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We report measurements of the thermal conductance of a structure made from commercial Acrylonitrile Butadiene Styrene (ABS) modules, known as LEGO® blocks, in the temperature range from 70 mK to 1.8 K. A power law for the sample’s thermal conductivity κ = (8.7 ± 0.3) × 10−5T 1.75±0.02 WK−1 m−1 was determined. We conclude that this ABS/void compound material provides better thermal isolation than well-known bulk insulator materials in the explored temperature range, whilst maintaining solid support. LEGO blocks represent a cheap and superlative alternative to materials such as Macor or Vespel. In our setup, 2 to over 1 K, without any significant change to the base temperature of the dilution refrigerator. This work suggests that custom-built modular materials with even better thermal performance could be readily and cheaply produced by 3D printing.

Since we still lack a theory of classical turbulence, attention has focused on the conceptually simpler turbulence in quantum fluids. Reaching a better understanding of the quantum case may provide additional insight into the classical counterpart. That said, we have hitherto lacked detectors capable of the real-time, non-invasive probing of the wide range of length scales involved in quantum turbulence. Here we demonstrate the real-time detection of quantum vortices by a nanoscale resonant beam in superfluid 4He at 10 mK. Essentially, we trap a single vortex along the length of a nanobeam and observe the transitions as a vortex is either trapped or released, detected through the shift in the beam resonant frequency. By exciting a tuning fork, we control the ambient vortex density and follow its influence on the vortex capture and release rates demonstrating that these devices are capable of probing turbulence on the micron scale. Previous work has shown the detection of quantum turbulence with mechanical resonators but with limited spatial and temporal resolution. Here, the authors demonstrate real-time detection of single quantum vortices in superfluid 4He with millisecond and micron resolution at temperatures of 10 millikelvin.

The ground state of a fermionic condensate is well protected against perturbations in the presence of an isotropic gap. Regions of gap suppression, surfaces and vortex cores which host Andreev-bound states, seemingly lift that strict protection. Here we show that in superfluid 3He the role of bound states is more subtle: when a macroscopic object moves in the superfluid at velocities exceeding the Landau critical velocity, little to no bulk pair breaking takes place, while the damping observed originates from the bound states covering the moving object. We identify two separate timescales that govern the bound state dynamics, one of them much longer than theoretically anticipated, and show that the bound states do not interact with bulk excitations., Understanding dynamics of fermionic bound states is important for their potential application in quantum devices. Here the authors study zero temperature dynamics and dissipation of fermions bound on a moving goal-post shaped wire in superfluid 3He-B.

Understanding the temperature dependence of thermal boundary resistance, or Kapitza resistance, between liquid helium and sintered metal has posed a problem in low-temperature physics for decades. In the ballistic regime of superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}B$, we find the Kapitza resistance can be described via scattering of thermal excitations (quasiparticles) with a macroscopic geometric area, rather than the sintered metal's microscopic area. We estimate that a quasiparticle needs on the order of 1000 collisions to successfully thermalize with the sinter. Finally, we find that the Kapitza resistance is approximately doubled with the addition of two monolayers of solid $^{4}\mathrm{He}$ on the sinter surface, which we attribute to an extra magnetic channel of heat transfer being closed as the nonmagnetic solid $^{4}\mathrm{He}$ replaces the magnetic solid $^{3}\mathrm{He}$.

In this work we study the influence of orbital viscosity on the dynamics of the order parameter texture in the superfluid B-phase of $^3$He near a moving bounda ry. Based on the redistribution of thermal quasiparticles within the texture, we develop a model which bestows a significant effective mass on the interface, an d gives a new mechanism for friction as the boundary moves. We have tested the model against existing data of a moving A-B interface whose motion was controlled using magnetic field. The model allows some predictions in experimental situations which involve texture rearrangement due to the B-phase boundary motion., Comment: 3 figures

Andreev reflection, familiar in superconducting systems, shows a much more extensive set of behaviors in the p-wave condensate of superfluid 3He. We discuss the basic ideas of Andreev reflection in the superfluid and its various manifestations. The fact that the process displays almost perfect retroreflection allows us to exploit the remarkable properties of the phenomenon for characterizing the pure quantum turbulence that can exist in these condensates. Finally, we discuss Andreev-reflection “optics” as a means of visualizing this turbulence in real time through the vortex video camera.

Superfluids, such as superfluid 3He and 4He, exhibit a broad range of quantum phenomena and excitations which are unique to these systems. Nanoscale mechanical resonators are sensitive and versatile force detectors with the ability to operate over many orders of magnitude in damping. Using nanomechanical-doubly clamped beams of extremely high-quality factors Q>106, we probe superfluid 4He from the superfluid transition temperature down to mK temperatures at frequencies up to 11.6 MHz. Our studies show that nanobeam damping is dominated by hydrodynamic viscosity of the normal component of 4He above 1K. In the temperature range 0.3-0.8K, the ballistic quasiparticles (phonons and rotons) determine the beams' behavior. At lower temperatures, damping saturates and is determined either by magnetomotive losses or acoustic emission into helium. It is remarkable that all these distinct regimes can be extracted with just a single device, despite damping changing over six orders of magnitude.

Flexural mode vibrations of miniature piezoelectric tuning forks (TFs) are known to be highly sensitive to superfluid excitations and quantum turbulence in 3He and 4He quantum fluids, as well as to the elastic properties of solid 4He, complementing studies by large scale torsional resonators. Here, we explore the sensitivity of a TF, capable of simultaneously operating in both the flexural and torsional modes, to excitations in the normal and superfluid 4He. The torsional mode is predominantly sensitive to shear forces at the sensor–fluid interface and much less sensitive to changes in the density of the surrounding fluid when compared to the flexural mode. Although we did not reach the critical velocity for the quantum turbulence onset in the torsional mode, due to its order of magnitude higher frequency and increased acoustic damping, the torsional mode was directly sensitive to fluid excitations, linked to quantum turbulence created by the flexural mode. The combination of two dissimilar modes in a single TF sensor can provide a means to study the details of elementary excitations in quantum liquids and at interfaces between solids and quantum fluid.Flexural mode vibrations of miniature piezoelectric tuning forks (TFs) are known to be highly sensitive to superfluid excitations and quantum turbulence in 3He and 4He quantum fluids, as well as to the elastic properties of solid 4He, complementing studies by large scale torsional resonators. Here, we explore the sensitivity of a TF, capable of simultaneously operating in both the flexural and torsional modes, to excitations in the normal and superfluid 4He. The torsional mode is predominantly sensitive to shear forces at the sensor–fluid interface and much less sensitive to changes in the density of the surrounding fluid when compared to the flexural mode. Although we did not reach the critical velocity for the quantum turbulence onset in the torsional mode, due to its order of magnitude higher frequency and increased acoustic damping, the torsional mode was directly sensitive to fluid excitations, linked to quantum turbulence created by the flexural mode. The combination of two dissimilar modes in a sin...

In this work, we study the influence of orbital viscosity on the evolution of the order-parameter and texture in the B phase of superfluid

The growing demands of quantum materials, engineering and technology make access to microkelvin temperatures ever more essential. Experience in Europe suggests that new working methods, encouraged by an imaginative funding atmosphere, can accelerate progress in this frontier field.

As a specific offering towards his festschrift, we present a review the various properties of the excitation gas in superfluid 3He, which depend on Andreev reflection. This phenomenon dominates many of the properties of the normal fluid, especially at the lowest temperatures. We outline the ideas behind this dominance and describe a sample of the many experiments in this system which the operation of Andreev reflection has made possible, from temperature measurement, particle detection, vortex imaging to cosmological analogues.

Coherent condensates appear as emergent phenomena in many systems. They share the characteristic feature of an energy gap separating the lowest excitations from the condensate ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation spectrum in the scatterer frame to become gapless, can create excitations at no energy cost, initiating the breakdown of the condensate—the well-known Landau velocity. Whereas, for the neutral fermionic superfluid 3He-B in the T = 0 limit, flow around an oscillating body displays a very clear critical velocity for the onset of dissipation, here we show that for uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and exceeded. Given the importance of the Landau velocity for our understanding of superfluidity, this result is unexpected, with implications for dissipative effects of moving objects in all coherent condensate systems.

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.

We present the first measurements of the response of a mechanical oscillator in solid 4He. We use a lithium niobate tuning fork operating in its fundamental resonance mode at a frequency of around 30 kHz. Measurements in solid 4He were performed close to the melting pressure. The tuning fork resonance shows substantial frequency shifts on cooling from around 1.5 K to below 10 mK. The response shows an abrupt change at the bcc-hcp transition. At low temperatures, below around 100 mK, the resonance splits into several overlapping resonances.

We have developed the use of quartz tuning forks for thermometry in normal liquid He-3. We have used a standard 32 kHz tuning fork to measure the viscosity of liquid He-3 over a wide temperature range, 6 mK

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.

We have developed a new “floppy wire” device for studying the motion through quantum fluids and solids at very low temperatures. The device is particularly well suited for producing large amplitudes of motion, for measuring drag forces at low frequency, and for studying “zero” frequency dynamics by measuring transient behavior. The device is very versatile and allows motion to be studied over a broad range of velocities and amplitudes. It generates negligible heat leaks and so is ideally suited for ultra low temperature experiments. The device has many potential applications in quantum fluids and solids research, including the study of drag forces at low frequencies in both the laminar and turbulent flow regimes, and the investigation of motion in (super)solid 4He. We discuss the principles and modes of operation of the device and present some preliminary measurements in vacuum, in normal liquid 3He and in superfluid 4He. We also present measurements of a “floppy grid” device, which could be used for generating large volumes of quantum turbulence in superfluids at low temperatures.

It is difficult to measure the turbulent energy in a classical system as the turbulence contributes only a small kinetic energy compared with the enthalpy of the system. A quantum system, however, such as liquid helium at absolute zero, has zero enthalpy. Added vorticity therefore accounts for the total energy, thus allowing the turbulent energy to be measured directly The lack of a general solution to the governing Navier–Stokes equations means that there is no fundamental theory of turbulence. In the simpler case of pure quantum turbulence, the tangle of identical singly quantized vortices in superfluids at T∼0 may provide a deeper understanding of turbulence in general. The well-known Kolmogorov theory1 predicts the energy distribution of turbulence and how it decays. In normal systems the turbulent energy is generally only a small perturbation on the total thermal energy of the supporting medium. In quantum turbulence, however, the energy is accessible. A stationary condensate is necessarily in its ground state with zero enthalpy. Thus quantum turbulence accounts for the entire free energy of the superfluid and there are no other contributions. Here, we exploit this property to make the first direct measurement of the energy released by freely decaying quantum turbulence. Our results are consistent with a Kolmogorov energy spectrum with an inferred Kolmogorov constant remarkably similar to those of classical fluids.

We report on the onset of turbulence in normal and superfluid 4He using several 13.5 μm diameter vibrating wire resonators placed in a cell, filtered from the surrounding helium bath. We measured the force-velocity characteristics of the wires in normal and superfluid helium over a velocity range up to several meters per second. The transition from laminar to turbulent behavior can be clearly identified. Surprisingly we find that, depending on the cooling history, turbulence in the superfluid does not always develop fully.

Recently, quartz tuning forks have been used to probe the dynamics of quantum fluids. For many of these measurements it is important to know the velocity amplitude of the tips of the vibrating fork prongs. We have used different techniques to establish, with an accuracy of a few percent, the relationship between the electrical and mechanical properties of several commercial quartz tuning forks with fundamental resonant frequency ∼32 kHz. The velocity is usually inferred from an electro-mechanical calibration that models a quartz prong as a clamped, rectangular cantilever beam. We have tested the accuracy of this calibration using three methods: measurement of the amplitude at which the fork prongs touch each other; direct optical measurement of the moving fork prongs using strobe microscopy; and a Michelson interferometry technique operating with a 670 nm laser. All three methods yield consistent results. The velocity so determined is found to be 10% lower than that of the standard electro-mechanical calibration.

We have measured the damping on a quartz tuning fork in the B-phase of superfluid He-3 at low temperatures, below 0.3T (c). We present extensive measurements of the velocity dependence and temperature dependence of the damping force. At the lowest temperatures the damping is dominated by intrinsic dissipation at low velocities. Above some critical velocity an extra temperature independent damping mechanism quickly dominates. At higher temperatures there is additional damping from thermal quasiparticle excitations. The thermal damping mechanism is found to be the same as that for a vibrating wire resonator; Andreev scattering of thermal quasiparticles from the superfluid back-flow leads to a very large damping force. At low velocities the thermal damping force varies linearly with velocity, but tends towards a constant at higher velocities. The thermal damping fits very well to a simple model developed for vibrating wire resonators. This is somewhat surprising, since the quasiparticle trajectories through the superfluid flow around the fork prongs are more complicated due to the relatively high frequency of motion. We also discuss the damping mechanism above the critical velocity and compare the behaviour with other vibrating structures in superfluid He-3-B and in superfluid He-4 at low temperatures. In superfluid He-4 the high velocity response is usually dominated by vortex production (quantum turbulence), however in superfluid He-3 the response may either be dominated by pair-breaking or by vortex production. In both cases the critical velocity in superfluid He-3-B is much smaller and the high velocity drag coefficient is much larger, compared to equivalent measurements in superfluid He-4.

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.

Although it is widely accepted that to resolve the ‘horizon’ problem the early Universe must have undergone a sudden expansion (cosmic inflation), what mechanism drove this process is less clear. In the braneworld scenario, it is suggested that inflationary epochs may have been initiated and terminated by brane collisions and annihilations1,2,3. Branes are objects of lower dimensionality embedded in a higher-dimensional matrix. For example, we may live on a three-dimensional brane embedded in a four-dimensional matrix. However, such structures are so far removed from everyday reality that bringing physical insight to bear is difficult. Here we report laboratory experiments where we simulate brane annihilation using the closest brane analogue to which we have access, the coherent phase boundary between the two phases of superfluid 3He. When two branes collide or annihilate, topological defects may be created, whose influence may still be detectable today. By creating a brane–antibrane pair in superfluid 3He and subsequently annihilating it, we can detect that defects are indeed created in the superfluid texture (the superfluid analogue of spacetime), thus confirming that the concept of defect formation after brane annihilation in the early Universe can be reproduced in analogous systems in the laboratory.

We present measurements of the response of the B-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at 16 bar pressure and at low temperatures. A variable magnetic field is applied such that the aerogel-confined superfluid may exist in the A-like or B-like phase, while the surrounding fluid is always in the bulk B-phase. The resonator response reveals a velocity dependence of the inferred aerogel-confined superfluid fraction. We discuss measurements of the temperature and magnetic field dependence of the response in the B-like phase. We find a significant field dependence indicating a strong magnetic distortion of the B-like phase order parameter.

Quantum turbulence consists of a tangle of quantised vortex lines which interact via their self induced flow. At very low temperatures there is no normal fluid component and no associated viscosity. These are very simple conditions in which to study turbulence which might eventually lead to a better understanding of turbulence in general. There are a number of interesting questions, such as how closely does quantum turbulence resemble classical turbulence and how does it decay in the absence of the viscous dissipation. We have recently developed techniques for detecting quantum turbulence in superfluid 3He-B in the low temperature limit. Using a vibrating grid, we find an unexpected sharp transition to turbulence via the entanglement of emitted vortex rings. Measurements also suggest that the quantum turbulence produced by the grid decays in a manner similar to that expected for classical turbulence, but the decay rate appears to be governed by the circulation quantum rather than viscosity.

We present measurements of the response of the A-like phase of superfluid 3He in aerogel to an applied flow. The measurements are made using a cylindrical piece of 98% silica aerogel attached to a vibrating wire resonator. The resonator is immersed in superfluid 3He at low temperatures and relatively high magnetic fields such that the aerogel confined superfluid is in the A-like phase, while the surrounding fluid is in the bulk B-phase. We observe a variety of interesting non-linear and hysteretic effects when the resonator is driven to higher velocities. We present some of our preliminary findings and speculate on their implications.

We present measurements of the transport of superfluid 3He quasiparticle excitations in the ballistic limit at temperatures well below Tc, and an interpretation of unexpected results as an experimental simulation of cosmological processes. Using a variable magnetic field profile we stabilize a layer of A phase across a cylinder of B phase, creating both an AB and a BA interface. These highly ordered interfaces may provide an ideal laboratory analogy for the branes and anti-branes of current cosmology. It has been suggested that brane interaction and annihilation are involved in inflation in the early Universe and leave behind topological defects such as cosmic strings. In our experiments we have annihilated our AB/BA branes by ramping down the magnetic field to remove the A phase layer. We then find that the quasiparticles face an extra impedance owing to defects left behind in the B phase texture. This is the first definitive observation of such a phenomenon.

Turbulence in classical fluids has far-reaching technological implications but is poorly understood. A better understanding might be gained from studying turbulence in quantum systems. In a pure superfluid (at low temperatures), there is no viscosity and vortex lines are quantised. Quantum turbulence consists of a tangle of quantised vortex lines which interact via their self-induced flow. We have recently developed techniques for detecting vortices in superfluid 3He–B in the low temperature limit. We find that the transition to turbulence from a moving grid occurs by the entanglement of emitted vortex rings. Here, we discuss the propagation of the ballistic vortex rings emitted at low grid velocities. We have measured the temperature at which the rings decay before reaching the detectors. Our results, at two different pressures, confirm that the vortex rings decay in accordance with mutual friction.

Superfluid He3−B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in He3−B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.

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.

The persistent precessing domain (PPD) is an isolated region of coherent spin precession which is observed in the B phase of superfluid 3He at the lowest achievable temperatures. It has many unusual properties and its free decay can exceed 1000s at the lowest temperatures. Previous observations of the PPD were highly irreproducible but we now find the PPD to be very reproducible when there is a field minimum along the cell axis. Here we discuss measurements of the PPD as we control the magnetic field profile, allowing the depth of the minimum to be adjusted.

We report preliminary measurements of the coupling between superfluid 3He-B and Kapton or Aerogel samples at very low temperatures. The small Kapton or Aerogel sample is placed in a quasiparticle black body radiator. The temperature of the ambient 3He is monitored while the magnetic field on the solid samples is changed. Initial results show that both samples produce large amounts of cooling (or heating) as the field is decreased (or increased). There is also evidence from a large heat capacity of ferromagnetic solid 3He on the surface of the aerogel as well as at least two distinct physical energy-exchange processes, one rapid and one slow.

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.

Superfluid He-3 has a hierarchy of properties, each manifest as a 'superfluid'. There is the mass superfluid, the spin superfluid and there should also be an orbital superfluid. These three 'super' fluids respond differently to the interpenetrating normal fluid and demand different temperature ranges to be studied fully. We discuss here the importance of work at very low temperatures, how we can cool to the lowest temperatures and finally present a selection of low temperature experiments which illustrate aspects of multiphase nature of the superfluid and of the three 'superfluids' mentioned above.

We have been measuring the surface tension of the AB interface at zero pressure, in high magnetic fields and low temperatures below 0.2 T c . We manipulate the phase boundary by controlling a magnetic field profile. We use the latent heat released/absorbed as the phase boundary moves to infer its position and velocity. We have observed that the motion of the interface through a small aperture is dependent on the magnetic field gradient. Here we extend numerical methods first used to calculate the shapes of liquid drops in a gravitational field to show that the gradient dependence can be accounted for by the deformation of the interface.

Using pulsed NMR we have been studying the properties of the persistent precessing domain (PPD) in superfluid 3He-B at ugtralow temperatures. These precessiog spin domains are very long-lived, persisting for periods of over half an hour under favourable conditions. In the current experiment, by using two NMR coils, we are able to monitor the spatial location of the domain. The PPD is trapped in a field minimum along the axis of the cell, the position of which we can manipulate by variation of the field gradient. We find that the signal lifetime becomes much shorter and independent of temperature when the region of precession is brought into close proximity to the closed end of the experimental cell, suggesting that an extra temperature-independent dissipation mechanism comes into play in the vicinity of the cell walls.

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.

From our long experience of using profiled magnetic fields to stabilize and manipulate the AB phase boundary in superfluid 3He in the zero-temperature limit, we have constructed a cell where we can place the AB interface in the vicinity of a pair of crossed vibrating wire resonators (VWRs). The VWRs provide sensitive mechanical probes of the A and B phase energy gaps and textures. Here we present preliminary resugts where we observe the dynamic response of the VWR at the AB interface.

We have made two different measurements of interfacial energies below 300 muK, at zero pressure and in magnetic fields up to 400 mT. A variable magnetic field profile allows us to stabilize and precisely manipulate the position of the A-B interface. First, we can derive the difference in wall wetting energies from the behaviour of the phase boundary as it enters and exits a stack of glass capillary tubes. Secondly, we can measure the surface tension from the level of over-or under-magnetization needed to force the interface through an aperture. These are the first surface energy measurements in high magnetic fields in the zero-temperature limit. Our results are in surprising agreement with earlier measurements at high pressure close to T-c.

The properties of superfluid 3 He in the regime of negligible normal fluid density is both of fundamental interest and yet very simple. The behaviour is dominated by the properties of the condensate, and several phenomena, otherwise masked by the normal fluid, become observable. We discuss the techniques needed to cool the superfluid to T⪡0.1 T c . We discuss some examples of the unique low temperature behaviour; quasi-persistent spin precession, possible orbital precession, imaging turbulence, nucleation and the phase diagram in aerogel.

We have measured the A-B boundary wall contact angle and the phase interface surface tension in superfluid He-3. The measurements have been made in the ballistic temperature regime at zero pressure in magnetic fields up to 400 mT. We infer the surface energies from the behaviour of the phase boundary moving in and out of a stack of glass capillary tubes. We measure the wall contact angle from the observed capillary height and obtain the interphase surface tension from the level of over- or under-magnetisation when the interface "pops" out of the capillaries. This is the first measurement of both the surface tension and contact angle in high magnetic fields.

Search for the superfluid state of dilute 3He dissolved to 4He is one of the major remaining problems of low temperature physics. We describe our two experiments designed to pursue the lowest achieved temperature in such mixtures essentially below the values reported before.

We report thermal conductivity measurements for normal phase liquid 3He inside 98 and 95% aerogels at dilution refrigerator temperatures (5 to 50 mK). In our measurements we use cylindrical samples of aerogel which have been fabricated inside quartz tubes. Each tube is enclosed at one end by a small chamber to which a known heat input is applied at a measured temperature. The other end is in an open volume of helium which is heat sunk to the refrigerator. Vibrating wire thermometry is used to measure the helium temperatures. The thermal conductivity measurements show clearly the effects of quasiparticle-“impurity” scattering, from which values of the mean free path are derived. These are 92 nm for the 98% aerogel and 56 nm for the 95% sample.

We present our first high resolution vibrating wire resonator data on dilute 3He-4He mixtures at ultra low temperatures. Measurements were performed at saturated vapor pressure with 3He concentrations below the phase separation limit. The behavior of the damping at very low temperatures does not follow the modified slip correction analysis previously applied to extend the validity of the hydrodynamic treatment.

We have studied the Fermi fluid, 3He in 3He-4He solution, confined within the narrow channels of Vycor glass. Continuous wave NMR signals were observed in two almost identical coils, one containing bulk solution and the other the solution in Vycor glass. Three different solutions (0.1, 1.6, and 6%) have been studied over the temperature range 3mK to above 1K. The measurements relate to two exclusion effects of 3He from Vycor glass. One concerns potential energy, and we demonstrate the partial exclusion of 3He independent of concentration as the temperature is lowered from high temperatures down to around 200mK, thus giving an experimental measure of the van der Waals forces between the wall and the helium. The second effect is the additional quantum exclusion which arises from the influence of quantum wire confinement on the kinetic energy, as the temperature is progressively lowered below 50mK in the very dilute (0.1%) solution.

Transport properties of superfluid He-3 in aerogel are governed by a fixed paean free path set by the typical dimensions of the strand separation. We describe preliminary measurements of the thermal conductivity of superfluid He-3 confined in 98% silica aerogel. The majority of the measurements are made in relatively high magnetic fields where the superfluid within the aerogel is in the A-phase like state. Since the quasiparticle mean free path is fixed, the temperature dependence of the thermal conductivity depends only on the superfluid energy gap and on the texture in the case of the A-phase. The results so far obtained are broadly consistent with the aerogel-confined superfluid having a temperature dependent energy gap close to the BCS prediction although there are significant deviations at the lowest temperatures.

We have investigated the behaviour of a large vibrating wire resonator in the B-phase of superfluid He-3 at zero pressure and at temperatures below 200 mu K. 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.

We have measured the drag force from quantum turbulence on a series of quartz tuning forks in superfluid helium. The tuning forks were custom made from a 75-$\ensuremath{\mu}$m-thick wafer. They have identical prong widths and prong spacings, but different lengths to give different resonant frequencies. We have used both the fundamental and overtone flexure modes to probe the turbulent drag over a broad range of frequencies $f=\ensuremath{\omega}/2\ensuremath{\pi}$ from 6.5 to 300 kHz. Optical measurements show that the velocity profiles of the flexure modes are well described by a cantilever beam model. The critical velocity for the onset of quantum turbulence at low temperatures is measured to be ${v}_{c}\ensuremath{\approx}\sqrt{0.7\ensuremath{\kappa}\phantom{\rule{0.16em}{0ex}}\ensuremath{\omega}}$ where $\ensuremath{\kappa}$ is the circulation quantum. The drag from quantum turbulence shows a small frequency dependence when plotted against the scaled velocity $v/{v}_{c}$.

We report the first measurements of the A-B phase transition of superfluid He-3 confined within 98% silica aerogel in high magnetic fields and low temperatures. A disk of aerogel is attached to a vibrating wire resonator. The resonant frequency yields a measure of the superfluid Fraction p,lp of the He-3 within the aerogel. The inferred rho (s)/rho value increases substantially at the A-to-B transition of the confined superfluid, allowing us to map the A-B phase diagram as a function of held and temperature. At 4.8 bars, the B-T transition curve looks very similar to that in bulk with a simple reduction factor of order 0.45 for both transition field and temperature.