Title: Quantum time reflection and refraction of ultracold atoms

Abstract: Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is introduced. The main features of time-reflected and refracted waves are the shift of frequency and conservation of momentum, which offer a new degree of freedom for steering extreme waves and controlling phases of matter. The concept was originally proposed for manipulating optical waves more than five decades ago. However, due to the extreme challenges in the ultrafast engineering of the optical materials, the experimental realization of the time boundary effects remains elusive. Here, we introduce a time boundary into a momentum lattice of ultracold atoms and simultaneously demonstrate the time reflection and refraction experimentally. Through launching a Gaussian-superposed state into the Su-Schrieffer-Heeger (SSH) atomic chain, we observe the time-reflected and refracted waves when the input state strikes a time boundary. Furthermore, we detect a transition from time reflection/refraction to localization with increasing strength of disorder and show that the time boundary effects are robust against considerable disorder. Our work opens a new avenue for future exploration of time boundaries and spatiotemporal lattices, and their interplay with non-Hermiticity and many-body interactions.