Measurements of the Critical Casimir Effect and Superfluid Density in $^4$He Films

We report the results of experiments on $^4$He films in the vicinity of the bulk superfluid transition temperature $T_\lambda$. A novel experimental apparatus allows measurements of film thinning due to the critical Casimir effect as well as the superfluid density of the film via third sound measurements. The temperature where the the Casimir film thinning begins to occur is found to be very close to the Kosterlitz-Thouless superfluid transition temperature in the film. Additionally, a new film-thickening effect is observed at $T_\lambda$ when the temperature is swept extremely slowly.