  Rydberg atoms in optical lattices and tweezers is now a well established
platform for simulating quantum spin systems. However, the role of the atoms'
spatial wavefunction has not been examined in detail experimentally. Here, we
show a strong spin-motion coupling emerging from the large variation of the
interaction potential over the wavefunction spread. We observe its clear
signature on the ultrafast many-body nanosecond-dynamics of atoms excited to a
Rydberg $S$ state, using picosecond pulses, from an unity-filling atomic
Mott-insulator. We also propose a novel approach to tune arbitrarily the
strength of the spin-motion coupling relative to the motional energy scale set
by trapping potentials. Our work provides a new direction for exploring the
dynamics of strongly-correlated quantum systems by adding the motional degree
of freedom to the Rydberg simulation toolbox.
