Ultracold Rydberg atom arrays are an emerging platform for quantum simulation
and computing. However, decoherence in these systems remains incompletely
understood. Recent experiments [Guardado-Sanchez et al. Phys. Rev. X 8, 021069
(2018)] observed strong decoherence in the quench and longitudinal-field-sweep
dynamics of two-dimensional Ising models realized with Lithium-6 Rydberg atoms
in optical lattices. This decoherence was conjectured to arise from spin-motion
coupling. Here we show that spin-motion coupling indeed leads to decoherence in
qualitative, and often quantitative, agreement with the experimental data,
treating the difficult spin-motion coupled problem using the discrete truncated
Wigner approximation method. We also show that this decoherence will be an
important factor to account for in future experiments with Rydberg atoms in
optical lattices and microtrap arrays, and discuss methods to mitigate the
effect of motion, such as using heavier atoms or deeper traps