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 $\frac{\Delta }{k_{\mathrm{B}}}=5.85\mathrm{}$ K and a "one-dimensional," $T^2$, phonon contribution. Near the transition temperature, $T_c=1.955\mathrm{}$ K, the superfluid density is found to vary as ${(T_c-T)}^{\zeta }$ with $\zeta =0.65\mathrm{}\pm 0.03$.