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.     

Scattering of 3He and 4He Atoms from 4He Clusters

We develop a microscopic theory of elastic and inelastic scattering and sticking of ³ He and ⁴ He atoms impinging on superfluid ⁴ He clusters. A number of essential aspects must be observed in a physically meaningful and reliable theory of such scattering processes. These are all connected with multiparticle processes, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying excitations which is manifested in a finite imaginary part of the self energy, (b) the interaction with roton–like excitations and the broadening of the roton minimum due to finite–size effects, and (c) the discreteness of low–lying excitations in helium clusters.     

Decay of Counterflow Quantum Turbulence in Superfluid 4He

We have simulated the decay of thermal counterflow quantum turbulence from a statistically steady state at T=1.9 K, with the assumption that the normal fluid is at rest during the decay. The results are consistent with the predictions of the Vinen equation (in essence the vortex line density decays as t ^?1). For the statistically steady state, we determine the parameter c ₂, which connects the curvature of the vortex lines and the mean separation of vortices. A formula connecting the parameter χ ₂ of the Vinen equation with c ₂ is shown to agree with the results of the simulations. Disagreement with experiment is discussed briefly.     

Quantum Statistics of Three-Dimensional Vortex Filament in Superfluid 4He

The quantum statistics of three-dimensional vortex filament in superfluid ⁴ He is investigated by the use of path integral techniques. The free energy evaluated in the saddle point approximation decreases abruptly at a certain critical value of the applied superflow velocity. This critical behavior is in quantitative agreement with the experimental result of vortex nucleation by a moving ion. The dissipation effects are also discussed within the damped harmonic oscillator approximation.     

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.     

Scattering of Elementary Excitations at the Surface of Superfluid 4He

We study the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He. We calculate the evaporation, condensation and reflection probabilities in the framework of linearized time dependent density functional theory accounting for elastic one-to-one processes. We explore the angular dependence of the scattering probabilities showing that most results are independent of the incidence angle and can be expressed in terms of a single energy dependent parameter.     

The Effect of Roton Backflow on Quantum Evaporation from Superfluid 4He

We investigate the effect of roton backflow on the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He at T=0 K by including backflow semi-phenomenologically in the form of a backflow potential in the theory of Sobnack et al. [M. B. Sobnack, J. C. Inkson, and J. C. H. Fung, Phys. Rev. B 60, 3465 (1999)]. We assume that all the surface scattering processes are elastic and that the quasiparticles and atoms are incident obliquely to the free surface. We calculate probabilities for the various one-to-one surface scattering processes allowed for a range of energies and compare the scattering rates with those obtained when backflow is neglected.     

The Energy Dependence of Roton Quantum Evaporation from Superfluid 4He

We have measured the energy dependence of roton quantum evaporation. A transiently heated cavity filled with superfluid ⁴ He generates R⁺ and R^– rotons. The emitted rotons are collimated and arrive at the free liquid surface with a narrow range of incident angles. We detect two beams of evaporated atoms, one due to R⁺ rotons and the other due to R^– rotons. Our numerical simulation of roton and atom trajectories, using an evaporation probability of 1, yields two angular distributions of atom flux which are similar to our experimental results, but do have systematic differences which we attribute to the evaporation probability. The ratio of the observed signal to the computed value at each bolometer position gives the relative roton quantum evaporation probability as a function of roton energy. We find that this probability increases with roton energy, except perhaps for low energy R^– rotons. We compare these results with theoretical predictions.     

Superfluid 3He Confined in a Single 0.6 Micron Slab

We present the preliminary results of our studies of superfluid ³He in a 0.6 μm thick slab using NMR. Below T _c the A phase is observed, and at low pressures the region of stability of the A phase extends down to the lowest temperatures reached, as described elsewhere. At pressures above 3.2 bar another, so far unidentified phase is observed at low temperatures. In this article we focus on the behavior of this phase and the transition between this phase and the A phase, all studied at 5.5 bar. The NMR response at low temperatures exhibits two possible frequency shifts and the transition is hysteretic in temperature.     

Time-of-Flight Measurements of Vortices Emitted from Quantum Turbulence in Superfluid 4He

An oscillating obstacle generates quantum turbulence in superfluids, when vortices remained attached to obstacle surfaces or vortex rings collided with it during oscillation. Turbulence provides a source of vortices; however, the characteristics of these vortices are not clear. In the present work, we report the flight of vortices emitted from quantum turbulence in superfluid ⁴He at low temperatures, using vibrating wires as a generator and a detector of vortices. A vortex-free vibrating wire can detect only the first colliding vortex ring, though it will be refreshed after low vibration and be able to detect a vortex ring again. By measuring a period from the start of turbulence generation to the vortex detection repeatedly, we find an exponential distribution of time-of-flights with a non-detection period t ₀ and a mean detection period t ₁, suggesting a Poisson process. Both periods t ₀ and t ₁ increase with increasing distance between a generator and a detector. A vortex flight velocity estimated from period t ₀ suggests that the sizes of the emitted vortex rings distribute to a range smaller than a generator thickness or a generator vibration amplitude. Vortices are emitted radially from a turbulence region, at least in the direction of oscillator vibration.     

Transition to Quantum Turbulence Generated by Thin Vibrating Wires in Superfluid 4He

We report the turbulent transition in superfluid ⁴He generated by a vibrating wire as a function of its thickness. The response of a vibrating wire with a 3 μm diameter in superfluid ⁴He at 1.2 K reveals a hysteresis at the turbulent transition between an up sweep and a down sweep of driving force, while no hysteresis appears for wires with a thickness larger than 4.7 μm diameter. These results indicate that the 3 μm wire is efficient for reducing the number of vortex lines attached to it. A cover box and slow cooling also prevent vortex lines from attaching to a wire, resulting in a vortex-free vibrating wire. The effective mass of the vortex-free vibrating wire is almost constant in a wide range of velocities up to 400 mm/s; however, the wire density estimated from the resonance frequency is a half of the expected value of wire material, suggesting that a wire mass becomes lighter or a wire diameter becomes larger in the superfluid effectively.     

Faraday Instability on a Free Surface of Superfluid 4He

We observed that the Faraday waves were parametrically generated on a free surface of superfluid ⁴He. Our sample cell was supported by plate springs and had a permanent magnet on the top. It was oscillated by applying oscillating current to a superconducting coil. We prepared the sample cell made of polycarbonate so as to optically observe the superfluid surface. Standing wave patterns appeared on the surface and their frequencies were one half of a driving frequency. We observed clear threshold amplitude of the oscillation for the instability. Threshold is usually determined by the viscosity of fluid and thus there must be a dissipation mechanism in superfluid for the threshold.     

The Vortex Lability In a Supersaturated Superfluid 3 He-4 He Mixture and the Quantum Phase-Separation Kinetics

The supersaturated superfluid ³ He-⁴ He mixture in the presence of quantized vortices is considered. A specific type of the lability against the vortex core expansion arises from concentrating ³ He atoms onto the vortex core. This affects significantly the region of the ³ He concentrations at which the rate of nucleating stable ³ He-concentrated phase can be noticeable. The most clear case of the vortex structure is a straight-line vortex with the uniformly distributed 3He atoms along the core. Such lability leads to some features in the thermal activation and quantum tunneling nucleation, resulting, in particular, in a relatively small supersaturation of about 1% which can be achieved. The critical value of the supersaturations corresponding to the vortex lability is dispersed because of the finite size of the ³ He-concentrated phase along the vortex core. We analyze this dispersion and its effect on the quantum separation in supersaturated ³ He-⁴ He mixtures. The value of the supersaturation conserves its order of the magnitude, changing only by a numerical factor. We also emphasize an important difference of the coefficient in the term responsible for the lability from the superfluid density s. The supersaturation observed in experiments lies within the range of the vortex lability and, probably, is connected with this lability.     

Observation of Anomalously Low Momentum Transfer in the Low Energy Scattering of Large 4He Droplets From 4He and 3He Atoms

The momentum transferred to large superfluid ⁴ He droplets in low energy ( 4–10 K) scattering from ⁴ He and ³ He atoms was determined from time of flight measurements after the droplets have passed through a low temperature (T = 1.7–4.2 K) scattering box filled with the gas of either He isotope. The results are compared with ³ He droplets scattered from either ⁴ He or ³ He gas for which all of the incident momentum is transferred, as expected for classical capture of the scattering gas atoms. In the case of the ⁴ He droplets a smaller momentum transfer is found amounting to 65% for ⁴ He atoms and 45% for ³ He atoms but only at the lowest collision energies. These results are consistent with transmission of some of the atoms through the droplets.     

4He Adsorption and Superfluid Transition on C60

We present adsorption isotherm data of⁴He on C₆₀ for 1.50 K<T<1.68 K determined by measurements of the frequency of quartz crystal microbalances (QCM’s) coated with C₆₀ films. We find a Kosterlitz-Thouless transition with a jump in the areal superfluid density close to predictions. By comparing the adsorbed⁴He on two QCM’s we derive an upper limit for the amount of⁴He intercalated into C₆₀ at low temperature of 0.05⁴He atoms per C₆₀ molecule. The low coverage portion of the adsorption data shows an apparent excess adsorption of⁴He onto the C₆₀.     

Vortex-Loops and Solid Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴He and ³He. Unique to the superfluid phases the solid nucleation involves an extremely fast solidification front. We depart from the usual quasi-static treatment of solid nucleation by proposing that the nucleation of a solid seed is helped by the simultaneous nucleation of vortex-loops in the superfluid around it. It is the composite entity which is nucleated out of the over-pressurized liquid. This occurs when the local release of pressure creates a velocity field in the superfluid which in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with many experiments on heterogeneous nucleation, where the energy barrier is found to differ with the classical theory of homogeneous nucleation by 8 orders of magnitude. We propose several experiments that could show the involvement of vortices with solid nucleation.     

Vortex-Loops and Phase Nucleation in Superfluid 4He and 3He

We propose a new model for the nature of the nucleation of solid from the superfluid phases of ⁴ He and ³ He. A fast solidification event in the superfluid results in a local release of pressure and a velocity field in the superfluid. This in turn facilitates the nucleation of vortex-loops. The kinetic energy gain of this process balances the surface tension, as the solid surface is quickly covered by many vortex-loops (hairy snow-ball). We show that this scenario gives good agreement with experiments on heterogeneous nucleation.     

Coherent Bragg Scattering of Light by a Vortex Lattice in Rotating Superfluid He

Proposed observation of coherent Bragg scattering by a lattice of vortices in uniformly rotating superfulid Helium is examined. We present the calculations of the cross section for different parameter values, as well as simulations of the detected intensity of the Bragg peaks for triangular arrays with varied degrees of distortion. Within this frame, a potentially feasible experiment is outlined to provide direct evidence of vortices with an atomic-scale core in superfluid Helium.     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.