5. Outline of talk 1.Superfluid 3 He in aerogel at ULT, a dirty metric. 2.Background on the techniques of the vibrating aerogel resonator. 3.First simple experiment - measuring the superfluid density. 4.The magnetic field - temperature phase diagram. 5.Gapless superfluidity in aerogel. * All experiments in the “zero temperature” regime where the normal fluid density is effectively nil.

6. Vibrating Wire Resonators: a Tutorial

22. Thus more quasiparticles scatter normally from front side. Inverse at rear side (more quasiholes scatter). This gives enormous force on the wire despite a “good vacuum” of excitations. The force is proportional to the excitation density thus providing an extremely sensitive thermometer/ excitation density/ energy detector. Frequency width/damping  f 2  exp(-  /kT) (or the damping measures the density of occupied states just above the gap).

23. This gives a very accurate temperature scale as the damping,  f 2, is changing over many orders of magnitude

24. OK, now let us look at an aerogel resonator.

27. How does the device work? It measures the superfluid density inside the aerogel but by an indirect method.

28. If the aerogel holds 100% superfluid then it is completely transparent. * Remember, at our temperatures the bulk liquid is 100% superfluid.

29. If the aerogel holds 100% normal fluid then it is opaque.

30. Giving a large backflow.

31. “The two-superfluid model”

32. The frequency of the resonator is determined by the backflow. Therefore the frequency gives immediately the value of the superfluid density inside the aerogel. The resonator looks like the poor man’s torsional oscillator but it works on a different principle – as well as being much simpler. Expt. 3 The superfluid density.

37. The frequency of the resonator is determined by the backflow. Therefore the frequency gives immediately the value of the superfluid density inside the aerogel. This can be thought of as the poor man’s torsional oscillator but in fact gives complimentary information – as well as being much simpler. And we note that the superfluid density tells us that the critical temperature is depressed (  s  0), and that the value of  s is much less than 100%.

42. ?

43. One thing we can immediately do with this resonator is distinguish between A phase and B phase since the superfluid densities in the two phases are completely different. That means that we can use this simple device to map out the phase diagram at ultralow temperatures as a function of temperature and magnetic field. The phase diagram probes the differences between the phases and thus any differential response of the two phases to magnetic fields. Experiment 4. The T-B Phase diagram

46. Good superfluid in all directions

48. Good superfluid around equator, non- superfluid along poles.

62. PRL. 86, 4580-4583 (2001)

63. It is interesting that the form of the B-T phase boundary line follows from a simple scaling in both B and T. That indicates that the aerogel interacts in the same way with the A and B phases although they have different symmetries. That was a surprise, certainly to us, anyway.

64. Experiment 5. Gapless Superconductivity in 3 He in Aerogel

65. We start with a modified Lancaster Quasiparticle Black-Body Radiator.

84. PRL. 91, 105303 (2003).

85. We can learn a lot about 3 He in aerogel in the zero temperature limit.