Session X16: Liquid Helium

Measurements of the Thermal Conductivity of Vycor Glass filled with Superfluid $^4$He

We report on experiments designed to measure the thermal conductivity of Vycor filled with superfluid $^4$He for temperatures in the range 1.2 - 2.0 K and pressures from 2 - 30 atm.. The experimental apparatus, which consists of a rod of Vycor held in a stainless steel tube, will be described. We will report available results for the thermal conductivity as a function of temperature and pressure.   

Phonon-roton modes, superfluidity and a Bose glass phase in nanoscale liquid $^4$He

We present neutron scattering measurements of the elementary phonon-roton modes of liquid $^4$He confined in nanoporous media. The aim is to compare phonon-roton (P-R) and superfluid density measurements in helium at nanoscales and in disorder. A specific goal is to determine the region of temperature and pressure in which well defined phonon-roton modes (and therefore BEC) exist and compare this with the superfluid phase region, i.e. with the superfluid-normal phase critical temperature T$_c$ and pressure p$_c$ in porous media. We find well defined P-R modes (BEC) extend to temperatures above T$_c$ (up to T$_\lambda$ = 2.17 K at SVP) and to pressures above p$_c$ (up to a pressure p = 36.3-36.8 bars at T $\simeq$ 0 but no modes above this pressure [1]). This suggests that there is a Bose glass phase consisting of local regions of BEC separated by normal liquid so that there is no phase coherence across the sample lying between the superfluid and normal liquid phase. The Bose glass phase surrounds the superfluid phase at all p and T. We compare this phase diagram with other dirty Bose systems. [1] Bossy et al. Phys. Rev. Lett. 101, 025301 (2008), Phys. Rev. B (in press)(2008)   

Thin $^4$He films on Nano-porous Diblock Copolymer Substrates

In recent years diblock copolymer templates have been a focus of attention due to their potential uses in nano-scale systems. The ability to produce regular arrays of cylindrical pores has applications in areas such as the production of nanowires and magnetic storage. Porous polymer films made by doblock copolymer techniques provide an interesting substrate for helium. Previously studied porous geometries e.g. nuclepore, anopore, aerogel, vycor, and porous alumina have provided interesting insights into capillary condensation, the Kosterlitz-Thouless transition and hysteresis. Here we report on the study of thin superfluid $^4$He films on diblock copolymer substrates by means of quartz crystal microbalance techniques.   

Evidence of a Proximity Effect in Liquid Helium

We report measurements of the specific heat of helium confined to $(2~\mu{\rm m})^3$ boxes connected via a 32~nm thick film. The spacing between the $\sim \!34$ million boxes arranged in a square array is $4~\mu{\rm m}$ edge-to-edge. The specific heat is compared to a similar measurement of helium confined to the same size boxes where the spacing between boxes is $2~ \mu{\rm m}$. Evidence of a coupling between the boxes in the tighter packed array is seen in a temperature region where the filling film is in the normal state. We also report measurments of the superfluid fraction of the film connecting the boxes in the present experiment. The superfluid state persists to higher temperatures than that expected on the basis of finite-size scaling for a 32~nm film. At the temperatures where the measurement of the film occurs, the helium in the boxes is already superfluid indicating, perhaps, the modification in behavior of a thin film in proximity to larger regions of superfluid.   

A Novel Method to Create Multielectron Bubbles

A multielectron bubble (MEB) in liquid helium is a fascinating object with a spherical two-dimensional electron gas on its surface. Recent theoretical studies of MEBs discuss a plethora of new phenomena$^{1}$. We describe a novel way of creating MEBs and discuss possible ways of trapping them. An electrically heated tungsten filament submerged in superfluid helium is surrounded by a vapor sheath containing electrons due to thermionic emission. We were able to pull MEBs from the sheath by applying electric fields up to 15kV/cm. The motion of MEBs was captured using a high-speed camera (6400 frames/sec). The trajectory of bubbles was clearly influenced by the electric field, which proved that bubbles were charged. In a separate experiment we measured the charge of such an MEB to be as high as 10$^{-9}$ C. We plan to trap MEBs using electromagnetic trap, which will enable extensive experimental studies of these elusive but exciting objects. [1] J. Tempere, I. F. Silvera, and J. T. Devreese, \textit{Surface Science Reports, }\textbf{62}, 159, 2007.   

Phase diagram for helium films on lithium substrates.

We have used an in situ cryogenic pulsed laser deposition system to deposit a lithium film onto a quartz crystal microbalance. Helium 4 adsorption isotherms were measured on a lithium substrate between 2K and 0.6K. Features of these isotherms such as superfluid mass decoupling and variations in the dissipation were used to construct a phase diagram for helium films including the KT line and the 2D liquid-vapor coexistence region. The liquid-vapor critical temperature is approximately 0.8K. The KT transition is anomalous inside the 2D liquid-vapor coexistence region, occurring at constant sub-monolayer coverage independent of temperature. No inert solid-like layers of helium form on lithium substrates, so superfluid films are in direct contact with the substrate. These results will be compared and contrasted with the behavior of helium on other intermediate strength substrates such as exfoliated graphite pre-plated with hydrogen, sodium and magnesium.   

Quantized vortices and superflow in arbitrary dimensions: Structure, energetics and dynamics

The structure and energetics of superflow around quantized vortices, and the motion inherited by these vortices from this superflow, are explored for the superfluidity of helium-four in arbitrary dimensions. The vortices may be idealized as objects of co-dimension two, such as two-dimensional surfaces in the case of four-dimensional superfluidity. The energy of the superflow is found to take on a simple form for vortices that are smooth and asymptotically large, compared with the vortex core size. The motion of vortices is analyzed in general, as well as for the special cases of hyper-spherical and weakly distorted hyper-planar vortices. In all dimensions, vortex motion reflects vortex geometry. In dimension four and higher, this includes not only extrinsic but also intrinsic aspects of the vortex shape. For the generalizations of the vortex rings of three dimensional superfluidity, the energy-momentum relation is determined. Simple scaling arguments recover the essential features of these results, up to numerical and logarithmic factors.   

$^3$He Spin Pump

The superfluid component of $^3$He A$_1$ phase is spin-polarized. The process of forcing the superfluid component through a spin filtering structure, in a manner of mechano-magnetic effect, can be used to increase the spin polarization beyond the equilibrium under a given applied magnetic field. We have constructed a test cell in which a glass capillary array acts as the spin (and entropy) filter and an electrostatically actuated diaphragm forces the superfluid flow through it. Preliminary results show that a maximum \underline{relative} increase of polarization by 50 \% could be achieved. The maximum increase in polarization appears to be limited by the critical superfluid flow through the channels in the glass capillary array. The dependence of the observed effects on temperature, pressure and magnetic field will be presented.   

The Spin Diffusion Coefficient of Superfluid $^{3}$He in the A$_{1}$- phase

Using the Boltzmann kinetic approach and perturbation theory, an approximate expression describing the variation with temperature, of the spin diffusion coefficient in the A$_{1}$-phase of $^{3}$He is derived. It is observed that for temperatures close to the transition temperature T$_{c}$, the spin diffusion coefficient D $\sim $ (T$_{c }$-- T)$^{1/2}$ + \textit{const}. Comparison of the theoretical result with related experimental measurements is discussed.   

Frequency Dependent Acoustic Properties of Superfluid $^{3}$He in Aerogel.

Recently, we have reported the absolute sound (9.5 MHz) attenuation in superfluid $^{3}$He impregnated in 98{\%} porosity aerogel for several different pressures in zero magnetic field [1]. It revealed and confirmed many interesting features directly associated with impurity scattering: collisional drag effect, absence of zero sound crossover and order parameter collective modes, and gapless superfluidity. In this work, we report an experimental effort to uncover the detailed gap structure that is expected to be significantly modified by the presence of impurity scattering. We conducted frequency dependent attenuation measurements, which might shed light on this problem as a tunneling experiment does in superconductors. For the B-like superfluid phase of $^{3}$He in 98{\%} aerogel, we report sound attenuation measurements performed between 14 and 33 bar, while using four frequencies between 3.7 and 11.2 MHz. \newline [1] H.C. Choi \textit{et al., }Phys. Rev. Lett. \textbf{98}, 225301 (2007).   

Superfluid $^3$He in Anistropic Aerogels

Anisotropic quasiparticle scattering has been predicted to modify the properties of superfluid $^3$He in high porosity silica aerogels.\footnote{K. Aoyama and R. Ikeda, Phys. Rev. B {\bf73}, 060504(R) (2006).} For example, anisotropic scattering produced by axial compression (or elongation) of the aerogel has been predicted to stabilize the axial (or polar) state of superfluid $^3$He. We have used a transverse acoustic impedance method to determine the phase diagram of superfluid $^3$He in a 98\% porous silica aerogel subjected to 17\% axial compression. We have found that this uniform axial anisotropy does not increase the stable region of A-like phase but does inhibit the nucleation of the B-phase at low pressure. We have performed optical cross-polarization experiments\footnote{J. Pollanen {\emph{et al.}}, J. of Non-Crystalline Solids {\bf354}, 4668 (2008).} to verify the presence and uniformity of the anisotropy in the aerogel samples. Additionally, we are performing nuclear magnetic resonance experiments on superfluid $^3$He in aerogels with anisotropy introduced with either axial or radial compression.