Phonons, rotons, and localized Bose-Einstein condensation in liquid He4 confined in nanoporous FSM-16

We present neutron scattering measurements of the phonon-roton and layer modes of liquid helium confined in 28 \AA{} 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 ($Q>0.8$ ${\AA{}}^{\ensuremath{-}1}$) 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 $⁴\mathrm{He}$ 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 $⁴\mathrm{He}$. However, a substantial P-R mode width at $T\ensuremath{\rightarrow}0$ K and at higher temperatures is observed.