Spin-motion coupled quantum many-body dynamics with polar molecules

Polar molecules promise new opportunities for quantum technologies. Their rotational states can encode highly coherent spin systems, and dipolar interactions mediate controlled quantum entanglement between molecules. Furthermore, molecular motion can be tuned by optical lattice or tweezer potentials. In lattices, motion and interactions have comparable rates, leading to a complex interplay between spin and motion dynamics, described by generalizations to the paradigmatic tJ model. Here, we have studied the out-of-equilibrium quantum many-body dynamics of such spin-motion-coupled molecules. We study magnetization relaxation in a Ramsey contrast experiment. The relaxation dynamics follow a stretched exponential whose decay rate strongly depends on the lattice depth. We have developed three different numerical methods that can capture the spin-relaxation for different spin-motion coupling, matching experimental observations. The transition from frozen to itinerant dynamics can be highly peaked for spin-exchange or smooth for Ising interactions. We extend these methods to develop a microscopic model to quantitatively predict gate fidelities of molecules in optical tweezers, which predicts that motion is the main noise source. These methods can inform future experiments with polar molecules.