Critical Point Coupling and Proximity Effects in 4He at the Superfluid Transition

We report measurements of the superfluid fraction rho(s)/rho and specific heat c(p) near the superfluid transition of He-4 when confined in an array of (2 mu m)(3) boxes at a separation of S = 2 mu m and coupled through a 32.5 nm film. We find that c(p) is strongly enhanced when compared with data where coupling is not present. An analysis of this excess signal shows that it is proportional to the finite-size correlation length in the boxes xi(t, L), and it is measurable as far as S/xi similar to 30 - 50. We obtain xi(0, L) and the scaling function ( within a constant) for xi(t, L) in an L-3 box geometry. Furthermore, we find that rho(s)/rho of the film persists a full decade closer to the bulk transition temperature T-lambda than a film uninfluenced by proximity effects. This excess in rho(s)/rho is measurable even when S/xi > 100, which cannot be understood on the basis of mean field theory.