Helium-4 superfluid density; action-at-a-distance effects

We report results from experiments with $^4$He confined in two concentric 277 nm thick planar regions that are connected across a ring which forms a thin film weak link 33~nm thick. Measurements of the superfluid fraction within rings of varying widths have shown that the planar regions affect the film in the ring over distances much longer than the correlation length $\xi$. These results are analogous to those reported for a different geometry of both the specific heat and superfluid fraction [1]. To investigate the width dependence of this proximity effect we have performed measurements with rings that are 8, 17, 40 and 100 $\mu$m wide. We will discuss our method of measurement and a possible mechanism for the long range action-at-a-distance effect suggested in [2] for the 2D Ising system. \\[4pt] [1] Perron J~K et. al. 2013 {\em Phys. Rev. B\/} {\bf 87} 094507 \newline [2] Abraham D~B et. al. 2014 {\em Phys. Rev. Lett.\/} {\bf 113} 077204