Excitations of nanoscale quantum liquids under pressure and the Bose glass phase

Abstract

We present neutron scattering measurements of the dynamic structure factor of liquid helium confined to nanoscales in 25 and $34\text{ }\text{\AA{}}$ mean pore diameter porous media over a range of pressures and temperatures. At low temperature and low pressure we observe well-defined phonon-roton (P-R) modes characteristic of liquid helium containing Bose-Einstein condensation (BEC). As pressure is increased above 25 bars, we observe that the high energy P-R modes broaden and become unobservable. At pressure $p=36.3--36.8\text{ }\text{bars}$ we observe loss of all modes, including the roton. The observation of modes up to 36.3--36.8 bars indicates that there is liquid containing BEC in the gelsils up to this pressure. The loss of modes at 36.3--36.8 bars indicates loss of BEC in the liquid or significant solidification in the gelsils at this pressure. At a pressure of 31.2 bars, we observe well-defined P-R modes up to $T\ensuremath{\simeq}1.4\text{ }\text{K}$ but loss of all modes above this temperature. At $p\ensuremath{\simeq}0$, we have previously observed modes up to ${T}_{\ensuremath{\lambda}}=2.17\text{ }\text{K}$. Yamamoto et al. have reported superfluidity in the same $25\text{ }\text{\AA{}}$ gelsil up to a pressure ${p}_{c}=34\text{ }\text{bars}$ at $T\ensuremath{\simeq}0\text{ }\text{K}$ and to a maximum temperature of ${T}_{c}=1.3\text{ }\text{K}$ at $p\ensuremath{\simeq}0$. The transition at ${p}_{c}=34\text{ }\text{bars}$ and $T\ensuremath{\simeq}0\text{ }\text{K}$ was interpreted as a quantum phase transition. The present observation of P-R modes at temperatures well above ${T}_{c}$ (and pressures slightly above ${p}_{c}$) indicates that there is a phase containing BEC above ${T}_{c}$ $({p}_{c})$ that is not superfluid. This is interpreted as a Bose glass phase containing islands of BEC that support P-R modes separated by normal liquid so that there is no phase coherence across the sample as needed for superflow. The Bose glass phase lies between the superfluid and normal liquid at all temperatures and pressures. Measurements of the static structure factor indicate that freezing in the gelsils is predominantly to an amorphous solid.