Spatiotemporal Non-Hermitian Skin Effect with Floquet-Engineered Ultracold Atoms

Non-Hermitian skin effect, the accumulation of bulk eigenstates at edges under open boundary conditions, has been observed across classical, quantum, and synthetic platforms. Whether it can be generalized to the genuine time dimension remains open. We propose a spatiotemporal NHSE in the Floquet phase space via Floquet engineering of a ring-trapped ultracold atomic gas. Placing spatial and temporal degrees of freedom on an equal footing, we show that a single parent skin effect projects onto either domain. The spatial projection yields an NHSE with arbitrarily tunable skin locations, eliminating the need for physical open boundaries. The temporal projection gives time-domain nonreciprocity and periodic temporal funneling, consistent with causality. This establishes a unified spatiotemporal paradigm for NHSE and opens a route to non-Hermitian topological physics in time.