Mean-field theory for interacting rotons in superfluid helium

It is shown within the framework of mean-field theory that the gas of roton excitations in superfluid helium becomes unstable at a critical temperatureT _c if the roton-roton interaction is attractive. The instability is characterized by a singularity of the specific heat and signals the transition into the normal fluid state. The roton energy gap remains finite atT _c .     

Size dependent ultrasonic absorption in superfluid helium

Ultrasonic waves in liquid He II at temperatures below 0.6°K can be absorbed by thermal phonons in 3- or 4-phonon processes. For the case that the mean free path of thermal phonons is sufficiently long 3-phonon processes are generally excluded because energy and momentum cannot be conserved. The conservation requirements cannot be fullfilled because the group velocity of thermal phonons is lower than the ultrasonic velocity due to dispersion. — The purpose of this note is to point out that insmall samples of liquid the uncertainty in phonon energy prevents a violation of the conservation laws for 3-phonon processes. In small volumes of liquid, ultrasonic waves are therefore strongly absorbed in 3-phonon processes, while in larger volumes of liquid this contribution to the absorption is absent. — A similiar size dependent absorption is to be expected for longitudinal waves at low temperatures in ideal crystals.     

Detection of 4He atoms separately evaporated by phonons and rotons at a free superfluid surface

Using heat pulses, we detect ⁴He atoms separately by phonons and rotons from a superfluid surface.     

On the mechanism of electromagnetic microwave absorption in superfluid helium

In experiments on electromagnetic (EM) wave absorption in the microwave range in superfluid (SF) helium [1?C3], a narrow EM field absorption line with a width on the order of (20?C200) kHz was observed against the background of a wide absorption band with a width of 30?C40 GHz at frequencies f ₀ ?? 110?C180 GHz corresponding to the roton gap energy ?? _r (T) in the temperature range 1.4?C2.2 K. Using the so-called flexoelectric mechanism of polarization of helium atoms (⁴He) in the presence of density gradients in SF helium (HeII), we show that nonresonance microwave absorption in the frequency range 170?C200 GHz can be due to the existence of time-varying local density gradients produced by roton excitations in the bulk HeII. The absorption bandwidth is determined by the roton-roton scattering time in an equilibrium Boltzmann gas of rotons, which is t _r-r ?? 3.4 × 10^?11 s at T = 1.4 K and decreases upon heating. We propose that the anomalously narrow microwave resonance absorption line in HeII at the roton frequency f ₀(T) = ??r(T)/2??? appears due to the following two factors: (i) the discrete structure of the spectrum of the surface EM resonator modes in the form of a periodic sequence of narrow peaks and (ii) the presence of a stationary dipole layer in HeII near the resonator surface, which forms due to polarization of ⁴He atoms under the action of the density gradient associated with the vanishing of the density of the SF component at the solid wall. For this reason, the relaxation of nonequilibrium rotons generated in such a surface dipole layer is strongly suppressed, and the shape and width of the microwave resonance absorption line are determined by the roton density of states, which has a sharp peak at the edge of the roton gap in the case of weak dissipation. The effective dipole moments of rotons in the dipole layer can be directed either along or across the normal to the resonator surface, which explains the experimentally observed symmetric doublet splitting of the resonance absorption line in an external dc electric field perpendicular to the resonator surface. We show that negative absorption (induced emission) of EM field quanta observed after triggering a Kapitza ??heat gun?? occurs when the occupation numbers for roton states due to ??pumping?? of rotons exceed the occupation numbers of EM field photons in the resonator.     

Calculation of the sound absorption in superfluid helium below 0.6 K

The sound absorption in superfluid helium is calculated using the renormalized perturbation expansion of the phonon self-energy. The second-orderωT ⁴-result is derived without the assumption of a Lorentzian form of the phonon spectral function. The fourth-order contribution leads to better agreement with experimental data. These results are compared with simple perturbation theory. A discussion of the Boltzmann-equation approach is also given.     

Trace detection of metastable helium molecules in superfluid helium by laser-induced fluorescence

We describe an approach to detecting ionizing radiation that combines the special properties of superfluid helium with the sensitivity of quantum optics techniques. Ionization in liquid helium results in the copious production of metastable He2 molecules, which can be detected by laser-induced fluorescence. Each molecule can be probed many times using a cycling transition, resulting in the detection of individual molecules with high signal to noise. This technique could be used to detect neutrinos, weakly interacting massive particles, and ultracold neutrons, and to image superfluid flow in liquid 4He.     

Atoms and ions in superfluid helium

Optical spectra of atomic impurities in liquid helium have been investigated. Comparison is made between the wavelength of the free atomic and ionic lines and those in the liquid helium matrix. Simultaneously, the line width and a possible asymmetry is recorded. Presence and absence of radiative transitions depend on the species of the atom implanted in the quantum fluid. The absence of any optical transitions from states lying as low as 1,8 eV below the ionization limit will be explained in this paper.     

Atoms and ions in superfluid helium

Optical spectra, level population and nonradiative deexcitation processes of atomic impurities in liquid helium have been investigated. The recombination of electrons and positive metal ions are described by the tunneling model. This model explains the population gap of 1.8 eV below the ionisation limit which was observed for several neutral defect atoms in liquid helium. In the framework of a pseudopotential theory excited singlet levels of Ba, Ca and Na atoms are recalculated and compared to experimental data. Non-spherical atomic defects for excited p-states are treated also. Quadrupole vibrations of these distorted defect structures are assumed to be responsible for inducing multiphonon transitions between excited atomic states.     

Vortex wheels in superfluid helium

It is suggested that the continuous reversal of apparent circulation around a vibrating wire in liquid He II is due to the motion of a vortex-line array called a “vortex wheel”.     

Rogue waves in superfluid helium

Rogue waves have been observed in superfluid helium. The experimental system consists of high intensity second sound (temperature-entropy) waves within a resonant cavity. Under steady state conditions, with a constant oscillatory driving force at the resonant frequency, the waves are turbulent and there are fluxes of energy towards both high and low frequencies. Rogue waves appear under the nonequilibrium conditions that prevail shortly after the drive has been switched on, prior to establishment of the steady state. The experiment is described briefly, relevant results are presented and discussed theoretically in terms of nonlinear wave interactions, and possible connections to rogue waves on the ocean are considered.     

UCN production in superfluid helium

Ultra-cold neutrons (UCN) are produced in superfluid helium by single- and multi-phonon excitation. The UCN production rate density R _II via multiphonons can be larger than that by one-phonon excitation R _I being due to the dependence of the incident neutron spectral flux density dφ/dλ on the wavelength λ. Received: 28 March 2002 / Accepted: 19 December 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: wschott@e18.physik.tu-muenchen.de RID="b" ID="b"On leave of absence from PNPI, Gatchina, Russia Communicated by T. Walcher     

Topological defects in superfluid helium

Some aspects of classical field-theoretic phenomenology of superfluid helium are presented.     

Phonon spectrum of superfluid helium

The phonon excitation spectrum of superfluid ⁴He is calculated self-consistently employing a renormalized hydrodynamic Hamiltonian. Our theoretical results for the sound velocity are in excellent agreement with experiment. The phonon spectrum agrees with the Woods-Cowley neutron measurements.     

Microscopic theory of superfluid helium

This paper discusses the properties of an interacting condensed Bose system, emphasizing those aspects which do not depend on the weakness of the potential, and which therefore apply to superfluid helium. A physical and mathematical characterization of Bose condensation is presented in terms of an additional macroscopic quantity, the wave function of the condensed mode, which is defined in terms of microscopic quantities. It is shown that in equilibrium the assumption of Bose condensation leads to a two-fluid model. The hydrodynamic generalization applicable to slowly varying disturbances from equilibrium is then discussed and rigorous microscopic expressions are derived for the parameters of this theory (including dissipative coefficients). The elementary excitation spectrum in this collision dominated regime is exhibited. The Landau quasi-particle theory is examined, as well as the relation of condensation and the excitation spectrum, to the property of super-fluidity. Under certain regularity assumptions the form of the long-wave-length excitation spectrum at vanishing temperature is deduced. The corre-sponding derivation at finite temperature is presented and criticized. Finally, techniques are discussed for evaluating properties of the Bose system starting from the interaction potential. Approximation schemes consistent with the conservation laws and with the absence of a gap in the elementary excitation spectrum are discussed. Previous approximations for the weakly interacting Bose gas are classified and summarized and additional approximations are examined.     

Surface tension of superfluid helium

Summary We present here the calculation of the expression for the surface tension depression by taking into consideration the finite size of the molecular superfluid helium. The agreement between the experimental results (J. R. Eckardt, D. O. Edwards, S. Y. Shen and F. M. Gasparini:Phys. Rev. B,16, 1944 (1977)) and the theoretical results is much better than previously published (K. R. Atkins:Can. J. Phys.,31, 1165 (1953)).