Phonons In Helium Research Articles

Phonon model of heat radiation into superfluid helium by a solid with a flat surface

This paper reviews the quasiparticle model of superfluid helium and its application to describe heat transfer between a heated solid and superfluid helium. In this case, a problem is considered in which the surface of the heater is flat and the helium is at practically zero temperature. Under these conditions, heat transfer between solid and superfluid helium is determined by the transformation of the phonons of the solid into helium phonons. The work considers certain types of such transformation—elastic processes of phonon transformation, in which the number of phonons is conserved, and inelastic processes, in which the number of phonons changes. The main attention in this work is paid to the development of a quantum-mechanical approach for calculating the contribution of various polarizations phonons of solid to the heat flux formation, its magnitude, and angular distribution. The results of the work are used to explain the experimentally observed features of heat transfer from a heated solid to superfluid helium.

Self-Diffusion in a Spatially Modulated System of Electrons on Helium

We present results of molecular dynamics simulations of the electron system on the surface of liquid helium. The simulations are done for 1600 electrons with periodic boundary conditions. Electron scattering by capillary waves and phonons in helium is explicitly taken into account. We find that the self-diffusion coefficient superlinearly decreases with decreasing temperature. In the free-electron system, it turns to zero essentially discontinuously, which we associate with the liquid-to-solid transition. In contrast, when the system is placed in the fully commensurate one-dimensional potential, the freezing of the diffusion occurs smoothly. We relate this change to the fact that, as we show, a Wigner crystal in such a potential is stable, in contrast to systems with a short-range inter-particle coupling. We find that the freezing temperature nonmonotonically depends on the commensurability parameter. We also find incommensurability solitons in the solid phase. The results reveal peculiar features of the dynamics of a strongly correlated system with long-range coupling placed into a periodic potential.

Interaction of phonons at superfluid helium - solid interfaces

A new method of obtaining the interaction Hamiltonian of phonons at superfluid helium-solid interface is proposed in the work. Equations of hydrodynamic variables are obtained in terms of second quantization if helium occupies a half-space. The contributions of all processes to the heat flux from solid to superfluid helium are calculated based on the obtained Hamiltonian. The angular distribution of phonons emitted by a solid is found in different processes. It is shown that all the exit angles of superfuild helium phonons are allowed. The obtained results are compared with experimental data and with previous theoretical works.

Transmission and reflection of phonons and rotons at the superfluid helium-solid interface

We solve the problem of the transmission and reflection of phonons and rotons at the interface between superfluid helium and a solid, for all angles of incidence and in both directions. A consistent solution of the problem is presented which allows us to rigorously describe the simultaneous creation of phonons, $R^-$, and $R^+$ rotons in helium by either a phonon from the solid or a helium quasiparticle incident on the interface. The interaction of all $HeII$ quasiparticles with the interface, and their transmission, reflection and conversion into each other, is described in a unified way. The angles of propagation and the probabilities of creating quasiparticles are obtained for all cases. Andreev reflection of helium phonons and rotons is predicted. The energy flows through the interface due to phonons, $R^-$, and $R^+$ rotons are derived. The small contribution of the $R^-$ rotons is due to the small probability of an $R^-$ roton being created by a phonon in the solid, and vice versa. This explains the failure to directly create beams of $R^-$ rotons prior to the experiments of Tucker and Wyatt in 1999. New experiments for creating $R^-$ rotons, by beams of high-energy phonons (h-phonons), are suggested.

Phonon propagation in nanoceramics

The low-frequency range of the phonon spectrum of nanoceramics is theoretically investigated for two limiting cases of the continuum limit and the ordered ceramic model. In both models a possibility for the gap formation in the phonon spectrum has been found for helium phonons, which allows the description of the experimentally observed anomalous dependences of the phonon diffusion coefficient. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron dynamics in quantum dots on helium surface

We study single-electron quantum dots on a helium surface created by electrodes submerged into the helium. The parameters of the dots are electrostatically controlled. We find the electron energy spectrum and identify relaxation mechanisms. The in-plane confinement significantly slows down electron relaxation. The energy relaxation is due primarily to coupling to phonons in helium. The dephasing is determined by thermally excited ripplons and by the noise from underlying electrodes. The decay rate can be further suppressed by a magnetic field normal to the helium surface. Slow relaxation in combination with control over the energy spectrum make localized electrons appealing as potential qubits of a quantum computer.

Semi-Microscopic Theory for Emission of Elementary Excitations into He II from a Heated Solid

I develop here a semi-microscopic quantum theory for description of creation of phonons and rotons in superfluid helium by a solid heater. Starting with a correct transfer Hamiltonian describing a coupling between solid and liquid 4He the probabilities of transformation of a single phonon in the solid into (i) single helium phonon, (ii) two helium phonons, and (iii) single helium roton are found out. All the obtained expressions account for different polarizations of phonons in the solid. The heat transfer associated with single phonon and single roton channels are calculated. Particularly, the obtained expression for heat flux via the single phonon channel calculated in the framework of present microscopic theory coincides exactly with the well known Khalatnikov formula obtained initially in the framework of acoustic-mismatch theory. The impossibility of direct creation of R(-) rotons becomes clear in the used framework due to accurate account of the boundary conditions at the solid–liquid helium interface, which is in agreement with recent experimental results.

Qubits with electrons on liquid helium

We study dissipation effects for electrons on the surface of liquid helium, which may serve as the qubits of a quantum computer. Each electron is localized in a 3D potential well formed by the image potential in helium and the potential from a submicron electrode submerged into helium. We estimate parameters of the confining potential and characterize the electron energy spectrum. Decay of the excited electron state is due to two-ripplon scattering and to scattering by phonons in helium. We identify mechanisms of coupling to phonons. An estimate of contributions from different scattering mechanisms shows that the decay rate should be $\ensuremath{\lesssim}{10}^{4}{\mathrm{s}}^{\ensuremath{-}1}.$ We analyze dephasing of the electron states due to quasielastic ripplon scattering off an electron. The dephasing rate is $\ensuremath{\lesssim}{10}^{2}{\mathrm{s}}^{\ensuremath{-}1}$ for $T=10\mathrm{mK}$ and depends on temperature as ${T}^{3}.$ Decay and decoherence of the electron states result also from classical and quantum electrode noise. We relate the corresponding relaxation rates to the power spectrum of the fluctuating electric field on the electron. The dependence of the rates on the electrode parameters is obtained.

Roton-phonon relaxation times in helium II

The conversion of rotons to phonons in helium II is considered as a diffusion process, rather than a phonon-assisted collision process.