
Galilean
transform E’ =
E - p.v
Contrary to Relativity
Motion of observer
(or scatterer)
The Vibrating Wire Resonator
Wire thin to reduce
relative internal friction
~1 micron
Few mms
The Vibrating Wire Resonator
The Vibrating Wire Resonator
DETECTING NEUTRONS
Capture process:
n + 3He++ → p+ + T+
+764 keV
Phase changes by 2p
round the loop
Nature 382, 322 (1996)
.
This is the Kibble-Zurek mechanism for the generation of
vortices by a rapid crossing of the superfluid transition but
driven by temperature fluctuations.
(And similar to the mechanism for creating cosmic strings
during comparable symmetry-breaking transitions in the
early Universe.)
BUT
The current large-scale structure of the Universe is thought to have
arisen from QUANTUM fluctuations rather than temperature
fluctuations.
How can we suppress the
superfluid transition to T=0, to achieve
a quantum phase transition?
We use aerogel***, that is we put the superfluid in the
dirty limit.
The coherence length becomes smaller as the pressure
becomes higher so that the aerogel suppresses the
transition more at low temperatures where the
coherence length is comparable to the typical
dimension of the aerogel.
*** 2% by volume of nanometre scale silica strands
with separations comparable to the superfluid
coherence length.
This would yield a Kibble-Żurek mechanism driven by
quantum fluctuations – not thermal fluctuations.
Some serious experimental difficulties to be overcome
on the way!!
Production of vorticity/turbulence by a moving wire
The Dependence of Velocity on Drive: the Ideal
The Dependence of Velocity on Drive: the Reality
PRL 84, 1252 (2000).
Detection of vorticity/turbulence by a moving wire
Without being too technical, the moving wire is
damped by the “illumination” of incoming thermal
excitations. In the presence of a flow field associated
with a tangle of vortex lines, the wire is partially shielded
from incoming excitations. In other words the vortices
throw shadows on the moving wire in the excitation
“illumination”.
We are going to look at the response of the
“detector wire” as we drive the source wire
at 0.431 vL
While we drive the source wire beyond the critical
velocity the quasiparticle wind increases the damping
on the second wire simply because there are more
excitations to provide damping.
OK. Let’s try a higher velocity.
Note a) the fall in
damping while source
wire is driven
Note b) the noisy signal
PRL 86, 244 (2001).
Conclusion
We detect the presence of vorticity as a fall in the damping by
incoming thermal excitations on the detector wire because of the
shielding effect of the vorticity.
The vortices throw “shadows” on the wire in the “illumination” of
thermal excitations.
It’s not a violation of the Second Law!
But note!
The wire is acting as a one-pixel “camera” taking photographs of
the shadows of the local vorticity. The noise on the signal shows
that the vorticity is unhomogeneous enough for the “camera” to
resolve on some scale the disorder.
Of course, if we instead have an array of say 33 detectors (we
are working on that now with miniature tuning forks) then we
have the makings of a vorticity video camera - but see below.
We can also detect the turbulent flow field by using the quasiparticle
black-body radiator in furnace mode (aided by Andreev reflection).
Here a heated blackbody radiator emits a thermal beam of
thermal quasiparticle excitations. This beam is ballistic and the
constituent particles are lost in the bulk 3He liquid in the cell.
However, if the vibrating wire in front of the hole is energised
and begins to create turbulence then the quasiparticles in the beam
are Andreev-reflected and return into the radiator container.
The temperature inside the box increases simply from the
existence of turbulence in the beam line.
At centre of figure vortex spacing ~0.2 mm
PRL 93, 235302 (2004)
The evolution of a gas of vortex loops into quantum turbulence.
A simulated micrograph of the grid
The oscillating flow interacts with loops of order 5 mm in
diameter
and generate ~5 mm rings
The grid thus produces a cloud of similar sized rings
Wire damping
suppressed when grid
is oscillated.
Let us look at the decay of the turbulence after
switching off the flapping grid (as seen by the two
wire resonators.
This appears to be the scenario:-
At low grid velocities, independent loops are created which travel fast
(~10 mm/s) and disperse rapidly.
Above a critical grid velocity, the ring density becomes high enough
for a cascade of reconnection to occur, rapidly creating fullydeveloped turbulence which disperses only slowly.
PRL 95, 035302 (2005)
Here is a simulation by
Akira Mitani in Tsubota’s
group, for conditions similar
to our grid turbulence with
low ring density.
And here is one with higher
ring density.
Simulating the time-development of a vortex tangle is entirely
analogous to simulating the evolution of a network of cosmic strings.
As the network develops
small loops (red) are
created which can then be
ignored as taking no further
part in the process
Let us take a closer look at the long time decay of our 3He
experiments.
PRL (to be published)
The A-B Interface or the Braneworld Scenario
Possibly our Universe is a 3-brane in
a 4-dimensional surrounding space.
Inflation may follow a collision of
branes
What is the structure of the A-B Interface?
How do we get smoothly from the anisotropic
nodes to . . .
A phase with gap
isotropic) gap?
. . . . the B phase with an isotropic (or nearly
We start in the A phase
with nodes in the gap
and the L-vector for
both up and down spins
pairs parallel to the
nodal line.
We start in the A phase
with nodes in the gap
and the L-vector for
both up and down spins
pairs parallel to the
nodal line.
The up spin and down
spin nodes (and Lvector directions)
separate
The up spin and down
spin nodes (and Lvector directions)
separate
. . . . . and separate
further.
The up spin and down
spin nodes finally
become antiparallel
(making the
topological charge of
the nodes zero) and
can then continuously
fill to complete
the transformation to
the B phase.
The up spin and down
spin nodes finally
become antiparallel
(making the
topological charge of
the nodes zero) and
can then continuously
fill to complete
the transformation to
the B phase.
We thus obtain the above complex structure across the interface.
B-phase
A-phase
The quasiparticle motion.
We thus obtain the above complex structure across the interface.
Having said that we have very little information on the
details of the A-B interface. There are several calculations but
experimentally there are early measurements of the surface energy
from Osheroff and more recent measurements from Lancaster, but
that is essentially all.
Magnetic Field Profile used to Produce “Bubble”
And for a final bit of fun:
Ergoregions:
These occur around rotating Black Holes. In an
ergoregion excitations may have negative energies usual with non-intuitive consequences.
Superfluid 3He waterfall
Superfluid 3He waterfall
Superfluid 3He waterfall
Quasihole now has enough energy to pairbreak
The outgoing article emerges with more energy
than the incoming one had originally:
The outgoing article emerges with more energy
than the incoming one had originally: the
analogue of extracting energy from a black hole.
The
End
Конец
Turbulence
Tutorial
TurbulenceDetection:
Detection: Tutorial
II II
Effective potential barrier for
incoming quasiparticles