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

We present neutron scattering measurements of the phonon-roton and layer modes of liquid helium confinedin 28 Å diameter nanopores of FSM-16. The goal is to determine the energy, lifetime, and intensity of themodes as a function of temperature. It is particularly to determine the highest temperature, denoted TPR, atwhich well-defined phonon-roton modes are observed at higher wave vector (Q > 0.8 Å−1) in the nanopores.The temperature TPR, which can be identified with loss of Bose-Einstein condensation (BEC), can be comparedwith the superfluid to normal liquid transition temperature, TO, and other transition temperatures of 4He 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, TO, observed in torsional oscillator measurements, i.e., TPR > TO. At SVP, TPR = 1.8 K and TO = 0.9 K. This supports theinterpretation that BEC exists in a localized or partially localized form in the temperature range TO < T < TPR;i.e., there is a localized BEC region lying between the superfluid and fully normal liquid phase, as observedin some other porous media. At close to full filling, the P-R mode energies in FSM-16 are similar to thosein bulk liquid 4He. However, a substantial P-R mode width at T → 0 K and at higher temperatures is observed.