We describe measurements of the decay of pure superfluid turbulence in superfluid 3 He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4 He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.PACS numbers: 67.57. Fg, 67.57.De, 67.57.Hi In this paper we present the first quantitative measurements of the decay of turbulence in a pure superfluid system. This is a subject of considerable interest since no conventional dissipation mechanisms are available.In a classical fluid, turbulence at high Reynolds numbers is characterized by a range of eddy sizes obeying the well-known Kolmogorov spectrum. On large length scales the motion is dissipationless, whereas on small scales viscosity comes into play. Decay of the turbulence proceeds as energy is transferred by non-linear interactions from the largest non-dissipative length scales d (typically the size of the turbulent region) to smaller length scales where the motion is dissipated by viscous forces. The dissipation per unit volume is given by ρνω 2 where ρ is the fluid density, ν the kinematic viscosity and ω 2 the mean square vorticity [1]. An interesting question, which has received much theoretical speculation [1], is what happens in a pure superfluid with no viscous interactions?Conceptually, turbulence in a superfluid is greatly simplified. Superfluids such as He-II and 3 He-B are described by macroscopic wavefunctions with a well defined phase φ. The superfluid velocity is determined by gradients of the phase, v S = ( /m)∇φ where m is the mass of the entities constituting the superfluid (the mass of a 4 He atom for He-II or twice the mass of a 3 He atom, 2m 3 , for the Cooper pairs in 3 He-B). Consequently, in contrast to classical fluids, superfluid motion is inherently irrotational and vorticity may only be created in the superfluid by the injection of vortex lines. A superfluid vortex is a line defect around which the phase changes by 2π (ignoring here more complex structures such as in 3 He-A). The superfluid order parameter is distorted within the relatively narrow core of the vortex where all the circulation is concentrated. The superfluid flows around the core with a velocity, at distance r, given by v S = /mr corresponding to a quantized circulation κ = h/m. Vortex lines are topological defects. They cannot terminate in free space, and therefore must either form loops or * Electronic Address: s.fisher@lancaster.ac.uk terminate on container walls. Turbulence in a superfluid takes the form of a tangle of vortex lines.Superfluid hydrodynamics is further simplified by the superfluid compon...

We present measurements of the drag forces on quartz tuning forks oscillating at low velocities in normal and superfluid 4 He. We have investigated the dissipative drag over a wide range of frequencies, from 6.5 to 600 kHz, by using arrays of forks with varying prong lengths and by exciting the forks in their fundamental and first overtone modes. At low frequencies the behavior is dominated by laminar hydrodynamic drag, governed by the fluid viscosity. At higher frequencies acoustic drag is dominant and is described well by a three-dimensional model of sound emission.

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4 He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution "turbulent drag". The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.

Superconducting quantum devices offer numerous applications, from electrical metrology and magnetic sensing to energy-efficient high-end computing and advanced quantum information processing. The key elements of quantum circuits are (single and double) Josephson junctions controllable either by electric current or magnetic field. The voltage control, commonly used in semiconductor-based devices via the electrostatic field effect, would be far more versatile and practical. Hence, the field effect recently reported in superconducting devices may revolutionise the whole field of superconductor electronics provided it is confirmed. Here we show that the suppression of the critical current attributed to the field effect, can be explained by quasiparticle excitations in the constriction of superconducting devices. Our results demonstrate that a miniscule leakage current between the gate and the constriction of devices perfectly follows the Fowler-Nordheim model of electron field emission from a metal electrode and injects quasiparticles with energies sufficient to weaken or even suppress superconductivity.

We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.