Observation of a New Casimir Effect in Saturated Superfluid $^4$He Films

We report the results of experiments on saturated superfluid $^4$He films in the vicinity of the bulk superfluid transition temperature $T_\lambda$, measuring the film thickness with a capacitance technique and the superfluid density with third sound. For moderately slow temperature sweep rates (0.5 mK/hr) we measure the critical Casimir film-thinning effect with good resolution, and find that the Kosterlitz-Thouless superfluid onset in the film occurs just at the start of the dip in film thickness. When warming through $T_\lambda$ at extremely slow rates (a few $\mu$K/hr), however, we have observed a sudden large increase in the film thickness (nearly 25 {\AA} in a film initially 480 {\AA} thick) within microkelvins of $T_\lambda$. We propose that this is a new type of Casimir effect arising from the viscous suppression of second sound modes in the film, leading to a large free energy difference in the superfluid state that disappears abruptly when second sound ceases to propagate in the bulk helium at $T_\lambda$.