Critical point coupling and proximity effects in ^{4}he at the superfluid transition

We report measurements of the superfluid fraction ρ_{s}/ρ and specific heat c_{p} near the superfluid transition of ^{4}He when confined in an array of (2 μm)^{3} boxes at a separation of S=2 μm 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 ξ(t,L), and it is measurable as far as S/ξ～30-50. We obtain ξ(0,L) and the scaling function (within a constant) for ξ(t,L) in an L^{3} box geometry. Furthermore, we find that ρ_{s}/ρ of the film persists a full decade closer to the bulk transition temperature T_{λ} than a film uninfluenced by proximity effects. This excess in ρ_{s}/ρ is measurable even when S/ξ>100, which cannot be understood on the basis of mean field theory.