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

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

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**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:**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:**First, we need a quick magic mystery tour around superconducting 3He. A quick explanation of our (quite simple) experimental tools: Two experiments: 1) Simulation of cosmic string creation. 2) Simulation of brane annihilation**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: 1) Simulation of cosmic string creation (which sparked off COSLAB). 2) Simulation of brane annihilation**We can cool the liquid to ~80mK**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. Pz Px Py**The superfluid state emerges as 3He atoms couple across the**Fermi sphere to create the Cooper pairs. Pz Py Px**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).**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 -**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:**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:-**D**The 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. L-vector pairs The 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:**D**The B-phase gap:- equal in all directions. (because all spin-pair species allowed).**pairs**pairs pairs pairs 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**pairs**pairs pairs pairs 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)**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.**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 have THE 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).**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 . 7 30 136**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(iωt) 7 30 136**How can we use a mechanical resonator to probe a pretty good**vacuum? It’s a trick of the dispersion curve! 7 30 136**Liquid static**Here we have the excitation dispersion curve – standard BCS form.**Liquid static**Liquid moving 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.**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. 7 30 136**Here’s our calibration**7 30 136**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 < 100µK.**This is a typical instrument package launched into the**seriously hostile sub-100 mK environment.**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**.**• 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 let’s think about branes -**• and also the justification of using superfluid 3He as a model “Universe”.