Quantum liquids.

This article is dedicated to Roger A Cowley and his seminal contributions to our understanding of quantum liquids, both liquid 4He and 3He. Roger Cowley's neutron scattering measurements of the collective and independent particle response of liquid 4He were made at Chalk River Laboratories in 1965-74 chiefly with A D B (Dave) Woods. They measured the phonon-roton (P-R) mode energy, intensity and width with new precision. Particularly, they extended the measurements to higher wave vector and identified both collective and single particle response regimes. They showed that the P-R mode terminated at a finite energy as predicted by Pitaeskii rather than continuing as predicted by Feynman and Feynman and Cohen. They determined both the single P-R mode and multimode contributions to the dynamics. They made direct comparison with theory which Roger understood well. They observed the Bose-Einstein condensate (BEC) fraction in liquid 4He for the first time. This appears to be the first ever observation of BEC in any Bose gas or liquid. Roger Cowley's pioneering measurements of the density excitations of liquid 3He were made at the Institut Laue Langevin (ILL) in the period 1973-80. Roger, Reinhard Scherm, W G (Bill) Stirling and collaborators showed for the first time that the density response of this highly neutron absorbing liquid could indeed be observed with neutrons. They documented with others the dynamic response as a function of temperature and pressure stimulating extensive theoretical and experimental interest that continues today.

Excitations in the quantum liquid 4He: A review.

Progress made in measuring and interpreting the elementary excitations of superfluid and normal liquid [Formula: see text] in the past 25 years is reviewed. The goal is to bring up to date the data, calculations and our understanding of the excitations since the books and reviews of the early 1990s. Only bulk liquid [Formula: see text] is considered. Reference to liquid [Formula: see text], mixtures, reduced dimensions (films and confined helium) is made where useful to enhance interpretation. The focus is on the excitations as measured by inelastic neutron scattering methods. The review covers the dynamical response of liquid [Formula: see text] from the collective excitations at low energy and long wavelength (i.e. phonon-roton modes) to the single particle excitations at high energy from which the atomic momentum distribution and Bose-Einstein condensate fraction are determined. A goal is to show the interplay of these excitations with other spectacular properties such as superfluidity and the test of fundamental calculations of quantum liquids that is possible. The role of Bose-Einstein condensation in determining the nature of the [Formula: see text] mode and particularly it's temperature dependence is emphasized. The similarity of normal liquid [Formula: see text] with other quantum and classical liquids is discussed.

Evidence for a common physical origin of the Landau and BEC theories of superfluidity.

There are two renowned theories of superfluidity in liquid (4)He, quite different and each with specific domains of application. In the first, the Landau theory, superflow follows from the existence of a well-defined collective mode supported by dense liquid (4)He, the phonon-roton mode. In the second, superflow is a manifestation of Bose-Einstein condensation (BEC) and phase coherence in the liquid. We present combined measurements of superfluidity, BEC and phonon-roton (P-R) modes in liquid (4)He confined in the porous medium MCM-41. The results integrate the two theories by showing that well-defined P-R modes exist where there is BEC. The two are common properties of a Bose condensed liquid and either can be used as a basis of a theory of superfluidity. In addition, the confinement and disorder suppresses the critical temperature for superfluidity, Tc, below that for BEC creating a localized BEC "phase" consisting of islands of BEC and P-R modes. This phase is much like the pseudogap phase in the cuprate superconductors.

Bose-Einstein condensation in solid 4He.

We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/mol) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200 mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.

One-dimensional and two-dimensional quantum systems on carbon nanotube bundles.

We report the first measurement of the structure of 4He atoms adsorbed on bundles of single-walled carbon nanotubes. Neutron diffraction techniques and nanotube samples closed at the end were used. At low coverage, 4He forms a 1D, single line lattice along the grooves between two nanotubes on the surface of the nanotube bundles. As coverage is increased, additional lines of 1D lattices form along the grooves. This is followed by an incommensurate, 2D monolayer covering the whole nanotube bundle surface. The lattice constants of these 1D and 2D systems are largely independent of filling once a single 1D line is formed. No occupation of the interstitial channels between nanotubes is observed in the present sample.

Excitations of metastable superfluid 4He at pressures up to 40 bars.

Neutron scattering measurements of the fundamental excitations of liquid 4He confined in 44 A pore diameter gelsil glass at pressures up to 40 bars in the wave vector range 0.41.6 A(-1), especially the rotons, are observed up to complete solidification of all the liquid at a pressure of approximately 40 bars where the roton vanishes. At and above a pressure of 35.1 bars, Bragg peaks are observed, indicating coexistence of liquid and solid in the pores at pressures 35 less than or approximately equal P less than or approximately equal 40 bars.

Quantum momentum distribution and kinetic energy in solid 4He.

We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.

Dynamics of quantum liquids in confinement, theory and experiment.

Liquid (4)He immersed in porous media such as aerogel, Vycor, and Geltech silica are excellent examples of bosons in disorder and confinement. Of special interest is the impact of disorder on Bose-Einstein condensation (BEC), on the elementary excitations of the superfluid and on their connection to the superfluid properties. Indeed, the modifications induced by disorder can be used to reveal the interdependence of BEC, the excitations and superfluidity. To date, the superfluid properties in porous media are much more completely documented than BEC or the excitations. In this paper, we review measurements of the excitations by neutron scattering, focusing particularly on their temperature dependence and the existence of phonon-roton excitations at higher temperatures. The weight of single excitation response at higher temperatures suggests the existence of localized BEC above the superfluid-normal transition temperature in porous media. We sketch several recent predictions made for BEC, the excitations, and the superfluid properties in disorder. Connections with other "Dirty Bose systems" are made.