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We report measurements of the superfluid density of 4 He confined between two Si wafers. These are the first measurements of helium confined in a sufficiently well-defined planar geometry to show a crossover from three-dimensional-like to finite-size to two-dimensional behavior. Data for confinement in 0.106-, 0.509-, 2.8-, and 3.9-pm-thickness cells are analyzed for scaling with the exponent of the bulk correlation length, v. We find that this scaling does not work: An exponent different from v is required. We discuss these results in light of finite-size scaling predictions and earlier measurements.

We report measurements of the superfluid fraction ρ(s)/ρ and specific heat c(p) near the superfluid transition of 4He 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 L3 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.

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