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.     

4He films on graphite studied by neutron scattering

The properties of ⁴He films adsorbed on graphite have been studied by neutron scattering. In particular excitations of the commensurate phase of the monolayer are discussed. The first two adsorbed layers are solid and the next ones stay liquid. At the boundaries of the superfluid film excitations could be studied. Also the phonons, maxon and rotons of the film are investigated. An explanation of the lower density of the very thin films compared to bulk ⁴He is given.Presented by H. J. Lauter.     

Layer- and Bulk Roton Excitations of 4He in Porous Media

Layer-roton excitations of ⁴He in porous media, such as aerogel, Gegtech or Vycor, depend on the number of atoms in the active liquid layer, which, in turn, depends on the substrate potential. Hence, by measuring or calculating the energetics of the layer modes, one can get first-hand information about the substrate potential. Layer rotons can have energies as high as 8 K, while calculated two-dimensional rotons never seem to reach 6 K. Further indication that layer modes are actually an intermediate case between two and three dimensions is given by the way layer modes show up in neutron scattering data of helium in porous materials. We argue that layer rotons should be regarded as a third, completely independent kind of excitation.     

A Fast Pulsed Source of Ballistic R− Rotons in Superfluid 4He

Superfluid ⁴ He is unique in having well-defined excitations (R ^– rotons) with momentum oppositely directed to their velocity. If a beam of R ^– rotons can be produced, it could be unambiguously detected by quantum evaporation because the atoms will emerge in the opposite quadrant to that for atoms evaporated by R ⁺ rotons and phonons. Previous work shows that a heated metal film which is immersed in superfluid ⁴ He only creates phonons and R ⁺ rotons. A sponge-like heater does appear to produce R ^– rotons but, because it has a long time constant, it cannot be used in time of flight studies. We have developed a source that produces fast pulses of R ^– rotons suitable for time of flight measurements. The method uses interactions between R ⁺ rotons to create R ^– rotons, so a transient high density of R ⁺ rotons in a small confined volume is needed. The source appears to operate as we expect from a model of the evolution of the R ⁺ and R ^– roton populations.     

Excitations of inhomogeneous liquid He4: A density functional study

Excitations of the free surface, films and bounded channels of liquid⁴He are investigated with a non-local density functional theory at zero temperature in the Feynman approximation. The nature of the various branches is discussed. At the free surface, for large momentum (k2 Å^–1), a hybridization occurs between ripplons and bulk rotons. For low momentum, the ripplon dispersion relation in thick films and the third sound mode in thin films are recovered, including the expected oscillations of the third sound velocity as a function of film thickness due to the layering of the film close to the substrate. Low energy 2-dimensional (2D) rotons confined at the liquid-wall interface are found on most substrates, except on the weakest binding surfaces such as Cs, for which we consider a channel geometry. In thin films, non trivial coverage dependence of the heat capacity may result from the interplay between the contribution of the low momentum part of the spectrum, characterized by the third sound velocity oscillations, and that of the large momentum part, dominated by the 2D rotons.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

Neutron scattering from liquid 4He

In this lecture the study of excitations in quantum fluids and solids using neutrons is briefly introduced. The remainder focuses on liquid ⁴ He, giving a brief historical sketch of ideas on phonons and rotons, a survey of some recent neutron scattering data particularly on the temperature dependence of S(Q, ) and a new interpretation of phonons and rotons in superfluid ⁴He.Now at Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716.     

The surface tension of4He: Low-temperature behavior

The low-temperature surface tension of⁴He is calculated in the excitation approximation based upon a fundamental microscopic theory. The low-temperature behavior is shown to be due entirely to the effects of the coexistence curve. The role of the excitations in surface tension calculations is clarified, and it is found that only bulk excitations contribute to the surface tension and that the excitations can be ignored up to 2.2 K with an error of about 1%. Consequently, the introduction of surface excitations must be interpreted as an attempt to calculate the effects of the coexistence curve on the surface tension.     

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.     

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.     

Dielectric model of roton interactions in dilute solutions of 3He in 4He

The analogy between the theory of superfluidity and the theory of dielectrics can be extended to account for some of the properties of rotons in dilute solutions of ³He in superfluid ⁴He. These include the normal fluid density ratio and the shifts in energy of roton excitations relative to those of pure ⁴He.This research is supported in part by National Science Foundation grant DMR 76-21814 and by the Air Force Office of Scientific Research under grant AFOSR 76-2880A.     

Quantum evaporation of 4He

Quantum evaporation is the process in which an excitation is annihilated at the free surface and an atom is ejected. With liquid ⁴He the excitation is a phonon or a R ⁺ or R ^– roton. The conditions necessary to observe this phenomenon are discussed and the various experiments that demonstrate the conservation of energy and parallel component of momentum are reviewed. It is shown that phonons, with energy >10K, and rotons have long lifetimes, tending to as T 0. These excitations can be injected into liquid He and collimated into beams so that angular and scattering measurements can be performed.     

Calculation of theJ=3 roton spectrum of solid hydrogen and deuterium

A model for collective rotational excitations (rotons) with angular momentumJ=3 in solid ortho-hydrogen and para-deuterium at low temperatures is proposed. The theory is an extension of previous Bloch-type models of librons in orthohydrogen and rotons in para-hydrogen. The present model gives fairly good agreement with the positions and relative intensities of the observed Raman lines. As is the case for the libron spectrum, a discrepancy between theory and experiment is found. Improvements of the theory, which may give better agreement with the observed Raman spectra, are discussed.Supported by NSF Grant GP-9042.     

Scintillation and Quantum Evaporation Generated by Single Monoenergetic Electrons Stopped in Superfluid Helium

An electron stopped in superfluid helium generates phonons and rotons in the liquid as well as uv photons via scintillation. We report recent measurements with single 364 ke V electrons. A sapphire wafer with a superconducting transition-edge sensor is mounted above the liquid and can measure energy and timing information of individual events. We observe both uv photons and the quantum evaporation of helium atoms resulting from phonons and rotons generated by the ionizing particle in the liquid. The production of photons and rotons is strikingly different for an electron and for an alpha particle. The origin of the differences is associated with the different density of excitations along the tracks of an alpha particle and an electron.     

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.     

Interactions of Phonons and Rotons with Interfaces in Superfluid Helium

We solve the problem of beams of phonons and rotons incident on, and interacting with, solid surfaces. Phonons and rotons are the quasiparticles of superfluid helium and have a unique dispersion curve. The dispersion curve controls the transmission, reflection and mode change of these quasiparticles at the interface with another medium. We develop a non-local hydrodynamic theory in a consistent and unified way. The structure of the solutions in the quantum fluid is discussed. The creation probabilities of all quasiparticles are derived when any one of them is incident on the interface. The dependencies on frequency and angle are analyzed and the backward reflection and refraction for R ^? rotons are discussed.     

Elementary excitations and sound speed in liquid 4He at negative pressures

No Heading We present neutron scattering measurements of the phonon-roton excitations of superfluid ⁴He at negative pressures in the porous medium MCM-41. The phonon and maxon energies decrease systematically below bulk values as the density is decreased below the bulk value due to stretching of the liquid. The negative internal pressures are estimated by comparison of the observed maxon energies with extrapolation of positive pressure values and from the sound speed. The maximum negative pressure realized, about –5.5 bar, is consistent with surface tension arguments and the MCM-41 pore diameter of 47 Å. Slight broadening of the intrinsic lineshape is observed, suggesting shorter lifetimes of the excitations.PACS numbers: 61.12.Ex; 61.25.Bi; 62.60.+v; 68.03.Cd; 68.03.Kn; 67.40.Mj     

Evaporation Probability of R− Rotons Relative to R+ Rotons in Superfluid 4He

The evaporation of superfluid ⁴ He by rotons is investigated using a recently developed pulsed source of both positive (R ⁺ ) and negative (R ^– ) group velocity rotons. The R ⁺ and R ^– rotons have very different momenta parallel to the free liquid surface and this causes angular dispersion of the two beams of evaporated atoms in the vacuum. On moving a bolometer horizontally through these beams, we find that the maximum flux of atoms from R ^– rotons occurs at an angle corresponding to an average R ^– roton energy of /k _B 10.5 K. The signal at this angle is compared with the evaporation signal at the maximum flux caused by R ⁺ rotons. These R ⁺ rotons have an average energy of 10.7K. The relative sizes of these two signals enables an estimate to be made of the probability of evaporation by R ^– rotons relative to that for R ⁺ rotons. We find that «P _–a »/«P _+a » 4 × 10^–3 where the brackets signify averages over the angles and energies allowed by the geometry of the experiment.     

Prediction of reentrant wetting of3He-4He mixtures on cesium

We examine the effect of ³ He impurities on the wetting behavior of⁴He on cesium, predicting a phase diagram which includes reentrant wetting transitions. This phase diagram is shown to be very sensitive to effects such as a theoretically predicted bound state of³He at the liquid-cesium interface, and the contact angle may be sensitive to interesting temperature dependences of the helium-cesium surface tension resulting from surface rotons or Rayleigh waves.     

Heat pulse propagation in liquid4He revisited

We have studied the propagation of heat pulses in superfluid helium at 0.1 K. Our experiments agree with a simple picture of a propagating cloud of interacting excitations, rather than with the surface rotons invoked by the Exeter group. The “Q-peak” observed in double pulse experiments is interpreted as a shock wave propagating in the cloud. We have observed for the first time that theQ-peak splits up in two distinct modes at intermediate helium pressures. We believe this is evidence fo a decoupling of the phonon and roton gasses as predicted by Castaing.     

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.