Coupling and proximity effects in the superfluid transition in 4 He dots

The superfluid transition in ⁴ He is associated with the onset of an order parameter that is a macroscopic wavefunction. This is similar to the onset of superconductivity in metals and alloys. Yet, some of the hallmark phenomena that are associated with wavefunctions, and are evident in superconductors, have not been identified in ⁴ He. Here we report proximity effects on the specific heat and superfluid density of a thin ⁴ He film in equilibrium with an array of larger boxes of ⁴ He. Comparison with previous data also enables us, by scaling, to deduce an excess specific heat associated with a collective behaviour of weakly coupled boxes. These effects should be relevant to the understanding of experiments where helium has been studied when confined in packed powders, porous materials or other inhomogeneous confinements, where proximity and collective effects must be present but not readily quantifiable. Our work also forms a point of comparison and contrast with the case of superconductors, and is relevant to studies of Josephson effects in superfluids, coupling effects in arrays of Bose-condensed atoms, and magnetic systems where, because of chemical composition, two separate but interacting ordering transitions take place.