Boson localization and excitations of liquid ⁴He confined in gelsil

We present neutron scattering measurements of the phonon-roton (P-R) modes of liquid ⁴He at saturated vapor pressure confined in 44 Å mean pore diameter gelsil in the wave vector range 0.4⩽Q⩽2.15 Å⁻¹. Layer modes, modes which propagate in the liquid layers adjacent to the porous media walls, were also observed at wave vectors in the roton region (Q≃1.95 Å⁻¹) but not at Q≲1.7 Å⁻¹. The first goal is to document the filling dependence of the dynamic response and of the P-R mode energies and widths more systematically than has been done in the past. As the gelsil is filled with ⁴He, the P-R and layer modes are first observed at a fractional filling of f=76% at low temperature (T=0.4 K). At fillings f=76%, the P-R mode energies lie below the bulk superfluid ⁴He values in the wave vector range 0.4⩽Q⩽1.7 Å⁻¹, especially at Q≃1.1 Å⁻¹, as observed in helium films. As filling is increased, the intensity in the P-R mode increases markedly and the P-R mode energies move toward bulk superfluid values taking bulk values at full filling. The second goal is to determine the temperature dependence of the intensity in the P-R modes in a media in which the superfluid-normal transition temperature T_c=1.92 K is independently known and lies well below the bulk liquid value T_λ=2.17 K. As temperature is increased, the intensity in the P-R and layer modes decreases. However, a well-defined P-R mode is observed at temperatures up to T≃2.15 K, above T_c=1.92 K. Since well-defined modes exist because there is Bose-Einstein condensation (BEC), this suggests that there is BEC above T_c, probably localized. Localized BEC appears to exist up to T≃T_λ.