Boson localization and excitations of liquid He confined in gelsil

We present neutron scattering measurements of the phonon-roton (P-R) modes of liquid He confined in 44 Å mean pore diameter gelsil in the wave vector range 0.4 ≤ Q ≤ 2.15 Å. 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) but not at Q ∼ 1.7 Å. As the gelsil is filled with He, the P-R and layer modes are first observed at a fractional filling of f = 76 % at low temperature (T = 0.4 K). At partial fillings, the P-R mode energies lie below the bulk superfluid He values in the wave vector range 0.4 ≤ Q ≤ 1.7 Å, especially at Q ' 1.1 Å, as observed in helium films and at partial fillings in other porous media. As filling is increased, the intensity in the P-R mode increases markedly and the P-R modes energies move toward bulk superfluid values. As temperature is increased at nearly full filling, the intensity in the P-R and layer mode decreases. However, a well-defined P-R mode is observed at temperatures up to T ' 2.15 K, above the superfluid normal transition temperature Tc = 1.92 K at saturated vapor pressure for this media. Since well-defined modes exist because there is Bose-Einstein condensation (BEC), this suggests that there is BEC above Tc, probably localized, up to T ' Tλ= 2.172 K as has been proposed previously in Vycor and in 25 Å gelsil.