Outline of my talk: First, we need a quick magic mystery tour around superconducting 3 He

Outline of my talk:

First, we need a quick magic mystery tour around superconducting 3He.

A quick explanation of our (very simple) experimental tools:

Two experiments:

1) Simulation of cosmic string creation.

2) Simulation of brane annihilation

Outline of my talk:


A quick explanation of our (quite simple) experimental tools:

Two experiments:

1) Simulation of cosmic string creation.


Outline of my talk:


A quick explanation of our (quite simple) experimental tools:

Two experiments:

1) Simulation of cosmic string creation (which sparked off COSLAB).


This gives a purity of = ~1 in 104000

The liquid us therefore absolutely pure even before we think anything about the superfluidity aspect.

The superfluid state emerges as 3He atoms couple across the Fermi sphere to create the Cooper pairs.PyPzPx

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). Since 3He atoms are massive, p-wave pairing is preferred, i.e. L = 1 which means S must also be 1.

With S = L = 1 we have a lot of free parameters and the superfluid can exist in several phases.

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.

Assume the global L vector lies in the z-direction -

That is fine as the constituent 3He fermion states can simply orbit the equator of the Fermi sphere:

We can easily have pairs like this:-L-vectorAssume the global L vector lies in the z-direction -

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:-

DThe A-phase gap:- large round the equator, zero at the poles.(because there are only equal spin pairs).

Thus the equal-spin pairs form a torus around the equator in momentum space, and there are no pairs at the poles.pairsL-vectorThe A phase is thus highly anisotropic.

Also very odd excitation gas.

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:

DThe B-phase gap:- equal in all directions. (because all spin-pair species allowed).

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

The equatorial equal-spin pairs torus is still there but along with the Sz = 0 pairs which now fill the gap at the poles. pairsL-vector(which add up to a spherically symmetric total)

The A phase has a higher susceptibility than the B phase (because all pairs are or no non-magnetic 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.

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.

The main interest in this system is that we know in principle just about everything about the fundamentals of the pairing mechanism and the condensate wavefunction.

In other words:

The superfluid 3He condensate is the most complex system for which we already haveTHE THEORY OF EVERYTHING.

And also know what our vacuum actually is. It is the zero-temperature ensemble of our input 3He fermion liquid states. That in a sense is our Planck scale, but we know what that is physically.

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.

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).

7 30 136This 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 .

7 30 136This 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 .BIo exp(it)

7 30 136How can we use a mechanical resonator to probe a pretty good vacuum? Its a trick of the dispersion curve!

Here we have the excitation dispersion curve standard BCS form.

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.

7 30 136The 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.

7 30 136Heres our calibration

First a quick look at some of the hardware.

We use a dilution refrigerator to cool the experiment to a few millikelvin and finally use the adiabatic demagnetization of copper (nuclei) to cool to T < 100K.

This is a typical instrument package launched into the seriously hostile sub-100 mK environment.

Neutron Detection

The Quasiparticle Scintillator (10-7 eV photons)

At 100 mK 1 cm3 has a total enthalpy of ~ 100keV.

Suggested long ago as a possible dark-matter detector PRL 75, 1887 (1995).

Absorption of a neutron by a 3He nucleus Capture process:

n + 3He++ p+ + T+

+764 keV

Phase changes by 2p round the loop

This is the Kibble-Zurek mechanism for the generation of vortices by a rapid crossing of the superfluid transition driven by temperature fluctuations.(And similar to the mechanism for creating cosmic strings during comparable symmetry-breaking transitions in the early Universe.)

.

Now lets think about branes -

and also the justification of using superfluid 3He as a model Universe.

Symmetries broken by the Universe

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.

Why would we want to do that?B phase

A phase

B-phase bubble

We need some fairly complicated coils as the AB transition occurs at >300mT (3 kG in old money).

Now for the serendipitous part.

Magnetic field profile used to produce the bubble

B phase

A phase

B-phase bubble

Lets look at this phase interface for a moment.

A-phase gapB-phase gap

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.

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.

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?

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.

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.

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.

This in turn affects the gap, reducing it along the L-vector direction and expanding it in the equatorial planeL-vectorD parallelD perpendicularpairspairs

This pattern however, is oriented on the L vector not on the field.

L-vectorD parallelD perpendicularpairspairs

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

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).

What we see with the magnetic field JUST below what is needed to create the A-phase slice.

Now with the slice present big increase from the impedance effect of two phase boundaries

After annihilation, we do NOT go back to the original state.

So here is our scenario:

Conclusion we certainly see defects in the our metric from the annihilation of our branes.

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.

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!

There is some interesting physics even in these simple scattering processes.

Normal scattering process

Andreev scattering process

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Outline of my talk: First, we need a quick magic mystery tour around superconducting 3 He