The Relaxation of High Energy Phonons in Anisotropic Distributions in Superfluid 4He

Anisotropic distributions of low energy phonons in momentum space, in superfluid helium, create high energy phonons with energy /k _B>10K. It has been shown that phonons with /k _B>11K cannot decay by the inverse of the process that creates them, if the low energy phonons are in such a momentum cone of 11°. Here we investigate other possible phonon scattering processes that could annihilate high energy phonons. We find that interactions between two high energy phonons, which can create one low and one high energy phonon, is effective. We calculate the scattering rates for all the four phonon processes as functions of momentum of the high energy phonon, cone angle and the temperature of the low energy phonons. We obtain analytic results from which we can understand the physical reasons for all the functional dependencies. The analytic results are in good agreement with our computer evaluations. We show that a dynamic equilibrium number of high energy phonons can be established in a propagating pulse of phonons and the distribution will be suprathermal.     

Superfluid Transition of a 4He Thin Film Pressurized by Bulk Liquid 3He

We measured transverse acoustic impedance Z of normal fluid ³He at 46.6 MHz on a surface coated with a thin ⁴He film. The real component of the impedance, Z′, in the coated samples deviates from Z′ in the pure ³He in the low temperature region. Z′ on the coated samples is almost identical with Z′ in the pure sample at high temperature and gradually deviates below a particular temperature T _onset . T _onset  is possibly the superfluid onset temperature of the ⁴He film pressurized by the bulk liquid ³He. The gradual decrease in Z′ means that the superfluid component in ⁴He film increases gradually, which is expected from the dynamic KT transition at high frequency. The thicker is the film, the higher is the T _onset . The range of T _onset we observed was between 40 and 160 mK. This is much lower than that at the saturated vapor pressure. Suppression of T _onset achieved by the applied pressure from bulk liquid ³He was presumably caused by the dissolved ³He in the film, thickening of the inert layers and/or by the strong correlation effect. The result shows that the specularity of ³He quasiparticle scattering is strongly affected by superfluidity of the ⁴He film.     

Diffusion Monte Carlo for Excited States: Phonons and Rotons in Superfluid 4He

We have applied the fixed-node and the released-node Monte Carlo techniques to calculate the phonon-roton excitation spectrum ((q)) of superfluid ⁴ He. An excellent agreement with the experimental spectrum is achieved both at the equilibrium and near the freezing densities. The strength of the single excitation peak Z(q) in the dynamic structure function S(q, ) shows an overall agreement with experimental data. New results for (q) and Z(q) at a negative pressure close to the spinodal point are also reported.     

Phonons Created in Superfluid Helium by a Thin Film Gold Heater

We show that a thin film gold heater, on polished sapphire, radiates phonons into liquid helium by both the acoustic and background channels. To analyse the measured angular distributions of phonons, at a pressure of 24 bar, we derive an expression for the phonon flux incident on a detector for a general spatial arrangement of heater and detector, when the phonons travel ballistically. We then develop an expression for the particular geometry of the experiments. We find that most of the energy flux, from the heater to the liquid helium, is transmitted by the background channel and this fraction increases with heater power. We discuss the implications for the Kapitza conductance problem.     

Quantum Evaporation from Superfluid 4He

The quantum evaporation experiments of Brown and Wyatt ² have been re-analysed in the light of a recent measurement of the high-energy phonon spectrum created by a pulse-heated thin film ¹⁰ . Two sources of systematic error become significant at the level of the precision required by this new analysis: firstly, in the detector position which is recalibrated by using large-angle roton evaporation; and secondly, in the liquid height due to capillary action affecting the level-detectors. These effects have been included in an improved simulation of the experiment which has brought the angular dependence of the measured and theoretical phonon-atom evaporation results into agreement within the mechanical tolerances of the apparatus. The reanalysis suggests that the roton-atom evaporation probability increases with wave vector.     

Observations of Vortex Emissions from Superfluid 4He Turbulence at High Temperatures

An immersed object with high velocity oscillations causes quantum turbulence in superfluid ⁴He, even at very low temperatures. The continuously generated turbulence may emit vortex rings from a turbulent region. In the present work, we report vortex emissions from quantum turbulence in superfluid ⁴He at high temperatures, by using three vibrating wires as a turbulence generator and vortex detectors. Two detector wires were mounted beside a generator wire: one in parallel and the other in perpendicular to the oscillation direction of the generator. The detection times of vortex rings represent an exponential distribution with a delay time t ₀ and a mean detection period t ₁. The delay time includes the generation time of a fully developed turbulence and the time-of-flight of a vortex ring. At high temperatures, vortices are dissipated by relative motion between a normal fluid component and the vortices, resulting that only large vortex rings are reachable to the detectors. Using this method, we detected vortex rings with a diameter of 100 μm, comparable to a peak-to-peak vibration amplitude of 104 μm of the generator. The large vortices observed here are emitted anisotropically from the generator. The emissions parallel to the vibrating direction are much less than those perpendicular to the direction.     

Lifetimes of Fast R+ Rotons due to Scattering by Thermal Phonons in Superfluid 4He

We have injected R ⁺ rotons into superfluid ⁴ He at low temperatures (0.05K     

The Density of High Energy Phonons Created from a Low Energy Phonon Pulse in Liquid 4He

We calculate the energy density of high energy phonons created from a pulse of low energy phonons spatially confined to a narrow cone. We include the tangential expansion of the propagating pulse and the interactions between high energy phonons within the pulse as well with low energy phonons. The expansion of the pulse causes it to cool so much that the creation of high energy phonons stops within 3 mm of the heater. The decay rate of high energy phonons governs the dynamic equilibrium inside the pulse. The magnitude of the high energy phonons, emitted by the pulse into the cold liquid helium, is calculated for different length pulses. It is found that small heaters can produce short pulses of high energy phonons from relatively long injected pulses.     

Quartz Microbalance Study of Thick 4He Film Near the Superfluid Transition

We present the resugts of a quartz microbalance measurement of a ～440 Å thick ⁴He film adsorbed on Au. This measurement confirms the resugt of an earlier capacitance measurement that showed a dip in the film thickness just below Ta due to the critical Casimir force. The magnitude of the dip in the two measurements agrees within 15% . In addition to the dip, we see a signal due to the onset of superfluidity in the film. An apparent peak in the film thickness, not observed previously, is also found coinciding closely with the bulk T _λ. This extra feature may be due to a sound resonance in the cell associated with the bulk fluid.     

Heat Capacities of Monolayer 3He Fluids Floated on A Superfluid 4He Thin Film

We have measured heat capacities of monolayer ³ He floated on a superfluid ⁴ He thin film (three atomic layers) adsorbed on graphite at low temperatures. The ³ He films behave as degenerate 2D Fermi fluids with m* 1.3m ₃, where m* is the quasiparticle effective mass and m ₃ is the bare mass of ³ He, in the whole temperature range we studied (1 T 80 mK). No anomalous behavior suggesting puddling nor other phase transitions is observed. In contrast to our previous measurements for pure ³ He films without the underlying ⁴ He film, the temperature independent heat-capacity contribution is not observed. This can be explained by the second-layer localized spins trapped on substrate heterogeneities being replaced by nonmagnetic ⁴ He.     

Polarization Effects in Superfluid 4He

A theory of thermoelectric phenomena in superfluid ⁴He is developed. It is found an estimation of the dipole moment of helium atom arising due to electron shell deformation caused by pushing forces from the side of its surrounding atoms. The corresponding electric signal generated in a liquid consisting of electrically neutral atoms by the ordinary sound waves is found extremely small. The second sound waves in superfluid ⁴He generate the polarization of liquid induced by the relative accelerated motion of the superfluid and the normal component. The derived ratio of the amplitudes of temperature and electric polarization potential was proved to be practically temperature independent. Its magnitude is in reasonable correspondence with the experimental observations. The polarity of electric signal is determined by the sign of temperature gradient in accordance with the measurements. The problem of the roton excitations dipole moment is also discussed.     

Acoustic Turbulence in Superfluid 4He

Recent work on nonlinear second sound wave propagation and acoustic turbulence in superfluid ⁴He is reviewed. Observations of direct and inverse turbulent energy cascades are described. The direct cascade arises due to the huge nonlinear dependence of the second sound wave velocity on its amplitude. The flux of energy injected at the driving frequency is transformed via successively higher harmonics until it is eventually attenuated by viscous dissipation at the short wavelength edge of the spectrum. The onset of the inverse cascade occurs above a critical driving energy density, and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomena is outlined and shown to be in good agreement with the experiments.     

Unusual Behavior of a MEMS Resonator in Superfluid 4He

Novel mechanical resonators based on micro-electro-mechanical systems (MEMS) technology were developed for the study of superfluid ⁴He. The MEMS device is composed of two parallel plates, the movable plate suspended by four serpentine springs above the substrate, forming a shear mechanical oscillator. A specific device with a 1.25 μm gap was tested in the superfluid phase of ⁴He. At temperatures below 400 mK the device exhibits nonlinear and hysteretic behavior when the excitation exceeds a threshold. The anomalies are reminiscent of quantum turbulence and vorticity effects observed in other mechanical oscillators such as tuning forks or vibrating grids.     

Experimental Survey of Wetting and Superfluid Onset of 4He on Alkali Metal Surfaces

We present a survey of the wetting behavior of ⁴ He on evaporated films of rubidium, potassium and sodium. ⁴ He wets these surfaces at all temperatures. Off coexistence on rubidium and potassium there is a prewetting transition that is closely coupled with superfluid onset and possibly a surface tricritical point where the prewetting transition and superfluid onset intersect. Sodium has a prewetting critical temperature well below 1 K. Wetting and superfluid onset phase diagrams for ⁴ He on rubidium and potassium are presented and compared with that of ⁴ He on cesium.     

The Wave-Vector Dependence of Quantum Evaporation from Superfluid 4He

Absolute measurements of the probability of quantum evaporation of atoms by rotons from the surface of superfluid ⁴ He are still problematic. However, it is possible to obtain information about the wave-vector dependence of the evaporation process by using a refined simulation ¹⁴ to interpret the experiments of Brown and Wyatt ¹² . Two theories (Guilleumas et al. ⁹ and Sobnack et al. ¹⁰ ) are compared with these experiments by incorporating their predictions for the quantum evaporation probability into a numerical simulation. Both theories over-estimate the probability of phonon-atom evaporation. For roton (R ⁺ –atom) evaporation, compared with a simulation that assumes all kinetically allowed events are equally probable, the theory of Guilleumas et al. does not significantly improve the agreement with experiment, and the theory of Sobnack et al. increases the discrepancy.     

Time-of-Flight Experiments of Vortex Rings Propagating from Turbulent Region of Superfluid 4He at High Temperature

We report the time-of-flight of quantized vortex rings generated by a vibrating wire in superfluid ⁴He which contains normal fluid component. A cover box of vibrating wires and slow cooling of superfluid reduce the number of vortices attached to wire surfaces, enabling us to study vortex rings propagating from a turbulent region. Using two vibrating wires as a generator and a detector of vortices, the time-of-flight of vortices propagating a distance of 0.88 mm was measured at 1.25 K. We find that the time-of-flights distribute from 0.06 s to 27.4 s, much larger than the lifetimes of circular vortex rings limited in the size of a generator amplitude. These results imply that large vortex rings with non-circular shape or vortex tangles are created by the generator, propagating slowly and colliding with the detector before complete disappearance.     

Universal Features of the Superfluid Transition of a Thin 4He Film on an Atomically Flat Substrate

We analyse recent observations, using a torsional oscillator, of the superfluid transition of a fluid ⁴ He bilayer, within the framework of a modified dynamic theory of the Kosterlitz-Thouless transition. A parametric plot of the real and imaginary parts of the complex superfluid density, determined from the measured period shift and dissipation, achieves a high degree of collapse of the experimental data at different coverages onto a universal curve. This is compared with the result of the recent theory.     

Thickness Dependence of Critical Current of Superfluid 3He Film

We have measured the critical current J _c , which is defined as the onset of dissipative flow, for a thickness range from 0.3 to 4 μm using inter-digitated capacitors. In the thickness dependence of J _c , two distinct dissipation regimes were observed. The crossover occurred at a thickness of ∼1 μm.