Persistent-Current Measurements of the Superfluid Density and Critical Velocity

Abstract

Gyroscopic measurements of superfluid persistent currents in liquid helium below and near the $\ensuremath{\lambda}$ transition are presented here. Measurements were conducted in a variety of sizes of porous material from 0.05- to 150-\ensuremath{\mu}average size. Near the $\ensuremath{\lambda}$ transition, both the superfluid density $\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$ and the critical velocity ${\ensuremath{\omega}}_{c}$ exhibit a $\frac{2}{3}$-power dependence on the temperature difference from the transition. A depression of the $\ensuremath{\lambda}$ transition is observed for both $\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$ and ${\ensuremath{\omega}}_{c}$ in the smallest pores. Data for $\frac{{\ensuremath{\rho}}_{s}}{\ensuremath{\rho}}$ and ${\ensuremath{\omega}}_{c}$ away from the transition and down to about 1.25\ifmmode^\circ\else\textdegree\fi{}K are given and are in agreement with measurements made by other methods.