Manipulation of nonequilibrium spin dynamics of an ultracold gas in a moving optical lattice

Ultracold quantum gases that feature spatial and spin degrees of freedom offer a powerful platform for simulating quantum magnetism in controlled, isolated settings. When combined with optical lattices, these simulation capabilities are exemplified by experimental studies featuring tunable dimensionality and filling factors. We have improved the programmability of the cold atom quantum simulator with a first realization of the dynamic interplay of spatial and spin degrees of freedom. We experimentally demonstrate that violent spatial evolutions tune long-lived coherent spin dynamics and develop a model of quantum spin-mixing incorporating the spatial evolution via time-dependent spin-spin interactions. Our results open new paths towards the simulation of quantum spin models with tunable interactions via tailored spatial dynamics. This tailored modulating of spatial profiles could be used to control the precise time dependence of the spin-spin interactions and realize Floquet-driven spin dynamics, which could have immediate applications for the dynamical generation of entangled spin states for quantum-enhanced sensing.