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 º Strong + weak + EM together

Symmetry corresponding to all forces together – who knows? GUT symmetry º Strong + weak + EM together Breaking this symmetry º 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 ÝÝ and ßß pairs (all with the same L value).

The B phase has all three ÝÝ, ßß and Ýß pairs (all giving J = 0, i.e. Sz + Lz= 0).

The B phase has Ýß and ßÝ spin pairs as well as ÝÝ and ßß 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 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 Momentum of incoming and outgoing quasiparticle not correlated

Andreev scattering Cooper pair Quasihole Quasiparticle Cooper pair has ~zero momentum, so incoming and outgoing excitation have same momenta (but opposite velocities).

Cooper pair

Normal scattering

Andreev scattering

Observer stationary

Galilean transform E’ = E - p.v Contrary to Relativity 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

Two vibrating wire resonators in an open volume inside stacks of copper plate refrigerant Thermometer (Detector) Wire Heater (Source) WireTwo vibrating wire resonators in an open volume inside stacks of copper plate refrigerant Thermometer (Source) 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

The grid thus produces a cloud of similar sized rings 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 fully-developed 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 A phase with gap nodes to . . .

. . . . the B phase with an isotropic (or nearly isotropic) gap?

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 L-vector directions) separate

The up spin and down spin nodes (and L-vector 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 pair-break

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 Detection: Tutorial II

Effective potential barrier for incoming quasiparticles