The Casimir effect: From quantum to critical fluctuations

The Casimir efiect in quantum electrodynamics (QED) is perhaps the best-known example of uctuation-induced long-ranged force acting on objects (conducting plates) immersed in a uctuating medium (quantum electromagnetic fleld in vacuum). A similar efiect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is afiected by the classical thermal uctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged at criticality. In turn, this universality allows one to investigate theoretically the temperature dependence of the force via representative models and to stringently test the corresponding predictions in experiments. In contrast to QED, the Casimir force resulting from critical uctuations can be easily tuned with respect to strength and sign by surface treatments and temperature control. We present some recent advances in the theoretical study of the universal properties of the critical Casimir force arising in thin fllms. The corresponding predictions compare very well with the experimental results obtained for wetting layers of various uids. We discuss how the Casimir force between a colloidal particle and a planar wall immersed in a binary liquid mixture has been measured with femto-Newton accuracy, comparing these experimental results with the corresponding theoretical predictions.