Superfluid Density in Porous Vycor Glass

Abstract

The superfluid density of $^{4}\mathrm{He}$ confined to porous Vycor glass has been determined from fourth-sound measurements over a temperature range from below 0.1 K to within 10 mK of the transition. For temperatures below 1.4 K the normal-fluid fraction can be described in terms of a roton contribution with gap $\frac{\ensuremath{\Delta}}{{k}_{\mathrm{B}}}=5.85$ K and a "one-dimensional," ${T}^{2}$, phonon contribution. Near the transition temperature, ${T}_{c}=1.955$ K, the superfluid density is found to vary as ${({T}_{c}\ensuremath{-}T)}^{\ensuremath{\zeta}}$ with $\ensuremath{\zeta}=0.65\ifmmode\pm\else\textpm\fi{}0.03$.