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.

Nanoelectronic primary thermometry below 4 mK

Cooling nanoelectronic structures to millikelvin temperatures presents extreme challenges in maintaining thermal contact between the electrons in the device and an external cold bath. It is typically found that when nanoscale devices are cooled to ∼10 mK the electrons are significantly overheated. Here we report the cooling of electrons in nanoelectronic Coulomb blockade thermometers below 4 mK. The low operating temperature is attributed to an optimized design that incorporates cooling fins with a high electron–phonon coupling and on-chip electronic filters, combined with low-noise electronic measurements. By immersing a Coulomb blockade thermometer in the ³He/⁴He refrigerant of a dilution refrigerator, we measure a lowest electron temperature of 3.7 mK and a trend to a saturated electron temperature approaching 3 mK. This work demonstrates how nanoelectronic samples can be cooled further into the low-millikelvin range.

When cooled to the millikelvin scale, nanoelectronic structures can become thermally detached from their environment, limiting nanoscale electronic thermometry. Here, the authors demonstrate the robust cooling of optimally-designed Coulomb blockade thermometer devices down to the millikelvin scale.

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.

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<<T(c). The evolution of the vorticity after arresting the grid shows a dramatic change in the decay rate at a critical grid velocity. We believe this to reflect a sharp transition from ballistic vortex-ring production at low grid velocities to quantum turbulence at higher velocities and that independent isolated vortex rings provide the precursors to the developed turbulence. Furthermore we believe that this may be a feature of all quantum turbulence arising from repetitive mechanical agitation.

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.

Repetitive single vortex-loop creation by a vibrating wire in superfluid 3He-B

Spectacular features are observed on the velocity-force characteristics of a vibrating wire resonator in superfluid 3He-B at ultralow temperatures. Both plateaus and discontinuities are seen in the characteristics. The plateaus seem to have two separate critical velocities where first some "event" occurs, which causes the wire to lose energy and slow down, followed by a second lower critical velocity where the event decouples. It is suggested that these events are due to vortex-loop creation at protuberances on the vibrating wire. This opens up the possibility of controlling the creation of vorticity through specially prepared protuberances.