4He in Nano-porous Media: Superfluidity and Quantum Phase Transition

This paper reviews recent findings of novel phenomena in ⁴He confined to a nano-porous glass. We examined pressure–temperature (P-T) phase diagram of ⁴He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter, by torsional oscillator and pressure studies. The obtained phase diagram is fairly unprecedented the superfluid transition temperature approaches zero at 3.4 MPa, and a novel nonsuperfluid phase exists between the superfluid and solid phase. These observations indicate that the confined ⁴He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. We propose that the nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the ⁴He atoms or by a random potential. ⁴He in nanospace is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential.     

Thermal Effects on the Microscopic Properties of 4He Drops

We present path integral Monte Carlo results of small ⁴He drops at very low temperatures around the transition temperature to the normal phase. The results obtained are compared with the ones obtained at zero temperature using the diffusion Monte Carlo method. The analysis is carried out for drops of different size and it is focused on the determination of their energetic and structural properties. Particular emphasis is devoted to the temperature dependence of the density profile, mainly to determine if any sign of the λ-transition could be observed on them.     

Energy transfer and phase slip by quantum vortex motion in superfluid4He

The purpose of the present article is to emphasize the usefulness of the ideas of E. R. Huggins in thinking about vortex motion and phase slip in superfluid⁴He, and is primarily pedagogical. Several explicit illustrations of vortex motion and phase-slip processes are considered. In addition, it is shown that Huggins's results lead to a generalization and a more complete understanding of the familiar expression E+v_s · p for the energy in the rest system of an excitation in the flowing superfluid, as applied to vortex excitations. Here, E is the energy and p is the momentum of the excitation in the moving system, and v_s is the superfluid velocity.     

Comparison between Torsional Oscillator and Ultrasonic Measurements of 4He Confined in Nano-Porous Media

We have performed torsional oscillator and ultrasonic measurements for ⁴He confined in 2D nano-porous substrate, hectorite. For ⁴He films, the resonance frequency of the torsional oscillator increases rapidly just below a superfluid transition temperature (T _C ), and then becomes constant at the lower temperature. In contrast, the sound velocity below T _C increases monotonically with decreasing temperature. For liquid ⁴He the sound velocity has a small bend at T _b of about 0.9 K. Its increase below T _b is enhanced as the pressure is increased.     

Torsional Oscillator Measurements of Liquid 4He Confined in 2.2-nm Channels of FSM

We have performed torsional oscillator measurements for liquid ⁴He confined in 2.2-nm channels of FSM up to 2.45 MPa. At 0.1 MPa, the resonant frequency increases with decreasing temperature. It shows a small bend at about 0.9 K, and then keeps increasing down to the lowest temperature, 0.16 K. The magnitude of the frequency increase below 0.9 K is suppressed with increasing pressure, while the temperature of the bend shows almost no pressure dependence.      

Low Frequency Elastic Measurements on Solid ^{4}He in Vycor Using a Torsional Oscillator

Torsional oscillator (TO) experiments involving solid \(^{4}\) He confined in the nanoscale pores of Vycor glass showed anomalous frequency changes at temperatures below 200 mK. These were initially attributed to decoupling of some of the helium’s mass from the oscillator, the expected signature of a supersolid. However, these and similar anomalous effects seen with bulk \(^{4}\) He now appear to be artifacts arising from large shear modulus changes when mobile dislocations are pinned by \(^{3}\) He impurities. We have used a TO technique to directly measure the shear modulus of the solid \(^{4}\) He/Vycor system at a frequency (1.2 kHz) comparable to that used in previous TO experiments. The shear modulus increases gradually as the TO is cooled from 1 K to 20 mK. We attribute the gradual modulus change to the freezing out of thermally activated relaxation processes in the solid helium. The absence of rapid changes below 200 mK is expected since mobile dislocations could not exist in pores as small as those of Vycor. Our results support the interpretation of a recent TO experiment that showed no anomaly when elastic effects in bulk helium were eliminated by ensuring that there were no gaps around the Vycor sample.     

Experiments on the Vortex Dynamics in Superfluid 4He with no Normal Component

We report results from ongoing experiments on the dynamics of quantized vortices in superfluid ⁴He at temperatures below 0.2 K. Charged vortex rings of micron size were used to detect the presence of vortices, to create a turbulent tangle, and to charge an array of rectilinear vortex lines. The results reveal that the ion technique has great potential for the study of vortices in ⁴He at very low temperatures.     

Nonlinear Second Sound Waves and Acoustic Turbulence in Superfluid 4He

The preliminary results of an investigation of nonlinear second sound waves in a high quality resonator filled with superfluid ⁴He are presented and discussed. It is found that, for a sufficiently strong periodic driving force, a cascade of second sound waves is formed at multiple harmonics of the driving frequency over the extremely wide frequency range 1–100 kHz. It can be described by a power law A _ω =const.×ω ^−m , where the scaling index m≈1. These observation can be attributed to the formation of a Kolmogorov-like turbulent cascade in the system of second sound waves, accompanied by directed energy flux through the frequency scales. It manifests itself as a limiting of the amplitude of a standing wave, a distortion of the shape of the initially harmonic waves, and a reduction of the effective quality factor Q of the resonator.     

Logarithmic Singularity of Specific Heat in Liquid Helium II at the λ Point

The experimental width of the second sound peak in Brillouin scattering is less than the instrumental width. It is also less than the width of the first sound peak near the λ point. The theoretical width of the second sound peak becomes infinitely large at the λ point in the traditional viewpoint. This discrepancy suggests that the second sound peak detected in Brillouin scattering is an elementary excitation. We calculate the specific heat of liquid helium near the λ point by considering the second sound peak. The calculated temperature-dependence of the specific heat has a logarithmic divergence at the λ point. Furthermore, the calculated values of the specific heat agree well with data derived from experiments.     

Simultaneous Measurement of Torsional Oscillation and Ultrasound Propagation in Solid 4He at Low Temperatures

Preliminary results of simultaneous measurements of 10 MHz longitudinal ultrasound propagation in solid ⁴He loaded onto torsional oscillator (TO) are reported. Temperature dependence of sound velocity and attenuation and that of amplitude and frequency of TO are measured. The properties of dislocation lines present in the solid samples are extracted from the ultrasound data and are compared with the shifts in TO frequency below 100 mK.     

Double Torsional Oscillator Measurements for 4He Confined in 1D Nano-porous Medium FSM16 with a 2.8-nm Channel

We have studied the frequency dependence of superfluid response for ⁴He confined in a one-dimension nano-porous medium, FSM16, with 2.8-nm channel. The measurements were performed for an identical sample at two frequencies of 2000 and 500 Hz, by means of a double torsional oscillator. It was made clear that the rapid growth of superfluid response for the low frequency mode occurs at several tens mK lower than those for the high frequency mode. The difference between the two frequency modes is enhanced by the application of pressure. The observed frequency dependence suggests a dynamical superfluid peculiar to one dimension.     

Boson Number in Bose–Einstein Condensate of Liquid Helium Near the λ Point

Bose–Einstein condensation has been well investigated in dilute atomic gases. For liquid helium system, the superfluid component is considered to be a background flow in the Landau theory. We study the relation between Bose–Einstein condensate and superfluid component. The concept of dressed bosons is introduced, which are eigenstates of the total Hamiltonian. The total energy is the sum of the kinetic energy of the center of mass and Galilean invariant terms. Therefore, the energy of the dressed boson has a nonlinear form for their number distribution function. If it is required that the excitation energy of a dressed boson be in agreement with the elementary excitation energy of the Landau theory near 0.0 K, then the functional form of the dressed boson energy can be determined. Because of this functional form, the dressed bosons with zero momentum have no friction against a vessel only in existence of a Bose–Einstein condensate. Consequently, the condensate of the dressed bosons with zero momentum is the superfluid component. The number n ₀ of dressed bosons with zero momentum is calculated. It shows temperature dependence (1−(T/T _λ ))^1/3 near the λ point, where T is the temperature and T _λ is the λ transition temperature.     

Visual Observation of a Sound-Induced Bubble in Liquid 3He–4He Mixtures

We report visual observation of a sound-induced bubble in superfluid ³He–⁴He liquid mixtures using a high-speed camera at a rate of 1 msec/frame. The experiments were performed in the ³He dilute phase of phase-separated mixtures at 300 mK. The resonant frequency of the piezoelectric transducer was 9.36 MHz and the diameter of the active electrode was about 4 mm. When an acoustic wave pulse of sufficient magnitude was applied to the dilute phase from the transducer under saturated vapor pressure, a single bubble was nucleated on the active area. The bubble expanded almost spherically on the transducer, as it reached maximum size, it started shrinking, detached from the transducer, and collapsed. We also investigated the motion of the bubble in mixtures with a ³He concentration of 25% at 750 mK. In this case, the bubble grew elliptically on the transducer and detached from it without much change in shape.     

Anomalous Response of 4He Confined in Nanoporous Media to Torsional Oscillation

The existence of “Non-Classical Rotational Inertia (NCRI)” in solid ⁴He below 0.2?K has been controversial and interpreted by a number of different theories. We report on torsional oscillator measurements for ⁴He in a nanoporous Gelsil glass, which has a network of nanopores with 3.5?nm in diameter. In addition to the usual “low-T NCRI” with an onset temperature 0.15?K, we find a larger decrease in rotational moment of inertia in a broad range of temperature from 0.2 to 1.9?K. This “high-T inertial anomaly” is accompanied with multiple dissipation peaks, but has no dependence on torsional oscillation velocity unlike the low-T NCRI. Since the high-T anomaly is observed also in confined liquid states, it originates in amorphous solid ⁴He layer near the pore wall. Our result shows that different types of supersolid—like phenomena, i.e. inertial anomalies, can coexist in a single ⁴He sample, even with genuine superfluidity of liquid ⁴He.     

Measurements of Torsional Oscillations and Thermal Conductivity in Solid 4He

Polycrystalline samples of hcp ⁴He of molar volume 19.5?cm³ with small amount of ³He impurities were grown in an annular container by the blocked-capillary method. Three concentrations of ³He, x ₃, were studied: isotopically purified ⁴He with the estimated x ₃≤10^?10, ‘well-grade’ helium with x ₃～3×10^?7 and a specially prepared mixture with x ₃=2.5×10^?6. The torsional oscillator response and thermal conductivity were investigated before and after annealing. The temperature and width of the torsional anomaly increase with increasing x ₃. Annealing resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them; this implies that these two properties are controlled by different types of crystal defects. It seems plausible that the mean free path of thermal phonos at ～200?mK is controlled by vibrating dislocations while the magnitude of the frequency shift of torsional oscillations is governed by static defects such as pinned dislocations and grain boundaries.     

Transverse Ultrasound Measurements in 4He Single Crystals

Recently, Kim and Chan (Science 305:1941, 2004; Phys. Rev. Lett. 97:115302, 2006) have reported an anomalous decoupling transition of solid ⁴He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of ⁴He. The detailed nature and properties of such a “supersolid” state in ⁴He are still far from being clear, although there are clues from experiments involving ³He impurities, different sample cell geometries, annealing effects and grain boundary flow. Defects produced during crystal growth or deformation (e.g. dislocations) may affect supersolidity, or even produce it, and they are expected to have significant impact on the elastic properties of the solid. The supersolid fraction could also decouple from the lattice and produce a decrease in the transverse sound speed. We have begun the experiments in this laboratory to study such effects, measuring the velocity and attenuation of transverse ultrasound at 10 MHz in ⁴He single crystals grown at constant pressure.      

Switching Phenomena between Laminar and Turbulent Flows of Superfluid 4He Generated by a Vibrating Wire

We have investigated the turbulence transition of the superfluid ⁴He flow generated by a vibrating wire. For a 1.2-kHz vibrating wire, we observed intermittent switchings between laminar and turbulent flows. The switching rate decreases with increasing temperature above 100 mK, until no occurrence of the switchings at 350 mK. For a 2.4-kHz vibrating wire, we find that the switching rate is much lower than that of the 1.2-kHz vibrating wire even at low temperatures. This result indicates that a mechanism causing the switchings is influenced by the temperature and the oscillation frequency of the superfluid flow.     

Experiments on the Self-Organized Critical State of 4He

When a heat flux Q is applied downward through a sample of ⁴He near the lambda transition, the helium self organizes such that the gradient in temperature matches the gravity-induced gradient in T _λ . All the helium in the sample is then at the same reduced temperature and the helium is said to be in the Self-Organized Critical (SOC) state. We have made the first measurements of the ⁴He SOC state specific heat, C _{∇ T} (T(Q)). There is no measurable difference between C _{∇ T} and the static zero-gravity ⁴He specific heat for temperatures between 650 and 250 nK below T _λ . Closer to T _λ , the specific heat is depressed and reaches a maximum value at 50 nK below T _λ . This depression is similar to that predicted theoretically as reported by R. Haussmann (Phys. Rev. B 60, 12349, 1999). Contrary to the expectations of theory, however, we see another depression far below T _λ . In addition, over the heat flux range of 30 nW/cm² to 13 μW/cm², we have made improved measurements of the speed of a recently discovered propagating thermal mode, which travels only upstream against the nominal heat flux of the SOC state. We are able to accurately predict the speed of this wave by treating the helium of SOC state as a traditional fluid with a temperature dependent thermal conductivity.     

Homogeneous Nucleation of 4He Crystals by Acoustic Waves

We have recently found experimental evidence for the homogeneous nucleation of crystals in metastable liquid ⁴He at high pressure. For this we combined the focusing of a high intensity spherical acoustic wave with a simple light scattering technique. We discuss the analysis used to distinguish between nucleation of bubbles in the negative pressure swings of the wave from nucleation of crystals in the positive swings. We also discuss the interest of our results and future developments of our experiment in the general context of the study of nucleation and instability limits in phase diagrams.