Outline of my talk: First, we need a rapid look at the fundamental structure of superfluid 3 He and then see how similar it is to the structure of the Universe. Then we will look at our latest ideas on using superfluid 3 He to simulate branes. Then our first efforts at simulating brane annihilation And finally some thoughts for the future.
We start from the most general (and simple) picture of superfluid 3 He.
We start from the most general (and simple) picture of superfluid 3 He. (The first thing we need to note is that the 3 He atom has an unpaired neutron in the nucleus, and thus has a nuclear spin ½ and is a fermion.) Thus the liquid behaves as a fermi gas just like we learned long ago for electrons in a metal.
The superfluid state emerges as 3 He atoms couple across the Fermi sphere to create the Cooper pairs. P z P x P y
The superfluid state emerges as 3 He atoms couple across the Fermi sphere to create the Cooper pairs. P z P x P y
Since 3 He atoms are massive, p-wave pairing is preferred (which is code for L = 1) which means S must also be 1. The pairs thus behave like mutually orbiting dimers. In the way I have arbitrarily drawn them above, L and S are in opposite directions. But they have to point somewhere.
Thus the most general wavefunction must have the following form: It must have an amplitude to give us the superfluid density; ρ s, It must have a phase; exp iφ, And it must have a further part defining the direction of the vector L and another to define the direction of S.
Giving the most general form: Where [S] defines the direction of S and [L] defines the direction of L.
These various choices of the superfluid parameters are the broken symmetries of the liquid after going through the superfluid transition. Choosing the phase means choosing some point around a circle, which breaks the symmetry U(1). Choosing the L and S directions is choosing a direction in 3-space and breaks the symmetry SO(3).
So in superfluid 3 He we can write:
So in superfluid 3 He we can write:
So in superfluid 3 He we can write:
So in superfluid 3 He we can write:
Given the reasonable supposition that the symmetries broken by the Universe are:
Then comparing superfluid 3 He and the Universe: we get 3 He
Now SO(3) x SO(3) x U(1) and SU(3) x SU(2) x U(1) are clearly not the same but the similarities are surprisingly close and do indeed allow us to use the superfluid condensate as a model Universe for probing ideas which we cannot test in the cosmological context.
For those not familiar with superfluids let me point out that at our very low temperatures (~100µK, around 1/10 of the superfluid transition temperature) virtually all the 3 He atoms are in the condensate state as Cooper pairs. This is what we term the superfluid liquid. Only ~ 1 in 10 8 atoms are left unpaired and these contribute to the normal fluid, so we can assume that ALL the liquid is in the condensate. In this case all the constituent Cooper pairs are delocalized and the dynamics of all of them is described by the wavefunction introduced above. Thus the whole behavior of the liquid is essentially described by a field theory the condensate wave function. This is quite different from the behaviour of a conventional liquid where the constituent atoms move independently.
One final point. We start from the fact that the Cooper pairs have angular momenta; L=1 and S=1. 1) That means that the pairs have a complex structure allowing the existence of several phases (more about that later). 2) And since all the pairs are in the same coherent condensed state, the directions of L and S are not simply functions of each individual pair but are global long range directions in the liquid.
Paradoxically, although we work at temperatures where there are essentially NO quasiparticle excitations (= residual unpaired atoms), we need the few remaining excitations to probe the behaviour of the condensate. So: - a short tutorial on the excitations.
Starting with our Fermi sphere
The Cooper pairs in superfluid 3 He 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 holeparticle.
When the ghost pair is above the Fermi surface it looks like an extra particle, with momentum and group velocity parallel.
When the pair is below the Fermi surface, it looks like an extra hole, but with momentum and group velocity antiparallel.
Liquid static This leads to the excitation dispersion curve shown below the standard BCS form with an energy gap at the Fermi momentum.
If the energy gap in the liquid can change (for example in going from one phase to another), the minimum in the dispersion curve acts as an effective potential energy preventing low energy excitations from propagating through the whole liquid. Low energy gap Higher energy gap So the effective potential for a particle at the right hand side minimum increases as shown by the line.
A while ago we used the superfluid as a model metric to simulate cosmic string creation.
A while ago we used the superfluid as a model metric to simulate cosmic string creation. On irradiating the superfluid with neutrons, a neutron capture process (big cross-section for the 3 He nucleus) sends a micronsized region of the liquid above the transition temperature and when it cools through T c again different regions in the hot spot become superfluid independently creating a phase glass which relaxes into a tangle of vortices, i.e. our analog of generating cosmic strings by the Kibble mechanism.
A while ago we used the superfluid as a model metric to simulate cosmic string creation. On irradiating the superfluid with neutrons, a neutron capture process (big cross-section for the 3 He nucleus) sends a micronsized region of the liquid above the transition temperature and when it cools through T c again different regions in the hot spot become superfluid independently creating a phase glass which relaxes into a tangle of vortices, i.e. our analog of generating cosmic strings by the Kibble mechanism. But today we are going to be considering Simulated Brane Annihilation
This experiment, as all new experiments tend to be, was an accident which came out of something completely different.
This 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 give a bubble of B phase surrounded by A phase.
This 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 give a bubble of B phase surrounded by A phase. We can do this since the susceptibility of the A phase is higher than that of the B phase so applying a magnetic field will switch the equilibrium phase from B to A.
A Phase B Phase Why would we want to do that?
We need some fairly complicated coils as the AB transition occurs at >300mT (3 kg in old money).
We need some fairly complicated coils as the AB transition occurs at >300mT (3 kg in old money).
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 A Phase B Phase
Magnetic field profile used to produce the bubble
B phase A phase B-phase bubble As we finally lower the field the A-phase slab disappears, but looked at another way, the two phase interfaces (one AB interface and one BA interface) annihilate.
Let us look at this phase interface for a moment. First, let us look at the gap structure of the 3 He A- and B-phases.
First, the A phase Δ The A-phase gap is large round the equator, zero at the poles. (which has only equal spin pairs).
and the B phase Δ The B-phase gap is equal in all directions. (because all spin-pair species allowed).
Therefore, if we have a phase boundary between the two phases we have to make a smooth transition between two coherent condensates. But these condensates have different symmetries (their gap structures, for example, are very different).
L L The question is:- how do we get smoothly from A to B?. A-phase gap B-phase gap
L L L L A-phase gap B-phase gap
L L L L L L A-phase gap B-phase gap
L L L L L L A-phase gap L L B-phase gap
L L L L L L A-phase gap L L B-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. The boundary itself is thus a coherent object with the component pairs still delocalized and thus again governed by a field theory. 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 may also leave topological defects in spacetime which might still be detectable today.
The motivation? Brane annihilation in some braneworld scenarios can initiate and terminate inflation. Brane annihilation may also leave topological defects in spacetime which might still be detectable today. Question, - when we annihilate a phase boundary and an antiphase 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 add a slab of A phase in the middle.
And have to add a vortex and defect to match the two textures at the top.
The effective vortex down the center of the slab begins to look like a tachyon defect joining our two branes. And the same at the bottom.
We are trying to make a map of this texture. In a high magnetic field the B-phase gap becomes distorted along the L direction.
Δ perpendicular Δ parallel pairs L-vector pairs
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.
We do the experiment in a cell like this
We simply 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).
This is the big question of the experiment. First we measure the quasiparticle impedance of the cylinder of B phase. We then introduce a thin slab of A phase (to create an AM and a BA boundary our brane and antibrane). We then annihilate these two boundaries (perhaps creating topological defects). We then measure the impedance again. Do we get the same result as earlier?
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.
What does this tell us about real branes? So far we simple have two coherent ~2D boundaries which we annihilate. The boundaries bear similarities to branes. However, one obvious complaint is that our branes are relatively low energy objects and thus there is no question of any analog gravity associated with them. But here we need to look again.
In the region of the boundary the order parameter is depressed in going through the pirouette from one bulk phase to the other. This reduces the free energy gain from the condensation since the wavefunction must be highly distorted across the boundary. But of course this manifested as a reduction in the energy gap which changes the dispersion curves as we approach the interface.
Starting in the bulk phase:
The gap falls as we approach the boundary.
And more.
This gives rise effectively to a reduction in the m 0 rest mass of the incoming excitations thus acting as a gravitational force and similarly would also provide a mutual attractive force between neighboring branes.
The underlying problem in these experiments is that we are microkelvin quantum fluidicists. We believe that there are many more analogies and potential observables we could do if we only had more insight into brane physics. We need a dictionary translating between the superfluid 3 He metric and the Universe metric. Which means we really need a post-doc knowledgeable in cosmology who would work with us for a couple of years. Impossible to fund that in the UK since it falls between our two funding agencies. Any ideas gratefully received.
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