Wigner lattice of ripplopolarons in a multielectron bubble in helium

The properties of ripplonic polarons in a multielectron bubble in liquid helium are investigated on the basis of a path-integral variational method. We find that the two-dimensional electron gas can form deep dimples in the helium surface, or ripplopolarons, to solidify as a Wigner crystal. We derive the experimental conditions of temperature, pressure and number of electrons in the bubble for this phase to be realized. This predicted state is distinct from the usual Wigner lattice of electrons: it melts by dissociation of the ripplopolarons when the electrons shed their localizing dimple as the pressure on the multielectron bubble drops below a critical value. Received 20 February 2003 Published online 11 April 2003 RID="a" ID="a"Also at: TU Eindhoven, Eindhoven, The Netherlands e-mail: devreese@uia.ua.ac.be     

Acoustic modes in 2D atomic hydrogen on the surface of superfluid <Superscript>4</Superscript>He

Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ? 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.     

Ions at helium interfaces

The boundaries between different phases of condensed helium provide an interesting testing ground for studying ions in a quantum matter matrix. Here we consider the simplest positive and negative ions in helium — snowballs and electron bubbles, respectively — being trapped at the liquid-liquid interface of phaseseparated³He–⁴He mixtures and at the liquid-solid interface of⁴He. A comparison of experimental results for the trapping with predictions of the snowball and the bubble models shows that the models are in qualitative accord with the observations, but disagree in detail. It is suggested to use such studies for refinements of the ion models. In addition multielectron bubbles (=mesoscopic ions) and electrons on helium films are briefly discussed.     

Hexatic order and surface ripples in spherical geometries

In flat geometries, two-dimensional hexatic order has only a minor effect on capillary waves on a liquid substrate and on undulation modes in lipid bilayers. However, extended bond-orientational order alters the long-wavelength spectrum of these ripples in spherical geometries. We calculate this frequency shift and suggest that it might be detectable in lipid bilayer vesicles, at the surface of liquid metals, and in multielectron bubbles in liquid helium at low temperatures. Hexatic order also leads to a shift in the threshold for the fission instability induced in the later two systems by an excess of electric charge.     

Atomic and molecular defects in solid He

The studies of defects formed by impurity particles (atoms, molecules, exciplexes, clusters, free electrons, and positive ions) embedded in liquid and solid ⁴He are reviewed. The properties of free electrons and neutral particles in condensed helium are described by the electron (atomic) bubble model, whereas for the positive ions a snowball structure is considered. We compare the properties of the defects in condensed helium with those of metal atoms isolated in heavier rare gas matrices.     

Spectroscopic studies on Yb+ ions in liquid helium

An emission spectrum of the - (D1) transition and excitation spectra of the - (J=1/2 (D1) and 3/2 (D2)) transitions of Yb⁺ ions in liquid helium have been observed by means of a laser-induced fluorescence method. It has been found that all these spectra are blue-shifted from the ones in the free space, and also that the D2 excitation spectrum has double peaks. To understand these spectra, theoretical calculations have also been carried out based on a vibrating bubble model, in which the bubble surface is assumed to vibrate in the spherical (breathing), dipolar and quadrupolar modes. As a result, it has been found that the blue shifts are well understood with this bubble model, and also that the dynamic Jahn-Teller effect due to the quadrupole vibration of the bubble plays an important role for the double-peaked profile of the D2 excitation spectrum. Received 27 December 1999 and Received in final form 31 July 2000     

Universal fault-tolerant quantum computation in the presence of spontaneous emission and collective dephasing

A universal and fault-tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is compatible with a number of promising solid-state and quantum-optical proposals for quantum computer implementations, such as quantum dots in cavities, electrons on helium, and trapped ions.     

Negative Ca− and Ba− ions of large radius on the surface and in the volume of liquid helium

Negative Ca⁻ and Ba⁻ ions of large radii on the surface of and in bulk liquid helium have been studied. Our results indicate that these ions are adsorbed on the helium surface. Ions on free liquid helium surfaces have not been studied previously because it was thought impossible to confine them on the surface. Ca⁻ and Ba⁻ ions have very low binding energies, therefore, like electrons, they form a bubble of large radius in bulk helium, whose energy is higher than on the surface. The behavior of ions on the surface exhibits a number of previously unknown features owing to their large masses and strong localization in the horizontal plane. Even in the absence of confining electric field, a hole is formed under an ion due to the polarization attraction between the liquid helium and the charged ion. This hole formation reduces the ion mobility by several orders of magnitude and increases its effective mass severalfold. The critical density of electrons and ions is approximately the same on the surfaces of thin and thick helium films. Zh. éksp. Teor. Fiz. 115, 593–604 (February 1999)     

Growth mode of helium crystal near dislocations in titanium

The helium bubble structure and growth modes near dislocations in titanium are studied using the molecular dynamics method. A helium crystal with an HCP structure in titanium is found to have a lattice constant of 1.977 A? at 0 K. On either side of the slip plane, helium bubbles form in the(001) plane, but they are in different growth modes. On the side of the slip plane with full atomic layers, helium bubbles grow toward the slip plane and easily cross the slip plane. In the growth process, the position of the top surface of the helium bubble remains almost unchanged. On the other side of the slip plane,the helium bubble grows initially toward the dislocation core, but it is difficult to cross the slip plane, which results in growth in the opposite direction upon reaching the slip plane.     

Condensation of the spin-polarized atomic hydrogen on the superfluid helium

The interaction of the spin-polarized hydrogen atoms in the bulk as well as on the surface of the superfluid helium with the third-sound ripplons is investigated. The dispersion relation is found to show a kink at a particular wave vector at which new quasiparticles appear.     

Cyclotron resonance for electrons over helium in a resonator

The cyclotron resonance (CR) problem for electrons over a helium film occupying the lower part of a resonator is solved. This problem is shown to represent an example of the well-known problem on the behavior of a system of coupled oscillators. For such oscillators, the coupling constant is determined as a function of the problem parameters with its minimal value in zero magnetic field and its maximal value at resonance conditions, when the cyclotron frequency coincides with one of the resonator modes. The details of the CR absorption of microwave energy by the coupled system formed by 2D electrons and a resonator are calculated. The results are discussed in application to the known CR experiments with electrons over helium.     

Nonlinear Evolution of Lower-Hybrid Drift Instability in Harris Current Sheet

We perform 2.5-dimensional particle-in-cell simulations to investigate the nonlinear evolution of the lower hybrid drift instability (LHDI) in Harris current sheet. Due to the drift motion of electrons in the electric field of the excited low hybrid drift (LHD) waves, the electrons accumulate at the outer layer, and therefore there is net positive charge at the inner edge of the current sheet. This redistribution of charge can create an electrostatic field along the z direction, which then modifies the motions of the electrons along the y direction by E×B drift. This effect strongly changes the structure of the current sheet.     

金属表面下氦泡融合与释放研究

采用分子动力学方法研究了钛金属表面下不同深度处氦泡的行为,分析了氦泡融合与释放的竞争,对比了不同深度处氦泡的释放对金属的影响。结果表明：在接近金属表面处,氦泡很难通过融合无限长大,当达到临界尺寸后,氦泡将会释放而不再与邻近的氦泡发生融合;植入深度对氦泡的融合有一定的影响,深度越大,越有利于形成具有较高氦密度的大氦泡;较深处氦泡的释放会在金属表面形成较大的突起和表面针孔。实验中观察到的不同尺寸的表面孔,其部分原因来自于金属表面下不同深度处氦泡的释放。     

温度及深度对钛中氦泡释放过程影响的分子动力学研究

利用分子动力学模拟方法对温度及He泡深度给金属Ti内He泡的体积、压强和释放过程等带来的影响进行了研究. 首先, 通过研究室温下He泡在金属Ti内不同深度处的状态, 得到He泡的形状、压强、体积等物理量随其深度的变化规律. 发现He泡压强随其深度增加逐渐变大, 体积则逐渐减小, 但当He泡深度增大到2.6 nm时, 二者均维持在某个固定值附近. 然后对包含有He泡的Ti体系在温度作用下的演化过程进行了模拟, 发现不同深度处He泡从金属Ti内释放出来所需要的临界温度有很大差别, 总体来看He泡越深, 释放所需的临界温度越高. 但不同温度下He原子的释放速率没有明显差别, 释放过程几乎均为瞬间完成. 最后通过对He泡内部压强和其上方金属Ti薄层的抗张强度进行统计对比, 阐述了金属Ti 体内He泡的释放机制: 当He泡内部压强大于其上方Ti薄层抗张强度时, He泡就会将Ti 薄层撕裂, 从而使He原子得到释放.     

金属表面下氦泡融合与释放研究

采用分子动力学方法研究了钛金属表面下不同深度处氦泡的行为,分析了氦泡融合与释放的竞争,对比了不同深度处氦泡的释放对金属的影响.结果表明:在接近金属表面处,氦泡很难通过融合无限长大,当达到临界尺寸后,氦泡将会释放而不再与邻近的氦泡发生融合;植入深度对氦泡的融合有一定的影响,深度越大,越有利于形成具有较高氦密度的大氦泡;较深处氦泡的释放会在金属表面形成较大的突起和表面针孔.实验中观察到的不同尺寸的表面孔,其部分原因来自于金属表面下不同深度处氦泡的释放.     

Dissipation of ripplon flow at the surface of superfluid <Superscript>4</Superscript>He

Within the framework of quantum hydrodynamics of a superfluid helium surface, the momentum relaxation rate caused by the annihilation of two ripplons with phonon creation, inelastic phonon scattering with ripplon annihilation, and in the case of helium films one-particle ripplon scattering from the surface-level inhomogeneities introduced by the substrate roughness (new relaxation mechanism) was obtained for a ripplon gas at T?0.25 K. The contribution from the inelastic phonon scattering is negligible at these temperatures. For a film at T≤0.15 K, one-particle scattering dominates, leading to a temperature dependence of the form K∝T^5/3 for the convective thermal conductance.At higher temperatures, phonon creation with annihilation of two ripplons is the dominant mechanism, giving K∝T^?3. These results are in quantitative agreement with the available experimental data.     

高应变率拉伸下纯铝中氦泡长大的动力学研究

 分析了高应变率加载下纯铝中氦泡长大的动力学过程,给出了含内压氦泡长大的动力学方程,并且分别研究了氦泡内压、基体材料惯性、粘性、表面张力以及基体环境温度对初始半径为1 nm氦泡长大的影响。研究结果表明：（1）初始内压可以促使氦泡快速长大,当氦泡直径超过1 μm时,内压对氦泡长大的影响可以忽略不计。（2）表面张力在氦泡整个长大过程中的影响都很小。（3）材料惯性对氦泡长大起抑制作用,并且随着氦泡半径的增长,抑制效应越来越明显。（4）在所有因素中,温度对氦泡长大的影响最为明显,温度升高,材料的粘性降低,氦泡的内压增加,促使氦泡加速长大。     

Molecular Dynamics Simulations of Helium Behaviour in Titanium Crystals

Molecular dynamics simulations are performed to investigate the behaviour of helium atoms in titanium at a temperature of 30OK. The nucleation and growth of helium bubble has been simulated up to 50 helium atoms. The approach to simulate the bubble growth is to add helium atoms one by one to the bubble and let the system evolve. The titanium cohesion is based on the tight binding scheme derived from the embedded atom method, and the helium-titanium interaction is characterized by fitted potential in the form of a Lennard-Jones function. The pressure in small helium bubbles is approximately calculated. The simulation results show that the pressure will decrease with the increasing bubble size, while increase with the increasing helium atoms. An analytic function about the quantitative relationship of the pressure with the bubble size and number of helium atoms is also fitted.     

Optimum conditions for pumping laser transitions of cadmium ions by various processes in a hollow-cathode discharge

The interaction of electrons of various energies with helium and cadmium atoms in a hollow-cathode discharge is analyzed. On the basis of the results of this analysis the conclusion is made that helium is ionized predominantly by electrons moving from the cathode wall to the cavity axis and having energies 70<ε<300 eV, whereas helium and cadmium are ionized predominantly by electrons with energies 9<ε<70 eV which move chaotically. For each of these energy ranges, the kinetic equation is solved and the electron energy distribution function (EDF) is determined, which is used for calculating pumping rates for laser transitions of cadmium ions. The conclusion is made that the rate of population of laser transitions through charge transfer is determined by electrons having a predominant direction of motion and an anisotropic EDF. The population rate associated with electron impact and the Penning ionization is determined by electrons moving chaotically and having an isotropic EDF. The analysis of the EDF made it possible to explain differences in discharge conditions (helium and cadmium pressures) providing optimum lasing for lines pumped by different processes. Radial profiles of pump rates obtained from the analysis made it possible to calculate and explain the dependence of the laser output power on the cathode diameter.     

Novel states of electrons on a helium film

Three novel states of electrons on a helium film are described. The first is a diplon, an electron trapped by a positive charge located on a substrate beneath the film, the second is a variation of the first leading to the possibility of a two-dimensional metal-insulator transition, and the third is a ripplonic polaron, an electron self-trapped in a surface dimple. From a survey of experimental searches for the ripplonic polaron state I conclude that no polaron transition occurs on films thicker than 14 nm at T>1.5 K.