Roton second sound and the roton-roton interaction potential

We report measurements of the roton second sound velocity and absorption at high pressure and low temperature. The velocity measurements show the existence of a dip over a very small range of temperature. Comparing this to the absorption measurements, we show that this dip corresponds to a pure roton second sound regime, which is at a constant number of rotons, in agreement with Maris' predictions. The departure toward the constantchemical-potential regime gives us an estimate of the characteristic frequency of the non-roton-conserving process. The absorption measurements give a roton-roton collision frequency in good agreement with previous measurements at higher temperature. In order to explain its value, we have proposed a new interaction potential between rotons, taking into account the exchange of virtual rotons between them. We then obtain very good agreement with experiment, without any adjustable parameter.Laboratoire associé au Centre National de la Recherche Scientifique.     

Rf SQUID in the nonhysteretic regime withk 2 Ql>1

A mean field approach, analogous to the Landau theory of Fermi liquids, is developed and applied to the interacting roton liquid present in superfluid⁴He at temperatures below the -point. We derive stability conditions for the parameters describing the effective roton-roton interaction and use one of these to place a bound on the variation with temperature of the roton energy. By fitting to experimental results on the specific heat and normal fluid density, we obtain the first two moments of the effective roton interaction.Research supported in part by NSF grant DMR78-21068.     

Scattering and binding of rotons

The interaction of rotons is studied by a direct examination of their orbital dynamics. It is found that upon representing rotons as point dipoles in the superfluid, obeying the Landau dispersion relation, negative energy states occur, some of which are stable and some unstable. The binding energy and effective mass of these states are found, but are too large to agree with experiment. Improvements in the Hamiltonian are explored which recognize the actual dispersion curve as well as higher moments in the interaction. Both modifications lead to binding energy and effective mass in better agreement with experiment. Scattering is also examined, and one finds that a representative roton-roton cross section may be obtained in the dipole approximation, again using Landau dispersion. The scattering cross section is shown to be in satisfactory agreement with neutron linewidths in the roton-dominated region, as well as the roton contribution to the shear viscosity.     

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.     

The evaporation of atoms from the surface of superfluid4He by rotons

A beam of rotons is directed toward the liquid surface at normal incidence. At the surface some rotons will evaporate atoms, with a wave-vector dependant probability p(q). The kinetic energy of the evaporated atom is equal to the difference in energy between the energy of the roton and the binding energy of a⁴He atom to the surface (7.16 K). The atoms which are evaporated are detected by a bolometer above the surface. The path length of the roton in the liquid, and the atom in the vacuum, are varied by changing the liquid level in the cell. By thus changing the liquid level, we change the flight time between heater and bolometer for a given wavevector of roton. We analyse the time-of-flight spectra received by the bolometer to reveal the product n(q)p(q) where n(q) is the distribution of rotons. If we assume that n(q) reflects the temperature of the phonons in the heater used to inject the rotons, we can deduce p(q). The resulting p(q) shows an unexpected decrease towards roton minimum at q < 2.1 Å^–1.     

High Resolution Measurements of the Temperature Dependence of the Roton Energy of Superfluid 4He

New measurements of the roton excitations in superfluid ⁴He have been made using the IRIS spectrometer (energy resolution 20 eV at the roton energy) at the ISIS spallation neutron source. The roton energy was determined over a temperature range of 0.56 to 1.61 K. High resolution (energy resolution <1 eV) neutron inelastic scattering measurements by Andersen et al.² of the dependence of the ⁴He roton energy on temperature have shown significant deviations from the expected behaviour; the temperature variation was found to be discontinuous and slower than predicted by the established roton-roton interaction theory due to Bedell, Pines and Zawadowski (BPZ). ³ We find that our results can be described well by the BPZ theory over this temperature range and we do not observe the anomalous behaviour reported by Andersen et al. We offer some explanations as to the origin of this apparent disagreement.     

Temperature dependence of the condensate fraction of superfluid4 He

The roton contribution to the temperature dependence of the condensate density is discussed. The analysis is carried out through the inclusion of a gauge symmetry breaking field. Under the hypothesis that the thermal excitation of rotons is the main responsible for the depletion of the condensate, we obtain an explicit result for the temperature dependence of the condensate density which rather well agrees with the available experimental data.     

The interaction of rotons in HeII

We have investigated the scattering of rotons as motivated by recent experiments with crossed roton beams. We assumed an excitation mediated interaction between rotons and used 2nd order perturbation theory to calculate scattering cross-sections as a function of total roton momentum. Comparison of experiment to quantum mechanical and classical theories is presented.     

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     

Influence of Backflow on Roton Quantum Evaporation

Sobnack et al. recently investigated theoretically the effect of roton backflow on the scattering of atoms, rotons, and phonons at the free surface of superfluid helium-II at T=0 K. They treated backflow semi-phenomenologically by modifying the potential in their earlier theory. This paper compares their predictions for the wave-vector dependence of roton quantum-evaporation with time-resolved experiments. It is found that the wave-vector dependence observed in the experiments is much less extreme than was predicted, and we discuss the implications of this result for this type of theory.     

Quantum evaporation from the free surface of superfluid4He

The scattering of atoms and rotons at the free surface of superfluid⁴He is studied in the framework of linearised time dependent mean field theory. The phenomenological Orsay-Trento density functional is used to solve numerically the equations of motion for the elementary excitations in presence of a free surface and to calculate the flux of rotons and atoms in the reflection, condensation, and evaporation processes. The probability associated with each process is evaluated as a function of energy, for incident angles such that only rotons and atoms are involved in the scattering (phonon forbidden region). The evaporation probability forR ⁺ rotons (positive group velocity) is predicted to increase quite rapidly from zero, near the roton minimum, to 1 as the energy increases. Conversely the evaporation fromR ^– rotons (negative group velocity) remains smaller than 0.25 for all energies. Close to the energy of the roton minimum, , the mode-change processR ⁺ R ^– is the dominant one. The consistency of the results with general properties of the scattering matrix, such as unitarity and time reversal, is explicitly discussed. The condensation of atoms into bulk excitations is also investigated. The condensation probability is almost 1 at high energy in agreement with experiments, but it lowers significantly when the energy approaches the roton minimum in the phonon forbidden region.     

Density matrix of superfluid4He and temperature dependence of the static structure factor

We have computed properties of superfluid⁴He on the basis of a new density matrix which is based on a shadow wave function for the roton excitation. We deduce the separate contribution of kinetic and potential energy to a roton and find that a roton lowers the potential energy of the system. We find that S (k; T) and g(r; T) have an anomalous T dependence as found experimentally and the extra correlations present at finite T are induced by rotons. By computing the condensate fraction n₀(T) we find that the Cummings et al relation between g(r; T) and n₀(T) is violated and that it leads to a value of n₀(T) larger of the true one.     

More about Rotons in Superfluid Helium 4

In a recent paper¹ it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.     

Recent progress in the theory of rotons in superfluid4He

The excitation spectrum of superfluid ⁴ He is discussed on the basis of a shadow wave function. The potential and kinetic energies of the excitations are computed at different densities. The theory has been extended at finite temperature and we obtain the roton contribution to the radial distribution function, to the depletion of the condensate and to the dynamical structure factor S(q,). We present also the first realistic microscopic computation of the roton energy at finite T. Possible role of thermally excited vortices on rotons is considered. With a simple model we show that some discrepancies between the linewidth of the roton response in neutron and in Raman scattering can be resolved.     

Dispersion of ripplons in superfluid4He

The excitations of the free surface of liquid⁴He at zero temperature are studied, with special emphasis to the short wave length region. The hybridization mechanism between surface and bulk modes is discussed on a general basis, investigating the scattering of slow rotons from the surface. An accurate density functional, accounting for backflow effects, is then used to determine the dispersion of both bulk and surface excitations. The numerical results are close to the experimental data obtained on films and confirm in an explicit way the general reflection mechanism exhibited by rotons. Moreover they reveal the occurrence of a damped ripplon branch above the roton threshold.     

Excitations in Two-Dimensional 4He

We present the study of the ground state and of the low-energy excited states of liquid⁴He in two dimensions (2D) within the Variational Monte Carlo method. As trial wave function a shadow wave function is used. The energies of the maxon and of the roton are close together at the equilibrium density ρ_eq due to the low value of ρ_eq in 2D but at higher densities a well developed roton minimum is present. The short range backflow effects are stronger in 2D than in 3D and close to freezing the roton energy is about 5 K. This value is close to the lowest branch of excitations found from inelastic neutron scattering from thin⁴He film on graphite and interpreted as due to layer rotons. Some strong similarities between the 2D and 3D case are present: the maxon energy close to freezing is about twice the roton energy, the relative strength of the single roton peak in the dynamical structure factor is essentially density independent and very close in value to the 3D case, there is a similar shift between the wave vectors of the roton and of the position of the main maximum of the static structure factor.     

Study of rotons in superfluid4He by Raman scattering

There is a long standing disagreement between neutron and Raman scattering from rotons in superfluid⁴He near T. In neutron scattering the linewidth becomes very large and the roton signal seems to disappear at T. A substantially smaller linewidth is observed with Raman scattering and the roton signal is present even at T. We have interpreted this difference (J. Low Temp. Phys. 93, 879 (1993)) as due to a modulation of the roton energy by a fluctuating local superfluid velocity due to proliferation of vorticity as T is approached. This gives rise to an extra contribution to the roton linewidth in neutron scattering but not in Raman scattering in which two rotons with almost opposite momenta are excited. We propose a test of this explanation with evanescent field Raman scattering. It has been suggested (A. Kuklov, A. Bulatov and J.L. Birman, Phys. Rev. Lett. 72, 3855 (1994)) that in such a measurement the scattering by a single roton should be measurable. In this case the presence of a fluctuating local superfluid velocity should show up as in neutron scattering and corroborate our proposal.     

Phonon Bands Associated with the Inner-Shell Electronic Absorption Lines of Eu Atoms in Bulk Liquid Helium

The phonon bands associated with the inner-shell electronic absorption lines of Eu atoms have been studied in bulk liquid helium in the temperature range between 1.6 and 3.1 K. Profiles of the phonon bands show the remarkable temperature dependence from a broad peak at 1.6 K to a monotonic decrease of the intensity by energy at higher temperatures. Two phonon bands, measured at about 1.9 K for two different lines with different interaction energies with the liquid, are found to show identical profiles, suggesting that the profiles depend only on the temperature. The broad peak at 1.6 K has been interpreted as temperature-broadened roton/maxon peaks, while the monotonically decreasing profiles have not been well understood yet.     

A comment on rotons in two-dimensional liquid helium II

The spectrum of rotons in two-dimensional liquid helium II is estimated within the Bijl-Feynman theory. Due to stronger short-range order and more effective back flow, the roton gap is found to be about half as big as the bulk roton energy.Supported by grants of the Deutsche Forschungsgemeinschaft and, in part, by the U.S. National Science Foundation through Grants DMR73-02363 and DMR72-02977 A03.     

Bound states of rotons to impurities in He II

Rotons and impurities such as ions or solvated ³He particles can interact via dipolar forces from the flow fields of the roton and the motion of the impurity through the background fluid. Stable bound states of rotons to impurities can occur with near-zero total momentum. We give explicit results of bound-state calculations for solvated ³He, the positive helium ion, and the negative electron bubble.Research supported by the National Science Foundation and the Air Force Office of Scientific Research under grants NSF DMR 76-21814 and AFOSR 76-2880.