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.     

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.     

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.     

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.     

A Beliaev Theory Incorporating a Semi-Phenomenological Roton Backflow Effect

We have developed a Beliaev theory incorporating a semi-phenomenological roton backflow effect in order to examine the effect of the backflow on the Quantum Evaporation of atoms from the free surface of superfluid ⁴ He. A theory of Quantum Evaporation based on a real-space Beliaev theory neglecting roton backflow was recently developed by Sobnack et al. [Phys. Rev. B 60, 3465 (1999)], and in this paper we discuss the extension of the theory to include the backflow physics from the Aldrich-Pines polarization potential theory of the 1970's. The calculation of the effect of the backflow on Quantum Evaporation is presented elsewhere.     

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.     

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.     

Resonance Microwave Absorption in He II

Microwave (MW) absorption in liquid ⁴He is investigated in the frequency range of 40–200 GHz at T = 1.4–2.5 K. “Whispering gallery” waves were generated by a dielectric disk resonator immersed into the liquid. Resonant absorption of MWs was detected at 180.3 GHz, which corresponds to the roton minimum of the liquid helium excitation spectrum. The creation of a single roton is possible because of the presence of the resonator wall which absorbs an extra momentum. The resonance frequency is shown to decrease with temperature in excellent agreement with the temperature dependence of the roton gap obtained previously in the neutron scattering experiment. The temperature dependence of the MW absorption data indicates an anomalous behavior near the λ-point and displays an hysteretic character.      

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.     

Variational density matrix approach to the temperature-dependent elementary excitation spectrum of two-dimensional liquid4He

Using the variational density matrix method, we obtain a temperature-dependent elementary excitation spectrum for two-dimensional liquid⁴He. For more precise results, we use a Jastrow-Feenberg-type trial wave function and include the contribution of elementary diagrams within the hypernetted chain approximation. The behavior of the excitation spectrum as a function of the temperature and density in two dimensions is similar to that of the bulk system, but has a smaller roton minimum. The roton minimum of the excitation spectrum decreases with increasing temperature and increases with increasing density at low densities but decreases at large densities. The results agree well with Monte Carlo calculations and are closer than pevious theories to experimental measurements of⁴He film adsorbed on substrates.     

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.     

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.     

Lowest order constrained variation calculations and backflow effects in liquid3He

Ground-state energy studies are carried out for liquid³He based on a correlated wave function which incorporates the Feynman-Cohen backflow correlation operator. Applying a lowest order constrained variation (LOCV) method, calculations have been performed for a number of realistic potentials. Our results indicate an improvement over those obtained by other LOCV calculations performed using the Jastrow ansatz and are in good agreement with other calculations involving higher order terms.     

Excitations and Stability of 2D Liquid 4He

The excitation modes of two-dimensional liquid ⁴He are approached from two angles: Firstly, the phonon-roton spectrum is calculated and the related transition currents examined to gain insight into the detailed microscopic structure of the excitations and to look for possible evidence of the proposed spontaneous formation of vortex-antivortex pairs at low densities. The roton excitation is interpreted as a resonance effect in which the wavelength of the long-range density fluctuation matches favorably with the short-range oscillations caused by two-particle correlations. Contrary to the 3D case, no backflow rolls are observed in the two-body current at high momenta. The calculations reproduce reasonably the density dependence of the spectrum, and the saturation of the high-momentum part following from the decay processes of excitations is satisfactorily predicted. The stability of the liquid ground state is then studied by searching for soft modes. It is found that at densities near the expected liquid-solid phase transition the energy of the liquid can be lowered by changing the symmetry of the pair distribution function from spherical to non-spherical. This two-body structure indicates the point-group symmetry of the emerging solid phase to be hexagonal.     

λ Transition of dilute3He in4He solutions

Based on an empirically extended Landau roton formula and on the fact that³He atoms participate in the movement of the normal component of liquid⁴He, the variation of the temperature with³He concentration is obtained at the saturated vapor pressure. The results are in good agreement with experiment. The present approach can also be applied to higher pressures.     

Vortex rings and the superfluid λ-transition

A vortex-ring formulation of the₄He -transition provides a clear physical picture of the superfluid transition. The thermally excited rings are dipoles which orient in an applied flow field, and their net backflow cancels part of the applied flow, reducing the superfluid density. At the -point rings of infinite size drive the superfluid density to zero as a power law of the reduced temperature, with an exponent of 0.672. By fitting to the experimental superfluid amplitude the core energy of the smallest rings is found to be 6.1K at T and their diameter is 2.3 Å. It is proposed that these can be identified as the roton excitations of the Landau model. The vortex theory also yields new insights into topics such as boundary effects at a wall, finite-size effects, and the dynamics of the transition.     

Pressure dependence of the roton spectrum in liquid helium

We suggest consistency checks on neutron scattering data on liquid helium under pressure. The theoretically calculated static structure functionS(k|P) leads to pressure dependence of the roton gap, momentum, and curvature in general agreement with experiment.Work supported in part by the U.S. Atomic Energy Commission, and in part by the National Science Foundation under Grant No. GP-29130 and through the Materials Research Center of Northwestern University.Resident Student Associate at Argonne National Laboratory, Summer 1972 and 1973.Alfred P. Sloan Research Fellow.     

Physical Mechanisms for Effective Mass Enhancement in 3He

We use structural information from simulations and from variational ground state calculations for calculating the effective mass of ³He at zero temperature. It is found that the relatively large effective mass is due to a combination of several physical effects: Density fluctuations cause an effective mass enhancement due to predominantly hydrodynamic backflow. This effect is, around the Fermi momentum, a smooth function of the single particle wave number; its magnitude is consistent with the effective mass of ⁴He impurities in ³He. Spin-fluctuations, on the other hand, cause a pronounced peak of the effective mass around the Fermi wave number. We also find, consistent with earlier work, an instability of the single particle spectrum at about 2.5 k _F, this is due to the coupling to density fluctuations in the maxon region.     

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.     

Multi-Pair and Exchange Effects in the Dynamic Structure of Two-Dimensional 3He

We examine the effect of fermionic exchange interactions on the dynamic structure function of two-dimensional ³He within a manifestly microscopic theory of excitations. These exchanges have, at different wave lengths and densities, different consequences: At low densities, exchanges are decisive to determine whether the phonon is Landau-damped or not. In the intermediate wave number regime, exchanges are relatively unimportant but they become important again at short wave length corresponding to about four times the Fermi wave number. A very important further aspect is the inclusion of pair fluctuations. These are fluctuations of the wave function that can not be described by the quantum numbers of a single particle. They do not change the features of long wave length excitations, but induce a finite width to the collective mode outside the particle-hole continuum. In the intermediate momentum regime, where one would expect a “roton minimum” in a Bose fluid with the same interaction and density, pair fluctuations cause a visible shift of the strength of the dynamic structure function towards lower energies and cause a very sharp collective mode. The effect, which was reported by Godfrin et al. (Nature 483:576, 2012), is slightly enhanced by exchange corrections.