Phonon-roton modes and localized Bose-Einstein condensation in liquid helium under pressure in nanoporous media

We show, using inelastic neutron scattering, that liquid helium in porous media, two gelsils and MCM-41, supports a phonon-roton mode up to a pressure of 36-37 bars only. Modes having the highest energy ("maxons") broaden and become unobservable at the lowest pressures (p approximately 26 bars) while rotons survive to the highest pressure. By comparing with the superfluid density observed by Yamamoto and co-workers in gelsil, we propose that there is a Bose glass phase containing islands of BEC surrounding the superfluid phase.