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.

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.

Introduction. Cosmology meets condensed matter.

At first sight, low-temperature condensed-matter physics and early Universe cosmology seem worlds apart. Yet, in the last few years a remarkable synergy has developed between the two. It has emerged that, in terms of their mathematical description, there are surprisingly close parallels between them. This interplay has been the subject of a very successful European Science Foundation (ESF) programme entitled COSLAB ('Cosmology in the Laboratory') that ran from 2001 to 2006, itself built on an earlier ESF network called TOPDEF ('Topological Defects: Non-equilibrium Field Theory in Particle Physics, Condensed Matter and Cosmology'). The articles presented in this issue of Philosophical Transactions A are based on talks given at the Royal Society Discussion Meeting 'Cosmology meets condensed matter', held on 28 and 29 January 2008. Many of the speakers had participated earlier in the COSLAB programme, but the strength of the field is illustrated by the presence also of quite a few new participants.

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.

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<

Quantum turbulence in superfluid 3He illuminated by a beam of quasiparticle excitations.

We have measured directly the Andreev scattering of a controllable beam of quasiparticle excitations by a localized tangle of quantum vortices in superfluid 3He-B at low temperatures. We present a microscopic description of the Andreev scattering from a vortex line allowing us to estimate the vortex separation scale in a dilute tangle of vortices, providing a better comparison of the observed decay time of the turbulence with recent numerical simulations. The experiments also suggest that below 200 microK we reach the low temperature limit for turbulent dynamics.

Interfacial energy of the superfluid 3He a-B phase interface in the zero-temperature limit.

We have measured the surface energy of the interface between the A and B phases of superfluid 3He in the low temperature limit at zero pressure. Using a shaped magnetic field, we control the passage of the phase boundary through a small aperture. We obtain the interphase surface energy from the over- or undermagnetization required to force the interface through the aperture in both directions, yielding values of the surface tension and the interfacial contact angle. This is the first measurement of the interfacial energy in high magnetic fields and in the zero-temperature limit.

Thermal conductivity of liquid 3He in aerogel: a gapless superfluid.

We have measured the thermal conductivity of liquid 3He in 98% aerogel at ultralow temperatures. Aerogel introduces disorder on a scale comparable to the superfluid coherence length. At low pressures the liquid in the aerogel shows normal-state behavior with conductivity linear in temperature. At pressures above approximately 6 bars the onset of superfluidity suppresses the conductivity and the thermal conductivity again tends towards linear behavior in the very low temperature limit, providing strong evidence that here the liquid 3He in the aerogel is behaving as a gapless superfluid.

Phase diagram of the A and B phases of superfluid 3He in aerogel.

We report the first measurements of the A-B phase transition of superfluid 3He 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 rho(s)/rho of the 3He 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 field 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.

Generation and detection of quantum turbulence in superfluid 3He-B.

We describe the first direct observations of turbulence in superfluid 3He-B. The turbulence is generated by a vibrating-wire resonator driven at velocities exceeding the pair-breaking critical velocity. It is detected by the resulting decrease in the thermal damping on a neighboring "detector" vibrating-wire resonator. The superfluid flow field associated with the turbulence Andreev reflects thermal quasiparticle excitations, effectively screening the detector wire, resulting in a decrease in the thermal damping.