Superfluid dripping: a new analog for continuous time crystals

Abstract Time crystals refer to a state realized in an open system that spontaneously breaks time translation symmetry. There are ongoing discussions, both theoretical and experimental, regarding their realization and potential extensions, which highlights the need to explore new demonstrations in non-equilibrium systems. In this study, we demonstrate that the dripping of a superfluid can exhibit time crystallinity. We visualized pendant droplets of superfluid ⁴He dripping from various shaped surfaces and observed that the dripping period became consistently discretized when the edge of the droplet was free to move along the surface. This edge motion resulted in oscillation periods that were independent of the droplet’s volume, effectively eliminating the influence of variations in volume and flow rates on the timing of the dripping. Consequently, the dripping process became regular. The unimpeded movement of the droplet’s edge is a characteristic of superfluids and is facilitated by a preexisting superfluid thin film on the surface, which minimizes the effects of surface roughness and enhances the mobility of the edge. We examined the stability of the discretized periods as a function of input flow rate and concluded that the superfluid dripping system spontaneously broke continuous time translation symmetry, making it analogous to a continuous time crystal, but with multiple stable phases. In contrast, when the edge of the droplet was pinned, the dripping period displayed a wide distribution, resembling the irregular dripping behavior seen in classical fluids.