Abstract In this introductory chapter, we begin by informing the reader about the fascinating history of superfluidity in bulk liquid helium. This is followed by relating attempts in using liquid helium as a low temperature matrix for spectroscopy. After a brief review of the thermodynamic properties of helium in Sect. 1.2, the different types of free jet expansions used in experiments to produce clusters and nanodroplets of different sizes are described in Sect. 1.3. First it is shown how they depend on the nature and location in the phase diagram of the isentropes which determine the course of the expansion. Depending on the four regimes of isentropes, different number sizes and distributions are expected. Next in Sect. 1.4, the results of theoretical and, where available, experimental results on the total energies, excited states, radial density distributions, and temperatures of clusters and droplets are discussed. Finally, in Sect. 1.5 the theoretical and experimental evidence for the superfluidity of nanodroplets is briefly reviewed. For more information on the production and characteristics of nanodroplets, the reader is referred to the chapters in this book and to the reviews in Appendix.
The experimental realization of a thin layer of spin-polarized hydrogen H↓ adsorbed on top of the surface of superfluid (4)He provides one of the best examples of a stable, nearly two-dimensional (2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid (4)He slab and the adsorbed H↓ layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied.
We study a submonolayer
4He adsorbed on fluorographene (GF) and on hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have been computed ab initio with a suitable density functional theory including dispersion forces. The properties of the adsorbed
4He atoms have been computed at finite temperature with path integral Monte Carlo and at
T=0K with variational path integral. From both methods we find that the lowest energy state of
4He on GF is a superfluid. Due to the very large corrugation of the adsorption potential this superfluid has a very strong spatial anisotropy, the ratio between the largest and smallest areal density being about 6, the superfluid fraction at the lowest
T is about 55%, and the temperature of the transition to the normal state is in the range 0.5--1 K. Thus, GF offers a platform for studying the properties of a strongly interacting highly anisotropic bosonic superfluid. At a larger coverage
4He has a transition to an ordered commensurate state with occupation of 1/6 of the adsorption sites. This phase is stable up to a transition temperature located between 0.5 and 1 K. The system has a triangular order similar to that of
4He on graphite but each
4He atom is not confined to a single adsorption site and the atom visits also the nearest neighboring sites giving rise to a novel three-lobed density distribution. The lowest energy state of
4He on hBN is an ordered commensurate state with occupation of 1/3 of the adsorption sites and triangular symmetry. A disordered state is present at lower coverage as a metastable state. In the presence of an electric field the corrugation of the adsorption potential is slightly increased but up to a magnitude of 1 V/\AA{} the effect is small and does not change the stability of the phases of
4He on GF and hBN. We have verified that also in the case of graphene such electric field does not modify the stability of the commensurate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}R{30}^{\ensuremath{\circ}}$ phase.
We report on the observation of vortices in superfluid 4He droplets produced in the expansion of liquid He. The vortices were traced by introducing Ag atoms, which clustered along the vortex lines, into the droplets. The Ag clusters were subsequently surface-deposited and imaged via electron microscopy. The prevalence of elongated track-shaped deposits shows that vortices are present in droplets larger than about 300 nm and that their lifetime exceeds a few milliseconds. We discuss the possible formation mechanisms and the stability of the vortices.
Quantum Monte Carlo simulations confirm the existence of a bound state of a single He-3 atom at a free superfluid He-4 surface in three dimensions, localized within a ~10-A thick low-density He-4 surface layer, with a binding energy of approximately 4 K with respect to vacuum. As the temperature is raised above ~ 1 K the He-3 atom leaves the surface to dissolve into the superfluid. The situation is entirely different in two dimensions, as the He-3 atom is excluded from the superfluid and no surface bound state exists. Results are also presented for the a He-3 atom binding to nanoscale size He-4 clusters adsorbed on weak substrates, a physical system that may allow for the observation of some of the physics predicted for extended surfaces. It is shown that a He-3 bound state localized at the perimeter of sufficiently small (a few tens of atoms) clusters exists not just on Cs, as previously reported, but on all alkali substrates.
The nuclear magnetic susceptibility of
3He adsorbed on the surface of graphite, plated with a monolayer of solid
4He, has been measured at surface densities less than 0.055 \AA{} $^{\mathrm{\ensuremath{-}}2}$ and at temperatures down to 6 mK. A temperature-independent susceptibility is observed at low temperatures, which is strongly enhanced over the ideal-gas value, due to quasiparticle interactions. The inferred Landau-Fermi-liquid parameters allow a comparison with microscopic theories of interacting Fermi systems.