Drag on Cylinders Moving in Superfluid 3He-B as the Dimension Spans the Coherence Length.

Vibrating probes when immersed in a fluid can provide powerful tools for characterising the surrounding medium. In superfluid 3He-B, a condensate of Cooper pairs, the dissipation arising from the scattering of quasiparticle excitations from a mechanical oscillator provides the basis of extremely sensitive thermometry and bolometry at sub-millikelvin temperatures. The unique properties of the Andreev reflection process in this condensate also assist by providing a significantly enhanced dissipation. While existing models for such damping on an oscillating cylinder have been verified experimentally, they are valid only for flows with scales much greater than the coherence length of 3He, which is of the order of a hundred nanometres. With our increasing proficiency in fabricating nanosized oscillators, which can be readily used in this superfluid, there is a pressing need for the development of new models that account for the modification of the flow around these smaller oscillators. Here we report preliminary results on measurements of the damping in superfluid 3He-B of a range of cylindrical nanosized oscillators with radii comparable to the coherence length and outline a model for calculating the associated drag.

Nanoscale real-time detection of quantum vortices at millikelvin temperatures.

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.

On the origin of the controversial electrostatic field effect in superconductors.

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.

Fundamental dissipation due to bound fermions in the zero-temperature limit.

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.

LEGO® Block Structures as a Sub-Kelvin Thermal Insulator.

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) × 10-5 T 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, <400 nW of power can heat an experimental area of 5 cm2 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.

Operating Nanobeams in a Quantum Fluid.

Microelectromechanical (MEMS) and nanoelectromechanical systems (NEMS) are ideal candidates for exploring quantum fluids, since they can be manufactured reproducibly, cover the frequency range from hundreds of kilohertz up to gigahertz and usually have very low power dissipation. Their small size offers the possibility of probing the superfluid on scales comparable to, and below, the coherence length. That said, there have been hitherto no successful measurements of NEMS resonators in the liquid phases of helium. Here we report the operation of doubly-clamped aluminium nanobeams in superfluid 4He at temperatures spanning the superfluid transition. The devices are shown to be very sensitive detectors of the superfluid density and the normal fluid damping. However, a further and very important outcome of this work is the knowledge that now we have demonstrated that these devices can be successfully operated in superfluid 4He, it is straightforward to apply them in superfluid 3He which can be routinely cooled to below 100 µK. This brings us into the regime where nanomechanical devices operating at a few MHz frequencies may enter their mechanical quantum ground state.

Visualizing Pure Quantum Turbulence in Superfluid 3He: Andreev Reflection and its Spectral Properties.

Superfluid 3He-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 3He-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.

Magnetic phase transition in a nanonetwork of solid 3He in aerogel.

When immersed in liquid 3He, the nanometer strands of aerogel are coated with a thin layer of solid 3He, forming a network of irregular nanotubes. Owing to its high purity and weak interactions, this system is ideal for studying fundamental processes. We report the first experiments on solid 3He in aerogel at ultralow temperatures, cooled by direct adiabatic demagnetization. Simultaneous nuclear magnetic susceptibility and heat capacity measurements indicate a magnetic phase transition.

Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B.

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.

Contrasting mechanical anisotropies of the superfluid 3He phases in aerogel.

There has been much recent interest in how impurity scattering may affect the phases of the p-wave superfluid 3He. Impurities may be added to the otherwise absolutely pure superfluid by immersing it in aerogel. Some predictions suggest that impurity scattering may destroy orientational order and force all of the superfluid phases to have an isotropic superfluid density. In contrast to this, we present experimental data showing that the response of the A-like phase to superfluid flow is highly anisotropic, revealing a texture that is easily modified by flow.

Melting curve of 4He: no sign of a supersolid transition down to 10 mK.

We have measured the melting curve of 4He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 micro bar. Crystals of different quality show the expected T4 dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid 4He and on the Debye temperature of solid 4He. Below 80 mK, we have observed a small deviation from T4 dependence, which, however, cannot be attributed to the supersolid transition, because instead of decrease the entropy of the solid rather remains constant, about 2.5 x 10(-6) R.

Decay of pure quantum turbulence in superfluid 3He-B.

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-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 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.

Emission of discrete vortex rings by a vibrating grid in superfluid 3He-B: a precursor to quantum turbulence.

We report a transition in the vorticity generated by a grid moving in the B phase of superfluid 3He at T<

Surface of a 3He crystal: crossover from quantum to classical behavior.

3He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To understand the reason for that, we have performed the first quantitative investigation on the growth dynamics of the basic (110) facet at 60-110 mK. The obtained values of the step free energy suggest an extremely weak coupling of the solid-liquid interface to the crystal lattice which we show to be the result of quantum fluctuations of the interface. The renormalization group approach by Nozières and Gallet, modified to incorporate quantum fluctuations, explains well the temperature dependence of the step energy measured in this work and at ultralow temperatures by Tsepelin et al., where the coupling is known to be strong. We have thus shown that, paradoxically, the role of quantum fluctuations is at higher temperatures much larger than at low temperature.

Anisotropy of growth kinetics of 3He crystals below 1 mK.

The growth anisotropy of different facets has been measured in 3He crystals at 0.55 mK using a low-temperature Fabry-Pérot interferometer and high-resolution pressure measurements. The observed linear dependence of the growth velocity on the driving force shows that facets grow due to the presence of dislocations. The values of the obtained step energies suggest that 3He has stronger coupling of the liquid-solid interface to the lattice than has been expected. The dependence of the step energy versus the step height is consistent with a quartic power law pointing out that the step-step interactions are of elastic origin.

Faceting on He crystals.

It has been predicted by Landau that, ideally at low temperatures, crystals should show many different types of facets, i.e., flat smooth faces on their surface, but this so-called "devil's staircase" phenomenon has been difficult to observe experimentally. In this paper we describe our recent experiments, in which altogether 11 different types of facets have been identified on growing (3)He crystals at the temperature of 0.55 mK by using a unique low-temperature Fabry-Pérot interferometer. Previously only 3 types of facets had been seen in this system. We have also measured the growth velocities of different facets, and our interpretation of the obtained results yields the conclusion that (3)He has much stronger coupling of the liquid-solid interface to the crystal lattice than has been expected. After an introduction we present a short theoretical background about the equilibrium crystal shape and the roughening transitions, which is followed by the description of our experimental results and discussion.

Observation of higher order facets on 3He crystals.

Faceting has been observed on 3He crystals investigated with a low-temperature Fabry-Pérot interferometer. Nine types of facets were clearly identified during growth of a bcc- 3He single crystal at a temperature of 0.55 mK, while previously only three types of facets have been seen. Because of the weak coupling between the liquid-solid interface and the solid lattice in 3He the facets are apparently too small to be observed in equilibrium. The number of facets observed in our experimental conditions is consistent with the theory of dynamic roughening.