Heat Capacity of Liquid 4He Confined in a Nanoporous Glass

We report a preliminary study of heat capacities of ⁴He confined in a nanoporous Gelsil glass that has nanopores of 2.5 nm in diameter. The heat capacity has a broad peak at a temperature far above the superfluid transition temperature obtained by torsional oscillator technique. The heat-capacity peak is attributed to formation of localized Bose-Einstein Condensates in the nanopores, in which the long-range superfluid coherence is destroyed by pore size distribution or random potential inherent to the porous glass.      

Simultaneous Measurement of Torsional Oscillator and?NMR in Solid 4He with 10?ppm of 3He

We have performed the simultaneous measurement of torsional oscillator and NMR in solid ⁴He with 10 ppm of ³He at 3.6 MPa. In this solid, NCRI response appears below about 400 mK. NMR measurement shows that there is the same kind of phase-separated ³He cluster which is found in our previous measurement in solid ⁴He with over a hundred ppm of ³He. When we warm the solid above the phase separation temperature, the cluster disappears gradually. Below and above the phase separation temperature, the distribution of ³He atoms changes significantly with long time constant, which is as long as a day. However, even in such a long time span, we do not observe any systematic changes in the torsional oscillator response. This result suggests that the phase separation and related changes of the distribution of ³He is not directly related to the impurity effect of the NCRI response.     

Study of a Helium Film in 10 μm Porous Glass by Torsional Oscillator in Free Decay Mode

Dissipation and superfluid density of a thin helium film (superfluid transition at temperature T_c=0.88 K), placed in 10 m porous glass are studied as a function of oscillation amplitude or AC amplitude at fixed temperatures near superfluid transition. The measurements are performed using a high-Q torsional oscillator in the free decay mode as well as constant drive mode. Results show decreasing superfluid density with increasing velocity and non-monotonic behavior of the dissipation in the film.     

Transition to Turbulence for a Quartz Tuning Fork in Superfluid 4He

We have studied the resonance of a commercial quartz tuning fork immersed in superfluid ⁴He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution “turbulent drag”. The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.     

A Novel Design of a Low Temperature Preamplifier for Pulsed NMR Experiments of Dilute 3He in Solid 4He

Recent experimental studies of solid ⁴He indicate a strong correlation between the crystal defects and the onset of a possible supersolid state. We use pulsed NMR techniques to explore the quantum dynamics of the ³He impurities in the solid ⁴He in order to examine certain theoretical models that describe how the disordered states are related to supersolidity. Because of the very small signal-to-noise ratio at low ³He concentration and the long spin-lattice relaxation time (T ₁), it is essential to significantly enhance the NMR sensitivity to be able to carry out the experiments. Here we present the design of a novel low temperature preamplifier which is built with a low noise pseudomorphic HEMT transistor that is embedded into a cross-coil NMR probe. With a low power dissipation of about 0.7 mW, the preamplifier is capable of providing a power gain of 30 dB. By deploying the preamplifier near the NMR coil below 4 K, the noise temperature of the receiver is reduced to approximately 1 K. This preamplifier design also has the potential to be adapted into a low temperature amplifier with both input and output impedance at 50 Ω or a low temperature oscillator.     

Particles-Vortex Interactions and Flow Visualization in 4He

Recent experiments have demonstrated a remarkable progress in implementing and use of the Particle Image Velocimetry (PIV) and particle tracking techniques for the study of turbulence in ⁴He. However, an interpretation of the experimental data in the superfluid phase requires understanding how the motion of tracer particles is affected by the two components, the viscous normal fluid and the inviscid superfluid. Of a particular importance is the problem of particle interactions with quantized vortex lines which may not only strongly affect the particle motion, but, under certain conditions, may even trap particles on quantized vortex cores. The article reviews recent theoretical, numerical, and experimental results in this rapidly developing area of research, putting critically together recent results, and solving apparent inconsistencies. Also discussed is a closely related technique of detection of quantized vortices by negative ion bubbles in ⁴He.     

Transverse Acoustic Impedance Measurements for Surface States of Superfluid 3He A1 and A2 Phases

We measured the complex transverse acoustic impedance in both superfluid ³He A₁ and A₂ phases. This impedance is sensitive to surface states. In our preliminary results, the temperature dependence of the impedance in the A₁ phase is similar to that in A phase, and the imaginary part shows an anomaly in the A₂ phase. These anomalies occurred at the temperature defined as T _k , which is lower as the frequency gets higher. The similar frequency dependence of T _k in each phase suggests that the anomaly is attributed to the same origin. The frequency dependence of the T _k /T _c indicates that the shape of the surface density of each spin pair state did not greatly change in the present experimental temperature range.     

Statistics of Intermittent Switching between Potential Flow and Turbulence around an Oscillating Sphere in Superfluid 4He below 0.5 K

The flow of superfluid helium at very low temperatures around an oscillating microsphere is known to be unstable slightly above the critical velocity. The flow pattern switches intermittently between potential flow and turbulence. From time series recorded at constant temperature and driving force the statistical properties of the switching phenomenon are discussed. Based on our recent understanding of the critical velocity v _c of oscillatory superflows, i.e., $v_{c}\sim \sqrt{\kappa\,\omega}$ , where κ is the circulation quantum and ω is the oscillation frequency, the analysis is being refined now. From the exponential distribution of the lifetimes of the turbulent phases quantitative information on the vortex density L can be inferred such as the distribution and the width of the fluctuations of L. The phases of potential flow show a Rayleigh distribution of the excess oscillation amplitude above the amplitude at turbulent flow. The rms value is found to scale as ω ^?3/2.     

History Dependence of Turbulence Generated by a Vibrating Wire in Superfluid 4He at 1.5 K

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.     

The Transition to Turbulent Drag for a Cylinder Oscillating in Superfluid 4He: A Comparison of Quantum and Classical Behavior

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.     

Infrared Absorption and Emission Spectrum of Electron Bubbles Attached to Linear Vortices in Liquid 4He

Within finite-range density-functional theory, we have addressed the infrared absorption and emission spectrum of electron bubbles attached to linear vortices in liquid ⁴He as a function of pressure. We have found that the presence of vortices affects very little the absorption spectrum, only causing a small shift in the 1s→2p peak. The energy of the lowest emission transition is also shown as a function of pressure for a vortex-free bubble and for a trapped bubble. In the emission energy the shift induced by the vortex line is proportionally bigger, especially when the waist around the electron probability density of the 1p state collapses, which happens at a pressure of ～8 bar.     

Observation of Zero-Sound at Atomic Wave-Vectors in a Monolayer of Liquid 3He

The elementary excitations of a strongly interacting two-dimensional Fermi liquid have been investigated by inelastic neutron scattering in an experimental model system: a monolayer of liquid ³He adsorbed on graphite preplated by a monolayer of solid ⁴He. We observed for the first time the particle-hole excitations characterizing the Fermi liquid state of two-dimensional liquid ³He, and we were also able to identify the highly interesting zero-sound collective mode above a particle-hole band. Contrarily to bulk ³He, at low wave-vectors this mode lies very close to the particle-hole band. At intermediate wave-vectors, the collective mode enters the particle-hole band, where it is strongly broadened by Landau damping. At high wave-vectors, where the Landau theory is not applicable, the zero-sound collective mode reappears beyond the particle-hole band as a well defined excitation, with a dispersion relation quite similar to that of superfluid ⁴He. This spectacular effect is observed for the first time in a Fermi liquid (including plasmon excitations in electronic systems).     

Coupled Dynamics for Superfluid $$^4\hbox {He}$$ in a Channel

We study the coupled dynamics of normal and superfluid components of superfluid \(^4\hbox {He}\) in a channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case where the dynamic of the normal component is “frozen.” We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore, coupling becomes stronger. The commonly measured flow properties also change when the coupling between the two components is taken into account.     

Sound Velocity Measurements in the Low and the High Field Phases of the Nuclear-Ordered bcc Solid 3He in Magnetic Fields

We have measured the temperature and magnetic-field dependences of the sound velocity for one longitudinal and two transverse waves in the low field phase (LFP) and the high field phase (HFP) of nuclear spin ordered bcc solid ³He crystals with a single magnetic domain along the melting curve. From sound velocity measurements for various crystal orientations as a function of the sound propagation direction, we determined the elastic stiffness constants, c _ij (T,B). In the LFP with tetragonal symmetry for the nuclear spin structure, we extracted six nuclear spin elastic stiffness constants Δc _ij ^ℓ (T,0.06 T) from the temperature dependence of the sound velocity at 0.06 T and Δc _ij ^ℓ (0.5 mK,B) from the magnetic-field dependence of sound velocity at 0.5 mK. In the HFP with cubic symmetry for the nuclear spin structure, we extracted three Δc _ij ^h (T,0.50 T) at 0.50 T and Δc _ij ^h (0.5 mK,B) at 0.5 mK. At the first-order magnetic phase transition from the LFP to the HFP at the lower critical field B _c1, large jumps in sound velocities were observed for various crystal directions and we extracted three . Using the thermodynamic relation between Δc _ij and the change in the internal energy for the exchange interaction in this system, ΔU _ex(T,B), Δc _ij are related to the generalized second-order Grüneisen constants Γ _ij ^X ≡∂ ²ln X/∂ ε _i ∂ ε _j as Δc _ij (T,B)=Γ _ij ^X ΔU _ex(T,B), where X represents some physical quantity which depends on the molar volume and ε _j is the j-th component of a strain tensor. In the LFP, the Δc _ij ^ℓ (T,0.06 T) were proportional to T ⁴, and Δc _ij ^ℓ (0.5 mK,B) were proportional to B ². We extracted for the spin wave velocity in the LFP, s ^ℓ , from Δc _ij ^ℓ (T,0.06 T) and for the inverse susceptibility, 1/χ ^ℓ from Δc _ij ^ℓ (0.5 mK,B). In the HFP, Δc _ij ^h (T,0.50 T) were proportional to T ⁴ and Δc _ij ^h (0.5 mK,ΔB) were proportional to ΔB(≡B−B _c1). We obtained for the spin wave velocity in the HFP, s ^h , from Δc _ij ^h (T,0.50 T) and for B _c1 from Δc _ij ^h (0.5 mK,ΔB). The values obtained for and were compared with the Multiple Spin Exchange model (MSE) with three parameters by using analytic expressions for s ^ℓ and χ ^ℓ . The three-parameter MSE does not agree with the observed Δc _ij in the LFP.      

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

Measurements of the A ⇄ B transition in a magnetic field for superfluid3He near the polycritical point

Measurements of both AB and BA transitions have been made as a function of magnetic field up to 100 G at temperatures and pressures close to the polycritical point (PCP). Forms for the specific heat differenceC _A–C _B=C ₀ (P)–(P)(T _c –T)/T _c and for the magnetization differenceM _A–M _B=H(T _c –T)/T _c fit the data satisfactorily except very nearT _c , where some other mechanism, thought to be a free energy difference due to residual heat flows, tends to stabilize the A phase. The pressure of the PCP, taken to be that at whichC ₀ =0, is found to be 21.22±0.02 bar.Work supported by the U.S. Energy Research and Development Administration under contract number E(04-3)-34, P.A. 143.     

Instability of Quantized Vortices Attached to Oscillating Boundaries in Superfluid 4He

The motion of quantized vortices is studied using a vibrating wire in superfluid ⁴He. A vortex filtering method provides a superfluid practically free of remanent vortices in which the vibration of a wire cannot generate turbulence. Vortex lines are produced by cooling through the superfluid transition and remain forming bridges between a wire and a surrounding wall. Bridged remanent vortices increase the resonance frequency of a vibrating wire: the rate of an increase due to the remanent vortices is constant in a laminar flow regime and steeply increases in a turbulent flow regime with increasing wire velocity. These results suggest that oscillation of the bridged vortices provides a linear contribution to the wire vibration in the laminar flow regime, until instability occurs in the oscillation of the vortices, causing turbulence.      

Developed Capillary Turbulence on the Surface of Normal and Superfluid 4He

The capillary turbulence on the surface of normal and superfluid liquid ⁴He has been studied experimentally. It is observed for the first time that the value of the high-frequency boundary ω _b of the inertial interval increases significantly when liquid helium transits from normal to superfluid state, and that in superfluid He-II the correlation function of the surface deviation from equilibrium state in frequency representation can be described well by a power dependence with the index m close to −4.3.      

Decay of Turbulence Generated by Spin-Down to Rest in Superfluid 4He

We report on the extension of the experiments (P.M. Walmsley et al., Phys. Rev. Lett. 99:265302, 2007) on the decay of quasiclassical turbulence generated by an impulsive spin-down from angular velocity Ω to rest of superfluid ⁴He in a cubic container at temperatures 0.15 K–1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Following the spin-down, the maximal density of vortices is observed after time t～10Ω^?1. By observing the propagation of ions along the axis of the initial rotation, the transient dynamics of the turbulence spreading from the perimeter of the container into its central region is investigated. Nearly homogeneous turbulence develops after time t～100Ω^?1 and decays as L ∝ t ^?3/2. The effective kinematic viscosity in T=0 limit is ν=0.003κ, where κ=10^?3 cm²?s^?1 is the circulation quantum.     

Development and Characterization of Microcalorimeters for a Next Generation 187Re Beta-Decay Experiment

It has been demonstrated in the past that observing the β-decay spectrum of ¹⁸⁷Re with microbolometers provides a suitable method to determine the mass of the electron anti-neutrino from β-endpoint measurements. In a first step, with the experiment MIBETA a sensitivity of m _νe≤15 eV/c² was achieved. To compete with the sensitivity of m _νe≤2.2 eV/c² established by the Mainz/Troitsk tritium β-decay experiment and the limit of m _νe≤0.2 eV/c² aimed at with KATRIN, a new experiment MARE has been initiated. As a first stage (MARE-1), 300 detectors consisting of silicon implanted thermistors, produced by NASA/GSFC, and absorbers of AgReO₄ crystals will be mounted. To optimize the experimental setup, a test array was equipped with 10 AgReO₄ crystals of various size and shape. The influence of the crystal quality as well as of different types of resin on rise time and energy resolution was investigated.