Outline of my talk:

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• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of brane annihilation

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• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of brane annihilation

4

• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of brane annihilation

5

• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of a Horizon

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• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of a Horizon

7

• Outline of my talk
• First, we need a quick magic mystery tour around
  superconducting 3He.
• A quick explanation of our (quite simple)
  experimental tools
• Two experiments
• Simulation of cosmic string creation
• 2) Simulation of a Horizon

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He4 is made up of bosons, so there is no problem
in their all dropping into the same ground state
to create a condensate but this particular
condensate is hard to understand. He3 on the
other hand is made up of fermions and can only go
into a single ground state by forming Cooper
pairs where two fermions couple to form a boson
as in superconductivity. (The He3 condensate
is thus composed of soft bosons, easily broken
whereas He4 is made of hard bosons and we would
need to ionize the atom to break it up.)
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We start with some simple facts about superfluid
3He beginning with the phase diagram.
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This gives a purity of 1 in 104000
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The liquid us therefore absolutely pure even
before we think anything about the superfluidity
aspect.
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The superfluid state emerges as 3He atoms couple
across the Fermi sphere to create the Cooper
pairs.
Pz
Px
Py
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The superfluid state emerges as 3He atoms couple
across the Fermi sphere to create the Cooper
pairs.
Pz
Py
Px
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Since 3He atoms are massive, p-wave pairing is
preferred, i.e. L 1 which means S must also be
1.
The ground state thus has S 1 and L 1 making
the Cooper pairs like small dimers (and easier
to visualise than the s-wave pairs in
superconductors).
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With S L 1 we have a lot of free parameters
and the superfluid can exist in several phases.
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With S L 1 we have a lot of free parameters
and the superfluid can exist in several phases
(principally the A- and B-phases) . Let us
start with the A phase which has only equal spin
pairs.
The directions of the S and L vectors are global
properties of the liquid as all pairs are in the
same state (this is the texture of the
liquid). However, that causes problems for the
pairs.
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Assume the global L vector lies in the
z-direction -
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Assume the global L vector lies in the
z-direction -
We can easily have pairs like this-
L-vector
That is fine as the constituent 3He fermion
states can simply orbit the equator of the
Fermi sphere
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However, if we try to couple pairs across the
poles of the Fermi sphere there is no orbit
that these pairs can make which gives a vertical
L.
Thus the liquid is a good superfluid in the
equatorial plane and lousy at the poles this is
reflected in the A-phase energy gap-
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D
The A-phase gap- large round the
equator, zero at the poles.
(because there are only equal spin pairs).
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Thus the equal-spin pairs form a torus around the
equator in momentum space, and there are no pairs
at the poles.
L-vector
pairs
The A phase is thus highly anisotropic. Also
very odd excitation gas.
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In the B phase we can also have opposite spin
pairs (the L- and S-vectors couple to give J 0)
This now allows us to have Lz Sz 0 pairs
which can fill in the hole left at the poles by
the A phase, giving an isotropic gap
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D
The B-phase gap- equal in all
directions.
(because all spin-pair species allowed).
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The equatorial equal-spin pairs torus is still
there but along with the Lz Sz 0 pairs which
now fill the gap at the poles.
L-vector
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The equatorial equal-spin pairs torus is still
there but along with the Sz 0 pairs which now
fill the gap at the poles.
L-vector
pairs
(which add up to a spherically symmetric total)
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The A phase has a higher susceptibility than the
B phase (because all pairs are ßß or ÝÝ no
non-magnetic Ýß components). Thus by applying a
magnetic field we can stabilise the A phase.
The A phase is the preferred phase at T 0 when
the magnetic field reaches 340 mT.
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Having made the five minute trip around the
superfluid the context for what follows is We
can cool superfluid 3He to temperatures where
there is essentially no normal fluid (1 in 108
unpaired 3He atoms). We can cool and manipulate
both phases to these temperatures by profiled
magnetic fields. That means we can create a
phase boundary between two coherent condensates,
itself a coherent structure, at essentially T 0.
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Excitations.
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The Cooper pairs in superfluid 3He form across
the Fermi surface. Thus an excitation is a
ghost pair with one of the component particles
missing. This excitation is thus a paired
hole-particle.
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When the ghost pair is above the Fermi surface it
looks like an extra particle, with momentum and
group velocity parallel.
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When the pair is below the Fermi surface, it
looks like an extra hole, but with momentum and
group velocity antiparallel. (and right at the
Fermi surface it doesnt know what it is and the
group velocity is zero.
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This leads to the excitation dispersion curve
shown below the standard BCS form.
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This dispersion curve is fixed to the rest frame
of the condensate.
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If the liquid is in motion then we see the
dispersion curve in a moving frame of reference.
Excitations approaching will have higher energies
and those receding lower energies.
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Before we look at a typical experimental set-up
we first introduce our workhorse microkelvin tool
which does a large fraction of all our
measurements for us.
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Before we look at a typical experimental set-up
we first introduce our workhorse microkelvin tool
which does a large fraction of all our
measurements for us. The vibrating wire
resonator (VWR).
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This consists of a croquet hoop shaped length
of superconducting wire which is placed in a
magnetic field and set into motion by passing an
ac current through it .
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This consists of a croquet hoop shaped length
of superconducting wire which is placed in a
magnetic field and set into motion by passing an
ac current through it .
B
Io exp(i?t)
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How can we use a mechanical resonator to probe a
pretty good vacuum? Its a trick of the
dispersion curve!
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The flow field provides a Maxwell demon which
allows only quasiparticles to strike the front of
the wire and only quasiholes to strike the rear
implication?
Anyway it provides a very sensitive thermometer
or quasiparticle number probe.
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Heres our calibration
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Now let us put this information to work for us.
In this talk I shall be talking about using the
superfluid as a model for cosmological problebs
(see Grisha Voloviks talk later).
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First we will think about (mem)branes - But
first a quick look at the justification of using
superfluid 3He as a model Universe.

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Symmetries broken by the Universe
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Now for the brane experiment. As all new
experiments tend to be, was an accident which
came out of something completely different. What
we were trying to do was to make a field profile
which would allow us to study a bubble of
(low-field) B phase levitated within a (high
field) A phase surrounding matrix.
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B phase A phase B-phase bubble
Why would we want to do that?
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Now a quick reference to the hardware. We use a
dilution refrigerator to cool our system to the
millikelvin region. And then nuclear cooling to
take us to a few microkelvin for metals of a few
tens of microkelvin for superfluid 3He.
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Since we only need a small volume of copper,
lets get it as close to the specimen as
possible, that is immerse it in the liquid.
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Since we only need a small volume of copper,
lets get it as close to the specimen as
possible, that is immerse it in the liquid. So
here is our inner stage, a stack of Cu plates,
immersed in the liquid, each with a layer of
sintered silver on the surface for thermal
contact.
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We wrap this in a thin-walled paper/epoxy box,
and add a silver sinter pad to make contact for
precooling and a filling tube.
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To cut down the heat leak we add a second stage,
also furnished with a precooling link, and
filling tube.
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To cut down the heat leak we add a second stage,
also furnished with a precooling link, and
filling tube. And we put the inner cell
inside. This allows the
inner cell to have a very thin wall (und thus low
slow-release heat leak) because the pressure is
supported by the outer cell wall.
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The thermal contact to the mixing chamber is also
made by silver sinter plates and connected to the
specimen via high purity Ag wires (rr103) Plus
a single crystal Al heat switch.
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We add the mixing chamber round the MC cooling
plates
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We add the mixing chamber round the MC cooling
plates and the rest of the dilution refrigerator
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We add the mixing chamber round the MC cooling
plates and the rest of the dilution
refrigerator, And finally the rigid thin-walled
plastic support tube for the nuclear stage.
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First, the nuclear stage is part of the
experiment and dispensible. Secondly, the whole
thing is built with very low level technology,
with glued plastic pieces more like schoolboy
model aeroplane methods. (This temperature
regime is marginal enough already.)
We add the mixing chamber round the MC cooling
plates and the rest of the dilution
refrigerator, And finally the rigid thin-walled
plastic support tube for the nuclear stage.
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Double s/c Al heat switch
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Now for the experiment.
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We need some fairly complicated coils as the AB
transition occurs at gt300mT (3 kG in old
money).
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We need some fairly complicated coils as the AB
transition occurs at gt300mT (3 kG in old
money).
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We need some fairly complicated coils as the AB
transition occurs at gt300mT (3 kG in old
money).
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Now for the serendipitous part.
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Magnetic field profile used to produce the
bubble
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Magnetic field profile used to produce the
bubble
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B phase A phase B-phase bubble
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Lets look at this phase interface for a moment.
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A-phase gap
B-phase gap
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A-phase gap
B-phase gap
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A-phase gap
B-phase gap
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A-phase gap
B-phase gap
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Here we have a coherent condensate on one side of
the boundary smoothly (and still coherently)
transforming across the interface to match the
condensate on the other side. This is our
closest laboratory analogy to a cosmological
brane.
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The motivation? Brane annihilation in some
braneworld scenarios can initiate and terminate
inflation. Brane annihilation also can leave
topological defects in space-time which might
still be detectable today.
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The motivation? Brane annihilation in some
braneworld scenarios can initiate and terminate
inflation. Brane annihilation also can leave
topological defects in space-time which might
still be detectable today. Question, - when we
annihilate a phase boundary and an anti-phase
boundary do we see defects in our space time -
the superfluid texture?
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Thus we need to look at the structure of our
metric (the superfluid texture) to see if any
defects are created by such an annihilation.
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This is the equilibrium direction of the L-vector
in the pure B phase. This is the flare-out
texture and satisfies the boundary condition that
L must hit the walls perpendicularly.
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We are trying to make a map of this texture.
And here we are helped by the structure of the
B phase with its distribution of ??, ?? and ??
spin pairs.
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This in turn affects the gap, reducing it along
the L-vector direction and expanding it in the
equatorial plane
L-vector
D parallel
pairs
D perpendicular
pairs
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This pattern however, is oriented on the L vector
not on the field.
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L-vector
D parallel
D perpendicular
pairs
pairs
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So in fields near the AB transition the minimum
gap follows the direction of the texture and thus
a simple quasiparticle transmission experiment
will probe this (since at our temperatures there
are only quasiparticles just above the gap, i.e.
T ltlt D) .
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We just measure the ratio of excitations at the
top of the cell and at the bottom to give a
measure of the excitation flux (a strictly
quantitative measurement of the flux is difficult
in this situation).
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What we see with the magnetic field JUST below
what is needed to create the A-phase slice.
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Now with the slice present big increase from
the impedance effect of two phase boundaries
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After annihilation, we do NOT go back to the
original state.
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So here is our scenario
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Conclusion we certainly see defects in the
our metric from the annihilation of our
branes.
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These experiments at present are primarily
providing insight for cosmologists. However,
there are more serious aspects and we are
currently trying to write the translating
dictionary between coherent phase boundaries and
branes. This is hard to fund as quantum fluids
and cosmology spans two funding agencies in the
UK and this is an interdisciplinarity too far as
far as they are concerned.. So we have applied
for funding from the Fq(x) Foundation here.
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These experiments at present are primarily
providing insight for cosmologists. However,
there are more serious aspects. Long term we are
trying to write the translating dictionary
between coherent phase boundaries and branes.
But short term we are trying to identify the
defects produced. La luta continua!
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These experiments at present are primarily
providing insight for cosmologists. However,
there are more serious aspects. In the short
term we are trying to identify the defects
produced. La luta continua!
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Finally A thought experiment on Black Holes. But
first we need to look at the special scattering
mechanisms at work in superfluid 3He. Dynamics
using dispersion curves.
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Normal scattering
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Andreev scattering
MomentumUp
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Andreev scattering
MomentumUp
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Andreev scattering
MomentumUp
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There is some interesting physics even in these
simple scattering processes.
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If we make a gentle round the minimum
scattering the excitation changes sex from
quasiparticle to quasihole or vice versa. This
conserves excitation number but what about
particle number?
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Normal process (large momentum change 2pF).
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Andreev process (but no momentum change).
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Normal scattering process
?
?
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Normal scattering process
?
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Andreev scattering process
?
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Andreev scattering process
?
?
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Andreev scattering process
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Andreev scattering process
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Finally a bit of fun. A superfluid 3He
horizon.
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We start with a superfluid 3He waterfall which
we can start with a moving plunger.
This sets up a velocity gradient in the liquid
and creates a horizon.
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What happens to an excitation approaching the
fall?
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Watch this quasihole, which starts in the static
liquid with energy only a little above the
dispersion curve minimum
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In the local frame of the moving liquid it now
has an energy far above the dispersion curve
minimum
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In this case with enough energy to break a cooper
pair in the condensate.
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Switching back to the lab frame Watch the high
energy hole.
It comes out with much higher energy than it went
in.
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How to extract energy from a superfluid 3He Black
Hole
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