Phonons, rotons, and localized Bose-Einstein condensation in liquid 4He confined in nanoporous FSM-16

We present neutron scattering measurements of the phonon-roton and layer modes of liquid helium confined in 28 angstrom diameter nanopores of FSM-16. The goal is to determine the energy, lifetime, and intensity of the modes as a function of temperature. It is particularly to determine the highest temperature, denoted T-PR, at which well-defined phonon-roton modes are observed at higher wave vector (Q > 0.8 angstrom(-1)) in the nanopores. The temperature T-PR, which can be identified with loss of Bose-Einstein condensation (BEC), can be compared with the superfluid to normal liquid transition temperature, T-o, and other transition temperatures of He-4 in the nanopores. The aim is to identify the nature of BEC in a narrow nanopore. Two pressures are investigated, saturated vapor pressure (SVP) and p = 26 bars. We find that well-defined P-R modes are observed up to temperatures much higher than the conventional superfluid to normal liquid transition temperature, T-o, observed in torsional oscillator measurements, i.e., T-PR > T-o. At SVP, T-PR= 1.8 K and T-o= 0.9 K. This supports the interpretation that BEC exists in a localized or partially localized form in the temperature range T-o< T < T-PR; i.e., there is a localized BEC region lying between the superfluid and fully normal liquid phase, as observed in some other porous media. At close to full filling, the P-R mode energies in FSM-16 are similar to those in bulk liquid He-4. However, a substantial P-R mode width at T -> 0 K and at higher temperatures is observed.