Anomalous Damping of a Low Frequency Vibrating Wire in Superfluid 3He-B due to Vortex Shielding

We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid ³He at zero pressure and at temperatures below 200 μK. The vibrating wire has a low resonant frequency of around 60 Hz. At low velocities the motion of the wire is impeded by its intrinsic (vacuum) damping and by the scattering of thermal quasiparticle excitations. At higher velocities we would normally expect the motion to be further damped by the creation of quasiparticles from pair-breaking. However, for a range of temperatures, as we increase the driving force we observe a sudden decrease in the damping of the wire. This results from a reduction in the thermal damping arising from the presence of quantum vortex lines generated by the wire. These vortex lines Andreev-reflect low energy excitations and thus partially shield the wire from incident thermal quasiparticles.     

The Onset of Vortex Production by a Vibrating Wire in Superfluid 3He-B

We present measurements of the force-velocity response of a vibrating wire resonator in superfluid ³He-B at very low temperatures. At low velocities the response is dominated by intrinsic (vacuum) damping whilst at high velocities it is dominated by pair-breaking. At intermediate velocities there is a series of small plateaus where the velocity often shows small oscillations. We believe that the behaviour results from the stretching of vortices pinned to the wire. The vortices grow and self-reconnect, emitting a vortex ring. The behaviour is very sensitive to the presence of surrounding vortices generated by a neighbouring vibrating wire.     

Andreev Reflection of Quasiparticles by a Vortex Tangle in Superfluid 3He-B?

We have made the surprising discovery that the thermal damping of a vibrating wire resonator in superfluid ³ He-B at ultra low temperatures is considerably depressed when a second wire in the vicinity is driven supercritically. The damping of a vibrating wire resonator at low velocities in the B-phase arises from the scattering of quasiparticle excitations and has a temperature dependence proportional to the Boltzmann factor exp(–/kT) at low temperatures. At higher velocities (v>v_L/3), the wire breaks Cooper pairs and emits a quasiparticle beam. At first sight it seems paradoxical that heating the superfluid can reduce the quasiparticle flux on a neighbouring wire. We can only understand this on the basis that vorticity emitted by the supercritical wire shields, via Andreev reflection, part of the background quasiparticle flux from reaching the other wire. If this interpretation is correct, these techniques will provide a sensitive probe of vortex dynamics in the ultra low temperature regime.     

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, 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.     

Vortex Generation in Superfluid 3He by a Vibrating Grid

Recently we have found that a vibrating wire resonator produces turbulence in superfluid ³He-B at low temperatures when driven above its pair-breaking critical velocity. The vorticity is produced along with a beam of excitations from pair breaking. Here, we discuss preliminary measurements of turbulence generated from an oscillating grid at low temperatures. The grid oscillator is made from a goal-post shaped vibrating wire resonator supporting a fine copper mesh. While the dissipation by a conventional wire resonator is dominated by pair-breaking at the velocities required for turbulence generation, the dissipation of the grid oscillator appears to be dominated by turbulence. This allows us to generate turbulence without the unwanted effects of a quasiparticle beam. Preliminary measurements suggest that the grid turbulence has a rather different behaviour from that generated by conventional wire resonators.     

The Thermal Damping of an Aerogel Resonator in Superfluid 3He-B at Ultra Low Temperatures

No Heading We present measurements of the thermal damping of a cylindrical aerogel sample oscillating in superfluid. ³He-B in the low temperature regime. The measurements are made at low pressures where the ³He confined in the aerogel is normal. As in the case of conventional vibrating wire resonators, the thermal damping arises from quasiparticle collisions at the wire surface and is enhanced by many orders of magnitude by Andreev scattering from the superfluid backflow around the resonator. However, in the case of aerogel, incoming quasiparticles must be absorbed and thermalised within the aerogel before being re-emilled.PACS numbers: 67.57.Bc, 67.57.De, 67.57.Hi, 67.57.Pq.     

High Quality Tuning Forks in Superfluid 3He-B Below?200?��K

We have investigated the influence of the damping force acting on high quality tuning forks (Q??10⁶) of different sizes and geometries in superfluid ³He-B at temperatures below 200 ??K and a pressure of 0.1 bar. The measurements show that at low velocities, the damping of the largest fork expressed in terms of its resonance characteristic width ??f ₂ rises up as its velocity increases. This is in contradiction to the damping of the fork due to Andreev reflection and it may be caused by the interaction of this fork with excitations trapped in the Andreev bond states. We present our preliminary experimental results.     

The Transition to Turbulent Drag for a Cylinder Oscillating in Superfluid 4He: A Comparison of Quantum and Classical Behavior

We have measured the drag and inertial forces on wire resonators in superfluid ⁴He at millikelvin temperatures. At low velocities the behavior is dominated by the intrinsic properties of the resonators which can be measured in vacuum. On increasing velocity we see a sharp transition corresponding to the sudden appearance of drag and inertial forces arising from quantum vortex lines in the superfluid. We present detailed measurements of the superfluid drag and inertial forces as a function of the resonator velocity. We discuss results for two different wire diameters and for different resonant frequencies. We compare and contrast the observed behavior with that measured for cylinders in oscillating classical fluids.     

Vibrating wire measurements in liquid3He II. The superfluid B phase

Measurements with a vibrating wire viscometer in superfluid³He-B at temperatures down to 0.6 mK are described. The need to consider compressibility of the superfluid component in any analysis of vibrating wire measurements is clearly demonstrated and a theoretical calculation of the force acting on a vibrating wire in a finite compressible superfluid is given. The experimental data are consistent with this calculation if theoretical values of the second viscosity ξ₃ are used in the analysis. The failure of the hydrodynamic theory when the quasiparticle mean free path1 is comparable to the wire radius a was observed, and an expression has been deduced for the force acting on the wire when1 is finite. Experimental and theoretical evidence is presented to show that this expression is valid for arbitrary1/a. Values of the viscosity obtained using this expression agree with those obtained in other experimental work and confirm the large discrepancy with theoretical calculations at low reduced temperatures.     

Investigation of quantized circulation in superfluid 3He-B

We have studied circulation in superfluid ³He-B with a vibrating wire. We find that the circulation quantum equals h/2m ₃ to within experimental error at several pressures. We have also measured circulation in rotating superfluid ³He-B, and have observed a precessional motion of a single vortex line. Finally, we have found the unexpected result that circulation around the wire does not affect the pair-breaking critical velocity.     

Hysteresis,Switching and Anomalous Behaviour of a Quartz Tuning Fork in Superfluid 4He

We have been studying the behaviour of commercial quartz tuning forks immersed in superfluid ⁴He and driven at resonance. For one of the forks we have observed hysteresis and switching between linear and non-linear damping regimes at temperatures below 10 mK. We associate linear damping with pure potential flow around the prongs of the fork, and non-linear damping with the production of vortex lines in a turbulent regime. At appropriate prong velocities, we have observed metastability of both the linear and the turbulent flow states, and a region of intermittency where the flow switched back and forth between each state. For the same fork, we have also observed anomalous behaviour in the linear regime, with large excursions in both damping, resonant frequency, and the tip velocity as a function of driving force.     

Transition to Quantum Turbulence Generated by Thin Vibrating Wires in Superfluid 4He

We report the turbulent transition in superfluid ⁴He generated by a vibrating wire as a function of its thickness. The response of a vibrating wire with a 3 μm diameter in superfluid ⁴He at 1.2 K reveals a hysteresis at the turbulent transition between an up sweep and a down sweep of driving force, while no hysteresis appears for wires with a thickness larger than 4.7 μm diameter. These results indicate that the 3 μm wire is efficient for reducing the number of vortex lines attached to it. A cover box and slow cooling also prevent vortex lines from attaching to a wire, resulting in a vortex-free vibrating wire. The effective mass of the vortex-free vibrating wire is almost constant in a wide range of velocities up to 400 mm/s; however, the wire density estimated from the resonance frequency is a half of the expected value of wire material, suggesting that a wire mass becomes lighter or a wire diameter becomes larger in the superfluid effectively.     

Observation of Laminar and Turbulent Flow in Superfluid 4He using a Vibrating Wire

No Heading We have investigated the laminar and the turbulent flow in superfluid ⁴He using a vibrating wire made of thin NbTi ( 2.5 m). The wire velocity as a function of applied force has shown a large hysteresis at the first cooling from normal fluid to the superfluid state. But after a couple of increasing and decreasing wire velocity we have found that the hysteresis vanished and the laminar and the turbulent flow are clearly separated at a critical velocity. The wire moving just after the first cooling must be influenced by remnant vortices nucleated through the superfluid transition. The appearance of the laminar flow below the critical velocity suggests that vortex strings on the wire seem to be selected as suitable sizes by a vibrating flow at higher velocities. We also measured the velocity dependence after immersing the wire directly into the superfluid and found that the laminar region expands up to a velocity much higher than the critical velocity observed above. This result indicates that remnant vortices are considerably reduced by the immersing method.PACS numbers: 67.40.Vs, 47.27.Cn     

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

No Heading We have measured responses of vibrating wire resonators in superfluid ⁴He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.PACS numbers: 67.40 Vs, 67.40 Pm     

Phase diagram of turbulence in superfluid 3He-B

No Heading In superfluid ³He-B mutual-friction damping of vortex-line motion decreases roughly exponentially with temperature. We record as a function of temperature and pressure the transition from regular vortex motion at high temperatures to turbulence at low temperatures. The measurements are performed with non-invasive NMR techniques, by injecting vortex loops into a long column in vortex-free rotation. The results display the phase diagram of turbulence at high flow velocities where the transition from regular to turbulent dynamics is velocity independent. At the three measured pressures 10.2, 29.0, and 34 bar, the transition is centered at 0.52–0.59 T_c and has a narrow width of 0.06 T_c while at zero pressure turbulence is not observed above 0.45 T_c.PACS numbers: 47.37, 67.40, 67.57     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

Microkelvin Thermometry with Bose–Einstein Condensates of Magnons and Applications to Studies of the AB Interface in Superfluid ^3He

Coherent precession of trapped Bose–Einstein condensates of magnons is a sensitive probe for magnetic relaxation processes in superfluid $^3$ He-B down to the lowest achievable temperatures. We use the dependence of the relaxation rate on the density of thermal quasiparticles to implement thermometry in $^3$ He-B at temperatures below $300\,\upmu $ K. Unlike popular vibrating wire or quartz tuning fork based thermometers, magnon condensates allow for contactless temperature measurement and make possible an independent in situ determination of the residual zero-temperature relaxation provided by the radiation damping. We use this magnon-condensate-based thermometry to study the thermal impedance of the interface between A and B phases of superfluid $^3$ He. The magnon condensate is also a sensitive probe of the orbital order-parameter texture. This has allowed us to observe for the first time the non-thermal signature of the annihilation of two AB interfaces.     

A microscopic calculation of the force on a wire moving through superfluid3He-B in the ballistic regime

When a macroscopic object moves through superfluid³He, it experiences a force arising from the effect of quasiparticle scattering. We develop a three-dimensional microscopic model to calculate the force on a smooth cylinder moving at constant velocityv as a model of a vibrating wire. At large (subcritical) wire velocity, the force tends to an asymptotic value as 1/v ², rather than exponentially as in a one-dimensional calculation. At lowv the force is linear inv. We briefly discuss the agreement of our calculations with experimental measurements on a vibrating wire below 0.2T _c, where the quasiparticle trajectories are ballistic.     

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid ^3He-B

We describe the development of a two-dimensional quasiparticle detector for use in visualising quantum turbulence in superfluid $^3$ He-B at ultra-low temperatures. The detector consists of a $5 \times 5$ matrix of pixels, each a 1 mm diameter hole in a copper block containing a miniature quartz tuning fork. The damping on each fork provides a measure of the local quasiparticle flux. The detector is illuminated by a beam of ballistic quasiparticles generated from a nearby black-body radiator. A comparison of the damping on the different forks provides a measure of the cross-sectional profile of the beam. Further, we generate a tangle of vortices (quantum turbulence) in the path of the beam using a vibrating wire resonator. The vortices cast a shadow onto the face of the detector due to the Andreev reflection of quasiparticles in the beam. This allows us to image the vortices and to investigate their dynamics. Here we give details of the design and construction of the detector and show some preliminary results for one row of pixels which demonstrates its successful application to measuring quasiparticle beams and quantum turbulence.     

Vortex Formation in Neutron-Irradiated Rotating Superfluid 3He-B

A convenient method to create vortices in meta-stable vortex-free superflow of ³He-B is to irradiate with thermal neutrons. The vortices are then formed in a rapid non-equilibrium process with distinctive characteristics. Two competing explanations have been worked out about this process. One is the Kibble-Zurek mechanism of defect formation in a quench-cooled second order phase transition. The second builds on the instability of the moving front between superfluid and normal ³He, which is created by the heating from the neutron absorption event. The most detailed measurements with single-vortex resolution have been performed at temperatures close to T_c. In the first half of this report we summarize the two models and then show that the experimentally observed vortices originate from the Kibble-Zurek mechanism. In the second half we present new results from low temperatures. They also weakly support the Kibble-Zurek origin, but in addition display superfluid turbulence as a new phenomenon. Below 0.6 T_c the damping of vortex motion from the normal component is reduced sufficiently so that turbulent vortex dynamics become possible. Here a single absorbed neutron may transfer the sample from the meta-stable vertex-free to the equilibrium vortex state. The probability of a neutron to initiate a turbulent transition grows with increasing superflow velocity and decreasing temperature. PACS numbers: 47.32, 67.40, 67.57, 98.80.