1. COSLAB-2004 HPD and Superfluid Hydrodynamics Yury Mukharsky

2. COSLAB-2004 Low Temperature Laboratory, Helsinki University of Technology Kapitza Institute Landau Institute Ioffe Institute J. S. Korhonen, Y. Kondo, M. Krusius, Ü. Parts, E. V. Thuneberg Yu. M. Bunkov, V. V. Dmitriev G. E. Volovik E. B. Sonin

3. COSLAB-2004 HPD and counterflow Magnetic field  anisotropy of  s  interaction with v s. H n n v l l Minimized at equilibrium by adjusting R. In the HPD Counterflow suppresses the HPD.

4. COSLAB-2004 Interaction of HPD with vortices.

5. COSLAB-2004 Vortex motion Vortex core rotates and rocks. Rocking motion causes the dissipation H  b 

6. COSLAB-2004 Interaction of HPD with vortices. When vortex end are pinned – twisting. Twisted vortex is more rigid and rocks less. When the vortex move – the ends are free.

7. COSLAB-2004 Effect of field tilting Tilting the field orients the vortex: No twisting Reduced rocking motion. Smaller dissipation.

8. COSLAB-2004 If we twist less? –Rocking motion is less suppressed. Difference in absorption smaller Shorted HPD – weaker twist.

9. COSLAB-2004 Cosmic-like soliton. Connects two half-quantum vortices.

10. COSLAB-2004 Olivier Avenel, Eric Varoquaux CEA-DRECAM, Service de Physique de l'Etat Condense, Centre d'Etudes de Saclay, France CNRS-Laboratoire de Physique des Solides, Universite Paris-Sud, Orsay, France

11. COSLAB-2004 The cell: Weak link: 198 0.10x0.10  m holes separated by 2  m in SiliconNitride membrane ~0.1  m thick. Membrane: 75x60  m, R a =16  m, R  =0.03  m Part of the membrane where edge effects can be strong is highlighted with yellow. ss   SD (H=0)=7 mm

12. COSLAB-2004 The current through the orifice/parallel path is determined as derivative of the diaphragm location. Measurements Technique. Flexible diaphragm+Fluid inertia=Resonator Position of the diaphragm (equivalent to the charge of the capacitor) is recorded. P el L 1 (orifice) C d L 2 Orifice P The pressure across the orifice is proportional to the diaphragm displacement plus electrostatic pressure. The phase across the orifice is proportional to the integral of pressure: Amplitude of phase oscillations  amplitude of diaphragm.  Pos. Sensor Cap. plate Flexible Diaphragm

13. COSLAB-2004 Rotation changes the phase across the weak link. Phase is determined by solving Measurement technique - rotation  current 1/L 1 xx 1/L 2 Max. f. Min. f Can be graphically represented by intersection of loadline with J(  ). The dependence has period: 0.842   =5.6 10 -5 rad/sec. Inductance of the orifice is inversely proportional to J(  ). As rotation changes the frequency changes. Driven oscillations Response to ambient vibrations Cap. plate. Pos. Sensor Cap. plate Orifice Flexible Diaphragm  P el  xx L L1L1

14. COSLAB-2004 Measurements Technique - rotation. Rotation results in the circulation in the sensing loop. Cap. plate. Pos. Sensor Cap. plate P el Orifice Flexible Diaphragm   xx Thus the rotation changes phase drop across the weak link. Earth - rotating platform. Change in rotation - reorient apparatus relative to the Earth. Effect has been calibrated in 4 He experiments: with 4.9 cm 2 two-turn loop we use, the Earth rotation produces circulation ~0.85 k 3.

15. COSLAB-2004 Data Analysis Large amplitude frequency (f0) 44

16. COSLAB-2004 Precision in the bias.

17. COSLAB-2004  -shift. Bias does not change much after going through T c, if it does not jump by  3 /2 We assign bias ~0 to the case which happens more often (see below). Bias at fixed T, P and magnetic field. T effect explains most of the scatter show on the picture to the left (local overheating of the inner cell while at nominally stable T).

18. COSLAB-2004  -shifted states.

19. COSLAB-2004 Explanations? Vortex?  -solitons? Salomaa-Volovik, 1988 Very large energy. Bind cores of double-core vortex. Thought to be unstable in bulk (are they?)

20. COSLAB-2004 T-dependence of the circulation. Bias is stable after each cooldown (save for some time-drift, see below. There are some minor variations from one cooldown to another. However there is strong temperature dependence – as T changes between ~0.99 and 0.5 T c the bias changes by almost  3 at P=0.2 bar and much stronger at P=10 bar. At 10 bar the effect is much stronger with 2 amp current in the field coil.

21. COSLAB-2004 “Mirror”  (  ). Often apparently the same state can have 0 or  bias. Not predicted by theory? –Changing n to –n will not do. (f/f 0 ) 2 k

22. COSLAB-2004 Cosmiclike solitons Have been predicted by Salomaa and Volovik. Though to be conecting cores of double-cores vortex, but have have been observed in free state. Solitons are thought to be unstable. But are they in toroidal geometry? For example – rotation of the torus may provide  /2 phase shift along it. Will then the soliton be stable configuration? Phase change We think that the observed p-shift can be provided by 1 or more solitons, crossing the flow loop. Alternative explanation – a single vortex pinned in a position exactly in the middle of the flow channel seems improbable.

23. COSLAB-2004 Why soliton? 100 gauss Coils

24. COSLAB-2004 Explanation of T-dependence Heat leak to inner cell, due, for example to heat release from Stycast or eddy heating in silver increases fountain pressure there and causes normal current flow from the inner cell and counterflow of superfluid into it. Q Q vnvn vsvs Ag Stycast As observed, the circulation should diverge towards T c. Change of the sign (weak), however, remains unexplained.

25. COSLAB-2004 Summary 1.A number (~8) of different current-phase relations (CPR) are observed. 2.Under certain conditions most of these relations are observed shifted by . 3.The shift appears to be unrelated to the shape of the CPR and does not change when CPR changes. 4.We argue that the most probable cause is a cosmic-like soliton(s) crossing the sensing loop. 5.Temperature dependence of the trapped circulation can be explained by thermomechanical effects. 1.This has important implication for superfluid gyroscopes – heat leaks and temperature stability become important. 2.It appears that there is no remnant vorticity in the cell.