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

The isolation and control of disparate degrees of freedom underpin quantum simulators. We advance the programmability of cold atom quantum simulators 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.