Henry R. Glyde

This article is dedicated to Roger A Cowley and his seminal contributions to our understanding of quantum liquids, both liquid ⁴ He and ³ He. Roger Cowley’s neutron scattering measurements of the collective and independent particle response of liquid ⁴ He 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 ⁴ He 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 ³ He 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.

Progress made in measuring and interpreting the elementary excitations of superfluid and normal liquid 4 H e 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 4 H e is considered. Reference to liquid 3 H e , 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 4 H e 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 P-R mode and particularly it’s temperature dependence is emphasized. The similarity of normal liquid 4 H e with other quantum and classical liquids is discussed.

This is an annual and the final report on DE-FG02-03ER46038 (ER46680) following a no cost extension of DE-FG02-03ER46038 from February 16, 2016 to November 15, 2016. The report period is February 16, 2016 to November 15, 2016. The contract DE-FG02-03ER46038 (ER46680) was closed on November 15, 2016. The contract institution is the University of Delaware, address: Room 210, Hullihen %%@ Hall, University of Delaware, Newark, DE 19716. The Principal Investigator is Henry R. Glyde, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (email: glyde@udel.edu). The Administrative Point of Contact is Dale S. Weiss Tel: 302 831 3634 dsweiss@udel.edu. The DOE Program is the Office of Basic Energy %%@ Sciences, U.S. Department of Energy, Germantown Building, 1000 Independence Ave., SW Washington, DC 20585. The program manager is Dr. P. Thiyagarajan, Neutron Scattering SC-22.2/ Germantown Bldg., Tel: 301-903-9706, email: P. Thiyagarajan@Science.DOE.GOV.

We present inelastic neutron scattering measurements of the dynamics of helium adsorbed on carbon nanotube bundles. The goal is to determine the vibrational properties of the 1D and 2D quantum solids that are stabilized on the nanotube bundle surfaces at different fillings of ⁴He. The mean square vibrational amplitude in the 1D solid is large with a Lindemann ratio of γ_1D=(u²)^1/2/a₁=0.25 comparable to bulk solid ⁴He. The γ_2D is significantly smaller. The frequency density of states of the 2D solid, g(ω), has a gap at ω 0.75 meV consistent with a commensurate lattice. The 1D solid has no gap or a gap smeared by disorder. The 1D and 2D g(ω) are well described by dispersion curves having no gap and a gap, respectively, with some vibration along additional dimensions indicated.