Phases of superfluid helium in smooth cylindrical pores

This paper reports an inelastic neutron scattering study of superfluid helium confined with highly monodisperse, smooth, and unidimensional silica pores only a few nanometers in diameter, previously studied only by means of macroscopic, thermodynamic techniques. Helium gas sorption isotherms show that the adsorption of helium gas proceeds by film growth, providing quantitative information about the thickness of the adsorbed film and its two-dimensional compressibility. Two different microscopic phases were observed using inelastic neutron scattering. When the adsorbed superfluid helium forms a thin film only a few atomic layers thick, it supports a dramatically modified phonon-roton spectrum as well as a compressed layer roton. The energies of these modified phonon-roton modes are consistent with those of a dilute, low-density film, one in which the average interatomic spacing is greater than in the bulk liquid. In contrast, when the pores are saturated with liquid, the modified phonon-roton spectrum disappears, and instead bulklike modes coexist with the compressed layer mode. The qualitative difference between these two pore-filling regimes is reflected in the effective vibrational density of states.